The Lyman-Alpha Forest

Summary

A quasar is one bright point of light, very far away.  On its way here that light crosses everything in between.  Hydrogen gas absorbs light at one particular wavelength — 1216 ångströms, called Lyman-alpha.  Every cloud of hydrogen along the path takes a bite out of the quasar's light at that wavelength.  But each cloud sits at a different distance, so each is carried away from us at a different speed, so each bite lands at a different place in the observed spectrum.  The result is a thicket of hundreds of narrow absorption lines packed on the blue side of the quasar's own Lyman-alpha emission.  Astronomers call it the Lyman-alpha forest.

The forest is a direct measurement of matter between here and there, sorted by distance.  It is also the most under-discussed line of evidence in cosmology, and it deserves better.

• Roger Lynds found the forest in 1971, in the spectrum of the quasar 4C 05.34. He reported "five separate absorption-line redshifts, all of which are less than the emission-line value."¹
• That last clause is the whole argument against intrinsic redshift, and it has held for fifty-five years. Wallace Sargent's team wrote in 1980 that high-redshift quasar spectra show the crowding on the blue side "so far without exception."² The DESI survey has now collected the forest in about 820,000 quasars.³ The thicket always stops at the quasar's own emission line and never continues past it. If a quasar's redshift were an intrinsic property of the quasar — the claim Halton Arp pressed for forty years — the absorbing gas would have no reason to respect that ceiling. See discordant redshifts.
• The lines are not a special population of objects. They are the ordinary intergalactic medium: sheets and filaments of gas at overdensities of a few, holding most of the ordinary matter in the universe at redshift 3. This was worked out by simulation between 1994 and 1996 and has held since.⁴⁵
• The gas is ionized, and that was established before the forest was discovered. In 1965 James Gunn and Bruce Peterson looked at the quasar 3C 9 and found the continuum blueward of Lyman-alpha depressed by only about 40 percent, not blacked out.⁶ A uniformly neutral intergalactic medium would have erased it completely. By their own arithmetic, at most one part in five million of the mass at that redshift could be neutral intergalactic hydrogen.⁶
• The blackout does appear, but only at the highest redshifts. In 2001 Robert Becker's team found a quasar at z = 6.28 whose flux just blueward of Lyman-alpha dropped by a factor of more than 150, "consistent with zero."⁷ That is the Gunn-Peterson trough, and its appearance marks the end of the era when the intergalactic gas was still neutral.
• The current best date for the end of reionization is z = 5.3, from 67 quasar sightlines observed with the Very Large Telescope. Sarah Bosman's team found that patchiness in the forest "persist[s] in the intergalactic medium until at least z = 5.3."⁸
• The forest measures structure on scales galaxy surveys cannot reach. The one-dimensional power spectrum of forest transmission has been measured from 43,751 quasar spectra across thirteen redshift bins from z = 2.2 to 4.6.⁹ With high-resolution spectra the measurement reaches wavenumbers of about 10 h per megaparsec, which is roughly fifty times smaller than the scales galaxy clustering can be trusted on.¹⁰
• Those small scales weigh neutrinos and constrain dark matter. A particle that moves fast erases small structures. Combining the forest with Planck gives a sum of neutrino masses below 0.09 eV at 95 percent confidence, and a lower bound on thermal warm dark matter of 5.3 keV.¹¹
• The forest carries the acoustic ruler too. In 2013 Nicolás Busca's team found the baryon acoustic peak in the three-dimensional correlation of forest absorption at z = 2.3, at "(1.01 ± 0.03) times the distance expected."¹² That was the first BAO detection at high redshift, and it was a prediction-then-measurement, not a fit.
• The forest is a chemistry sample. Carbon and silicon absorption lines appear alongside the hydrogen at z = 3, which means stars had already lived and died and spilled their products into the intergalactic medium before that point.
• And it is the best baryometer there is. Deuterium absorption in a handful of very clean high-redshift systems measures the ratio of deuterium to hydrogen to one percent, which fixes the cosmic density of ordinary matter without using the microwave background at all. That argument belongs to big bang nucleosynthesis.

Two honest problems.

• Everything the forest says about cosmology is filtered through a hydrodynamic simulation. The observable is transmitted flux, not density. Turning one into the other requires modelling the ultraviolet background, the gas temperature and its thermal history. The published error bars now include those uncertainties as nuisance parameters, but the dependence is real and it is why the forest's constraints moved as much as they did between 2013 and 2020.
• Reionization does not currently add up. A 2024 paper by Julián Muñoz and colleagues shows that the galaxies actually observed by JWST "not only can drive reionization, but would end it too early," putting the observations in tension with both the microwave background's optical depth and the forest.¹³ The authors' own list of candidate fixes is "systematics in either theory or observations," which is an honest way of saying nobody knows yet.

What a young-earth reader should take from this.  The forest has been engaged three times from the creationist side, and the three engagements disagree with each other.  Bill Worraker, writing in the Journal of Creation in 2006, proposed that quasars are nearby objects with intrinsic redshifts and that "quasars ejecting gas clouds that intersect our line of sight would produce series of absorption features at redshifts below their own, just as observed."¹⁴  That idea had already been tested and rejected twenty-six years earlier.  Wallace Sargent's team measured the forest lines as if they were ejected clouds, found their number density flat in ejection velocity out to 0.2c and identical across five different quasars, and concluded:  "we regard it as inherently unlikely that such a theory could be constructed."²  John Hartnett, in 2011, conceded that the forest "seems to be very good evidence that the quasars are at their large redshift distances" and that it "would seem to contradict the claim of Arp and others," then argued around it.¹⁵  Danny Faulkner, writing in Answers Research Journal in 2018, took the opposite view and accepted the forest outright:  "This is a powerful argument that the Hubble relations holds for all sorts of extragalactic objects over a wide range of redshifts."¹⁶  Faulkner has the better of that argument, and this article sides with him.  Since 1980 the case has hardened further.  The forest thins out near the quasar rather than thickening, which is backwards for ejection.  The same absorbers appear in the spectra of two different quasars separated on the sky.  The forest has been measured against ordinary galaxies as background lights, not just quasars.  And the metal content of the forest does evolve with redshift, contrary to the claim Worraker relied on.  Each of those is discussed below with its measurement.

What is still missing is a young-earth account of what the absorbers are.  Faulkner accepts the forest as evidence for cosmological redshifts and then leaves the hard part open, saying the answer for quasars "likely will be related to how one answers the light travel time problem."¹⁶  Neither Jason Lisle's anisotropic synchrony convention, nor Russell Humphreys' white-hole model, nor John Hartnett's Carmelian cosmology says what the hundreds of absorbers on a single sightline are, or why their statistics come out as they do.  A full-text search of the Creation Research Society Quarterly archive returns no article on the forest at all.¹⁷  Any model that shortens the light travel time has to answer the same four questions:  what are the hundreds of absorbers on each sightline, why are their redshifts always below the quasar's, why does their statistical pattern match what gravity acting on expanding gas predicts, and why do only the very highest-redshift quasars show the neutral-hydrogen blackout.  Until those are answered, the forest is a straightforward consequence of light travelling a long way through structured gas, and it works.

What you actually see

Start with the atom.  A hydrogen atom sitting in its lowest energy state can absorb a photon and jump its electron up one level.  The jump costs 10.2 electron volts.  A photon carrying exactly that much energy has a wavelength of 1215.67 ångströms — deep ultraviolet, blocked by Earth's atmosphere.  That transition is called Lyman-alpha, after Theodore Lyman, who identified the ultraviolet hydrogen series in the years before the First World War.

Hydrogen is about three-quarters of the ordinary matter in the universe by mass, and the Lyman-alpha transition is one of the strongest absorption lines any atom has.  So a cloud of neutral hydrogen is very good at removing light at 1215.67 ångströms and almost transparent everywhere else in the visible band.  Michael Rauch's 1998 review of the field puts the consequence bluntly:  "The large cross-section for the Lyα transition makes this technique by far the most sensitive method for detecting baryons at any redshift."¹⁸

Now add expansion.  A quasar at redshift 3 is far enough away that its light has been travelling for most of the age of the universe.  Along the way it passes through clouds of hydrogen.  A cloud sitting at redshift 2.5 absorbs at 1215.67 ångströms in its own frame, but by the time that gap in the spectrum reaches Earth it has been stretched by a factor of 3.5, so it appears at 4255 ångströms.  A cloud at redshift 2.8 puts its gap at 4620 ångströms.  A cloud at redshift 2.9 puts one at 4741.  The quasar's own Lyman-alpha emission — the light its own hydrogen emits — lands at 4863 ångströms.

Every absorber is therefore stamped with its own distance, and they sort themselves automatically.  The nearest absorbers land furthest to the blue.  The absorber right next to the quasar lands right next to the quasar's emission line.  Nothing can land redward of it, because nothing between here and the quasar has a redshift larger than the quasar's.

What a spectrograph shows is a bright emission peak with a dense picket fence of narrow absorption lines crowded on its blue side, and comparatively clean continuum on its red side.  In a high-resolution spectrum of a bright z ≈ 3 quasar the fence has several hundred pickets.  Somebody looked at that and said it resembled a forest, and the name stuck.

Some vocabulary, because the literature uses it constantly

• Column density, written N or N_HI, is how many hydrogen atoms sit in a one-square-centimetre tube through the cloud. Forest lines run from about 10¹² to 10¹⁷ atoms per square centimetre.
• Optical depth, τ, measures how much light is removed. Transmitted fraction is e^−τ. τ = 1 removes 63 percent of the light; τ = 5 removes 99.3 percent; τ > 6 or so is indistinguishable from black.
• b-parameter is the line width in velocity units. Forest lines have b ≈ 20 to 40 kilometres per second. If all of that width were thermal it would mean gas between about 24,000 and 97,000 kelvin. Some of it is bulk motion, so the real temperatures are lower, around 10,000 to 20,000 kelvin. Either way this is photoionized gas, not shock-heated gas, and that fact does a lot of work later on.
• Damped Lyman-alpha systems are the rare very strong absorbers, N > 2 × 10²⁰, which are gas discs in real galaxies rather than intergalactic filaments. They are a different animal and a different literature.
• Effective optical depth, τ_eff, is the average absorption over a stretch of spectrum: τ_eff = −ln⟨F⟩, where ⟨F⟩ is the mean transmitted flux. It is the number most reionization work reports.

How it was found

1965: three teams predict a trough, and the trough is not there

Quasars were only two years old in 1965.  Maarten Schmidt had identified 3C 273 as an extragalactic object at redshift 0.158 in 1963, and by 1965 he had 3C 9 at redshift 2.01 — far enough that its Lyman-alpha line, normally ultraviolet, had been stretched into visible blue light and could be photographed from the ground.

Three groups independently realised what that meant.  James Gunn and Bruce Peterson at Caltech, Peter Scheuer in Cambridge, and Iosif Shklovsky in Moscow all worked out that if the space between galaxies contained neutral hydrogen spread smoothly, then a quasar's light would be eaten alive on the blue side of its Lyman-alpha emission.¹⁸  Every photon leaving the quasar slightly bluer than Lyman-alpha would eventually be redshifted into resonance with some hydrogen atom on the way, and get scattered out of the beam.  The result would be a black trough, not a picket fence.

Gunn and Peterson stated the mechanism plainly:

Consider, however, the fate of photons emitted to the blue of Ly-a.  As we move away from the source along the line of sight, the source becomes redshifted to observers locally at rest in the expansion, and for one such observer, the frequency of any such photon coincides with the rest frequency of Ly-a in his frame and can be scattered by neutral hydrogen in his vicinity.⁶

Then they looked, and the trough was not there.  This is the part that popular retellings usually get backwards.  Gunn and Peterson did not predict a trough and find it.  They predicted a trough, found only a modest dip, and drew the correct and rather startling conclusion:

The blueward component and the wing of the line are noticeably depressed … but the exact amount is difficult to measure;  best estimates place the depression at about 40 per cent, which corresponds to an optical depth of about ½.  This yields, for q₀ = ½, a number density n_s = 6 × 10⁻¹¹ cm⁻³ …  For the q₀ = ½ model, the total density at z = 2 is 5 × 10⁻²⁸ gm cm⁻³;  thus only about one part in 5 × 10⁶ of the total mass at that time could have been in the form of intergalactic neutral hydrogen. …  We are thus led to the conclusion that either the present cosmological ideas about the density are grossly incorrect, and that space is very nearly empty, or that the matter exists in some other form. …  It is possible that this interpretation is still valid but that essentially all of the hydrogen is ionized.⁶

The last sentence turned out to be right.  The intergalactic medium is there;  it is simply not neutral.  Their own arithmetic gives the scale of the result:  at most one part in five million of the mass at z = 2 could be neutral intergalactic hydrogen.  The absence of the Gunn-Peterson trough is one of the strongest limits in astrophysics, and it comes from a four-page note filed under "Notes" at the back of the journal.

A warning about that quotation.  The ADS scan of this paper carries no text layer, and machine transcription of it turns the fraction "½" into the digit "3."  This article's numbers were read off the page images at 200 dots per inch, pages 1633 and 1634.  Anyone citing Gunn and Peterson from an automatic extraction should check the fractions by eye.

In the same volume of the Astrophysical Journal, John Bahcall and Edwin Salpeter added the piece Gunn and Peterson had not:

As we shall show [cf. Gunn and Peterson (1965)] neutral hydrogen (or other atoms) at various distances between the source and us will give rise to an "absorption trough" in the continuous spectrum of a distant source.  If the neutral hydrogen is instead concentrated in clusters of galaxies, this trough is replaced by a number of sharp absorption lines.¹⁹

That is the forest, predicted six years before it was seen.  Bahcall and Salpeter guessed wrong about what the clumps would be — they suggested clusters of galaxies, and the real answer is diffuse filaments — but they got the observable exactly right.

1971: Lynds finds the picket fence

Roger Lynds, at Kitt Peak National Observatory, had the highest-redshift quasar then known:  4C 05.34, at z = 2.877.  He photographed it in the spring of 1970 with an image-tube spectrograph on the 84-inch telescope, at about 5 ångström resolution, and published in March 1971.

His abstract is worth reading in full because it contains the entire argument this article is built on:

The absorption lines in the spectrum of the large-redshift QSO 4C 05.34 are reported, and a preliminary analysis is presented.  Evidence is found for five separate absorption-line redshifts, all of which are less than the emission-line value.  The distribution of absorption lines is striking in that essentially all unidentified lines are located on the short-wavelength side of the Lα emission line.  A probable explanation of this effect is discussed.¹

He described what he saw in the body of the paper as well:  "there are many prominent absorption lines and … their most distinguishing characteristic is that they are almost exclusively located on the short-wavelength side of the strong Lα emission line."¹

Two facts, on day one.  Many lines.  All blueward.  Fifty-five years and a million quasars later, both still hold.

1980: Sargent's team shows the clouds are intergalactic

Between 1971 and 1980 the debate was not whether the lines were real but what they were.  Were they gas ejected by the quasar itself?  Gas in the halos of ordinary galaxies that happened to lie in front?  Or genuinely intergalactic material with no galaxy attached?

Wallace Sargent, Peter Young, Alec Boksenberg and David Tytler settled it with high-resolution spectra of six quasars, published as a forty-page supplement in 1980.  Their method was to look for the fingerprints each hypothesis would leave.

Their negative results were the decisive ones.  Across a homogeneous sample of five quasars spanning 2.2 < z_em < 3.3 they found "no significant variation in the average number density of lines among the QSOs," "no significant variation in equivalent width with redshift," and "a two-point correlation function … that is flat on all scales from 300 to 30,000 km s⁻¹, quite unlike the expected correlation function for galaxies at these redshifts."²  Lines that clustered like galaxies would mean galaxy halos.  Lines that did not cluster at all meant something more evenly spread.

Their conclusion:

We conclude that the single Lα absorption lines and the metal line systems arise from physically distinct populations of clouds.  Both types of system are produced by cosmologically distributed intervening material not associated with QSOs.  The metal line systems probably arise in galaxy halos, and the Lα clouds must be an intergalactic population which is not associated with galaxies.²

And they tested the ejection hypothesis directly, which matters enormously for what follows.  They took the absorption redshifts, converted them into ejection velocities as if the quasar had fired the clouds out itself, and asked what an ejection model would have to reproduce:

When the Lα absorption redshifts are interpreted in terms of velocities of ejection from the QSOs, we find that (i) the number density of clouds is uniformly distributed in ejection velocity, v_ej, over the observed range 0 < v_ej/c < 0.2;  (ii) the number density is statistically the same in all five QSOs;  and (iii) there is no correlation between line strength and ejection velocity.  We emphasize that any successful ejection theory must conform to these constraints;  we regard it as inherently unlikely that such a theory could be constructed.²

Read what those three constraints demand.  An ejection mechanism would have to fire clouds outward with a velocity distribution that is flat from zero to twenty percent of the speed of light — no preferred speed, no falloff.  It would have to do so identically in five different quasars of different luminosities.  And the clouds' column densities would have to be independent of how fast they were thrown.  No physical ejection process behaves like that.  A cosmological distribution of intervening gas produces all three trivially, because a flat distribution in redshift is exactly what a roughly uniform medium looks like along a line of sight.

The forest kills intrinsic redshift

Halton Arp spent four decades arguing that quasar redshifts are not distance indicators.  His case rested on apparent physical associations between high-redshift quasars and low-redshift galaxies, which he read as ejection from the nearby galaxy with a redshift intrinsic to the ejected object.  That argument is handled on its own terms in discordant redshifts.  This section covers the piece of evidence that Arp's programme never answered, and that its young-earth borrowers have not answered either.

The forest sets a ceiling, and the ceiling is always the quasar's own redshift.

If a quasar at apparent redshift 3 is really a nearby object whose redshift is intrinsic, then the gas in front of it is nearby gas, and its redshift has nothing to do with the quasar's.  Some of it should be blueshifted.  Some of it should be at higher redshift than the quasar, since the quasar's high redshift is by hypothesis not a distance.  Absorbers should scatter on both sides of the emission line.

They never do.  Lynds saw that in one object in 1971.  Sargent's team saw it in six in 1980, and wrote that high-redshift quasar spectra had revealed "(so far without exception)" a greater density of absorption lines on the short-wavelength side of the Lyman-alpha emission line than on the long-wavelength side.²  DESI's second data release carries "Lyα forest spectra of more than 820,000 quasars."³  The ceiling has never been broken.

There is one apparent exception, and it is worth naming so that nobody thinks it has been hidden.  A small class of associated absorbers sit within a few hundred kilometres per second of the quasar's own redshift, and a few of those are formally at slightly higher redshift.  These are gas clouds in and around the quasar's host galaxy, falling inward.  A few hundred kilometres per second at z = 3 is a redshift difference of about 0.004.  That is a rounding error on the emission redshift, and it is exactly what gas orbiting a galaxy does.  It is not a forest of lines at z = 4 in front of a z = 3 quasar, and nothing like that has ever been reported.

The ejection hypothesis was tested in 1980 and failed

Sargent's four ejection constraints are given above.  They are worth restating as a challenge, because no one has met them.  An ejection model must produce a cloud population whose number per unit velocity is flat from zero to 0.2c, identical in five quasars of different luminosity, with line strength uncorrelated with ejection speed.  Sargent's team said they regarded it as "inherently unlikely that such a theory could be constructed."²  Forty-six years later, nobody has constructed one.

The proximity effect runs the wrong way for ejection

Here is a measurement that ejection gets exactly backwards.

If the clouds were thrown out by the quasar, there should be more of them near the quasar and fewer far away, because ejecta spread out and thin as they travel.  What is actually observed is the reverse.  In 1988 Stanislaw Bajtlik, Robert Duncan and Jeremiah Ostriker analysed nineteen quasars and reported:

The number density of Lyα lines generally increases with redshift z, but there exists a countervailing trend of diminishing number density within individual quasar spectra as z → z_q.²⁰

In plain terms:  the forest gets thinner as you approach the quasar's own redshift.  They showed why, and the explanation is a clean piece of physics.  The quasar is an intense source of ultraviolet light.  Gas near it gets more strongly ionized than gas far away, so it absorbs less.  Fitting that model let them measure the general ultraviolet background at high redshift for the first time — "log J_ν = −21.0 ± 0.5" in the usual units — and the fit worked.²⁰

Note what this argument requires.  It requires the absorbing gas to be physically near the quasar in space when it is near the quasar in redshift.  That is a distance interpretation of redshift, and the data confirm it quantitatively, through a photoionization calculation with no free parameters other than the background intensity.

The same absorber appears in two different quasars

If a cloud is intergalactic and large, two quasars close together on the sky should show the same absorption line at the same redshift, because the two beams pass through the same cloud.  If a cloud was ejected by one quasar, it has no business appearing in a different quasar's spectrum.

This has been measured repeatedly since the early 1990s.  Nadine Dinshaw and colleagues observed the quasar pair Q1343+2640A and B, separated by 9.5 arcseconds on the sky, and reported:

We detect eight absorption lines of Lyα common to both spectra and not attributable to metal-line systems in the redshift range 1.7 < z < 2.1 and four lines which are seen in one spectrum but not the other.²¹

Eight shared, four not.  From that ratio and the beam separation they set a lower limit on the absorbers' characteristic size of 40 h⁻¹ kiloparsecs and, under a simple spherical model, an upper limit near 310 h⁻¹ kiloparsecs.²¹

The measurement has since been done on much wider separations.  Emmanuel Rollinde's group used five quasar pairs and a group of four quasars observed with the Very Large Telescope, at separations from 0.6 to 10 arcminutes, and found that the transverse flux correlation is "clearly detectable at separations smaller than 3 arcmin," with a shape "in good agreement with those expected from absorption by the photoionized warm intergalactic medium associated with the filamentary and sheet-like structures predicted in CDM-like models."²²

Ejected clouds cannot do this.  A cloud fired out of quasar A at 0.15c is not also sitting in front of quasar B.

The forest can be read against galaxies, not just quasars

In 2006 Worraker, following Arp's collaborator Morley Bell, wrote that "Lyα absorption forests have not 'convincingly' been found in the spectra of normal galaxies."¹⁴  In 2006 that was close to true, and it was a fair thing to notice:  galaxies are far fainter than quasars, and getting a usable absorption spectrum against one is hard.

It is not true now.  The COSMOS Lyman-Alpha Mapping and Tomography Observations survey did exactly that.  Its first data release states the method in its opening sentence:

Faint star-forming galaxies at z ∼ 2 − 3 can be used as alternative background sources to probe the Lyman-α forest in addition to quasars, yielding high sightline densities that enable 3D tomographic reconstruction of the foreground absorption field.²³

They used 240 background sources — galaxies as well as quasars — with a mean transverse separation of 2.37 h⁻¹ megaparsecs, and reconstructed a three-dimensional map of the absorbing gas over 315,000 h⁻³ cubic megaparsecs at 2.05 < z < 2.55.²³

Two things follow, and both are fatal to ejection.  First, the forest is seen against ordinary galaxies, which have no quasar to eject anything.  Second, the map they built is consistent between sightlines:  the overdensities and voids line up, and they "visually agree with the distribution of coeval galaxies from spectroscopic redshift surveys in the same field, including overdensities associated with several recently-discovered galaxy protoclusters in the volume."²³  Absorbing gas ejected independently by hundreds of separate background sources cannot assemble itself into a coherent three-dimensional structure that matches an independently measured galaxy map.

Absorbers sit where galaxies are, at the absorber's redshift

The Keck Baryonic Structure Survey put the two datasets side by side directly:  high signal-to-noise forest spectra of fifteen bright quasars, and a dense galaxy redshift survey in the same fields.  Gwen Rudie's 2012 analysis catalogued about 6,000 individual absorbers and 886 star-forming galaxies at 2.0 < z < 2.8, then asked whether the absorbers know where the galaxies are.

They do.  "Absorbers with N_HI > 10^14.5 cm⁻² are tightly correlated with the positions of galaxies," and the strongest absorption sits within about 300 kiloparsecs of a galaxy and within ±300 km s⁻¹ of its systemic redshift.²⁴

The galaxy redshifts come from emission lines in the galaxies' own spectra.  The absorber redshifts come from hydrogen absorption in an unrelated quasar's spectrum.  Two independent measurements, and they agree about where the matter is.  On an intrinsic-redshift model there is no reason for them to agree at all.

The forest contains the acoustic ruler

The last item is the strongest and the least expected.  The baryon acoustic oscillation is a preferred separation of about 147 megaparsecs frozen into the matter distribution when the universe went neutral.  Its length is computed from microwave-background densities alone, with no galaxy data — see large-scale structure.

In 2013 Nicolás Busca's team looked for it in the three-dimensional correlation of Lyman-alpha forest absorption, using 48,640 BOSS quasars at 2.1 ≤ z ≤ 3.5, and found:

A peak in the correlation function is seen at a separation equal to (1.01 ± 0.03) times the distance expected for the BAO peak within a concordance ΛCDM cosmology.¹²

One percent, at a mean redshift of 2.3, on a scale predicted in advance from completely different data.  A model in which the absorbers are locally ejected clouds has no mechanism that would put a bump at 147 megaparsecs into their correlation function, and no reason for that bump to land within one percent of a number computed from the microwave background.

The Gunn-Peterson trough and the end of reionization

Why the trough is a one-sided measurement

The Lyman-alpha transition is so strong that a tiny amount of neutral hydrogen produces a lot of absorption.  That is what makes the forest sensitive.  It is also what makes the Gunn-Peterson trough nearly useless as a thermometer once it appears.

Work the numbers.  A uniform intergalactic medium with the cosmic mean density, entirely neutral, gives a Lyman-alpha optical depth of order 10⁵ at z = 6.  Transmitted flux would be e^−100000, which is zero to any precision anyone will ever have.  But the optical depth scales with the neutral fraction, so a medium that is only one part in 10,000 neutral still gives τ ≈ 10, and e⁻¹⁰ is 0.00005 — also indistinguishable from zero with real instruments.

So the trough saturates.  Once you see a black trough, all you know is that the neutral fraction exceeds roughly 10⁻⁴.  It could be 10⁻⁴ or it could be 1.  Becker's team said this in the same abstract that announced the discovery, and honest treatments have to quote both halves:

Even a small neutral hydrogen fraction in the intergalactic medium would result in an undetectable flux in the Lyα forest region.  Therefore, the existence of the Gunn-Peterson trough by itself does not indicate that the quasar is observed prior to the reionization epoch.  However, the fast evolution of the mean absorption in these high-redshift quasars suggests that the mean ionizing background along the line of sight to this quasar has declined significantly from z ∼ 5 to 6, and the universe is approaching the reionization epoch at z ∼ 6.⁷

The evidence for reionization is therefore not "we saw a trough."  It is "the absorption changes fast, in a particular way, over a narrow range of redshift."  That is a much better argument, and it is the one the field actually makes.

The discovery

In 2001 Robert Becker and colleagues, using Sloan Digital Sky Survey quasars followed up on Keck, published the first complete trough:

in the highest redshift object, SDSSp J103027.10+052455.0 (z = 6.28), the average transmitted flux is 0.0038 ± 0.0026 times that of the continuum level over 8450 Å < λ < 8710 Å (5.95 < z_abs < 6.16), consistent with zero flux.  Thus the flux level drops by a factor of > 150, and is consistent with zero flux in the Lyα forest region immediately blueward of the Lyα emission line, compared with a drop by a factor of ∼ 10 at z_abs ∼ 5.3. …  This is a clear detection of a complete Gunn-Peterson trough, caused by neutral hydrogen in the intergalactic medium.⁷

The comparison inside that sentence is the point.  At z ≈ 5.3 the forest removes about 90 percent of the light.  At z ≈ 6.1 it removes essentially all of it.  Something changes fast between those two redshifts.

The rate of change, measured

Xiaohui Fan's group followed this up with nineteen quasars at 5.74 < z_em < 6.42 and three independent probes:  the effective optical depth, the length of completely dark stretches of spectrum, and the sizes of the ionized bubbles quasars blow around themselves.  Their results:

• The effective optical depth's rate of growth jumps. Below z ≈ 5.7 it grows as (1 + z)^4.3. Above it, as (1 + z)¹¹ or steeper.²⁵
• The average length of dark gaps with τ > 3.5 grows from under 10 comoving megaparsecs to over 80.²⁵
• The scatter between sightlines increases sharply, implying that the ultraviolet background varies by more than a factor of 4 from place to place at z > 6.²⁵
• The ionized bubbles around quasars shrink with redshift, implying the neutral fraction rose by a factor of at least 10 between z = 5.7 and z = 6.4.²⁵

Their conclusion:  "The mass-averaged neutral fraction is 1 − 4% at z ∼ 6.2 …  The observations suggest that z ∼ 6 is the end of the overlapping stage of reionization, and are inconsistent with a mostly neutral IGM at z ∼ 6, as indicated by the finite length of dark absorption gaps."²⁵

Note the honesty in that last clause.  The dark gaps are long but finite.  If the medium were mostly neutral at z = 6, there would be no transmitted flux anywhere, and there is.  So z = 6 is the tail of reionization, not its middle.

The current answer: it ends at z ≈ 5.3

The date moved later as the data improved.  The best current measurement comes from the XQR-30 programme on the Very Large Telescope, which obtained deep spectra of 30 quasars at z > 5.7 and combined them with existing data for a sample of 67 sightlines.  Sarah Bosman's 2022 analysis compared the observed scatter in transmission against simulations that assume a uniform ultraviolet background:

Using all known systematics in a forward modelling analysis, we find excellent agreement between the observed Ly-α transmission distributions and the homogeneous-UVB simulations Sherwood and Nyx up to z ≤ 5.2 (< 1σ), and mild tension (∼ 2.5σ) at z = 5.3.  Homogeneous UVB models are ruled out by excess Ly-α transmission scatter at z ≥ 5.4 with high confidence (> 3.5σ).  Our results indicate that reionisation-related fluctuations, whether in the UVB, residual neutral hydrogen fraction, and/or IGM temperature, persist in the intergalactic medium until at least z = 5.3 (t = 1.1 Gyr after the Big Bang).⁸

The logic is subtle and worth spelling out.  After reionization is complete, the ultraviolet background is smooth, so different sightlines should show similar amounts of absorption.  While reionization is still patchy, some sightlines run through fully ionized bubbles and some do not, so the sightline-to-sightline scatter is large.  Bosman's team measured that scatter as a function of redshift and found it consistent with a smooth background up to z = 5.2 and inconsistent from z = 5.4 upward.  The last patches of neutral hydrogen therefore survived to z ≈ 5.3.

The microwave background says the same thing, from completely different physics

Free electrons scatter microwave-background photons.  The amount of scattering is the optical depth τ, and it is measured from the large-angle polarization of the microwave sky — an entirely different instrument, an entirely different wavelength, and an entirely different physical effect from hydrogen absorption in a quasar spectrum.

Planck's final analysis gives τ = 0.0544 ± 0.0073, and:

Assuming simple tanh parameterization of the ionization fraction, this implies a mid-point redshift of reionization z_re = 7.68 ± 0.79 (68 %, TT,TE,EE+lowE), and a one-tail upper limit of z_re < 9.0 (95 %).  This is consistent with observations of high-redshift quasars that suggest the Universe was fully reionized by z ≈ 6.²⁶

These do not measure the same thing, and they should not be expected to give the same number.  The microwave background gives the midpoint of reionization, weighted over the whole sky.  The forest gives the end, along particular sightlines.  A midpoint near z ≈ 7.7 and an end near z ≈ 5.3 describe one extended, patchy transition.  That two measurements with nothing physical in common bracket the same era is a real, if modest, success for the model.

What the forest is made of

For twenty-five years after Lynds, "Lyman-alpha cloud" was taken literally.  The picture was of discrete objects — little balls of gas, each one held together somehow, floating in a hot medium that squeezed them.  Sargent's own 1980 paper worked in that frame:  clouds with densities of 10⁻⁴ to 4 × 10⁻³ per cubic centimetre, temperatures near 30,000 kelvin, and diameters from 10²⁰ to 10²³ centimetres, "photoionized by the integrated QSO light" and "pressure confined by the general medium."²

That picture was wrong, and it was overturned not by better spectra but by better computers.

1994-1996: the simulations rewrite the object

Between 1994 and 1996 several groups ran cosmological hydrodynamic simulations — gravity, gas pressure, shock heating, photoionization by an ultraviolet background — and simply looked at what absorption spectra the simulated universe would produce.

Renyue Cen, Jordi Miralda-Escudé, Jeremiah Ostriker and Michael Rauch went first, with a cold-dark-matter model including a cosmological constant.  They found that the weak lines come from a specific kind of structure:

We find that low column density (N_HI ≤ 10¹⁴ cm⁻²) lines originate in regions resembling Zel'dovich pancakes, where gas with overdensities in the range 3-30 is enclosed by two shocks but is typically re-expanding at approximately the Hubble velocity.⁴

Lars Hernquist, Neal Katz, David Weinberg and Miralda-Escudé confirmed it with a completely different numerical method — smoothed-particle hydrodynamics rather than a grid — on a different cosmological model.  Their result is the clearest statement of the new picture:

The distribution of HI column densities agrees with existing data to within a factor of ∼ two over most of the range from 10¹⁴ cm⁻² to 10²² cm⁻² …  Most of the low column density absorption arises in large, flattened structures of moderate or even relatively low overdensity, so there is no sharp distinction between the Lyα forest and the "Gunn-Peterson" absorption produced by the smooth intergalactic medium.⁵

That last sentence dissolves the old category.  There are no clouds.  There is a continuous, mildly lumpy medium, and what a spectrum records is the density along one line through it.  A "line" is simply a place where the sightline crossed a filament or a sheet.  Where the medium is thin, the absorption is weak;  where it is denser, the absorption is strong;  where it passes through the outskirts of a galaxy, you get a damped system.  It is one physical object described by a continuum of column densities.

Two independent codes with opposite numerical philosophies, on different cosmological models, produced the same forest.  That is why the result stuck.

Rauch's 1998 review, written at the end of that revolution, summarised the consequence for cosmology:  "If the inferences … are interpreted correctly the intergalactic medium is the main repository of baryons down to redshifts at least as low as z ∼ 2.  If so, then high redshift galaxies … are mere tracers of the matter distribution."¹⁸

Most of the ordinary matter in the young universe is not in galaxies.  It is in the forest.

The forest weighed the baryons before the microwave background could

Here is a result that deserves far more attention than it gets, because it was a successful prediction made against the grain of the data available at the time.

The amount of absorption in the forest depends on how much gas there is and on how hard the ultraviolet background is ionizing it.  Turn that around:  if you can put a floor under the ionizing background — say, by counting the quasars you can actually see — then the observed absorption puts a floor under the gas density.  Michael Rauch's 1997 paper did exactly that, using seven high-resolution Keck spectra and both simulation codes:

Estimating the lower limit Γ > 7 × 10⁻¹³ s⁻¹ from the abundance of known QSOs, we derive a lower limit on the baryonic matter density, Ω_bh² > 0.021 (0.017) for the ΛCDM (SCDM) model.²⁷

They then said what that implied, and they said it plainly:

The large Ω_b we infer is inconsistent with some recent D/H determinations (Rugers & Hogan 1996a,b), favoring a low deuterium abundance as reported by Tytler, Fan & Burles (1996).²⁷

Deuterium measurements were split in 1997.  One camp had high deuterium and therefore low baryon density;  the other had low deuterium and high baryon density.  The forest's opacity said the baryon density had to be high.  The modern value from the microwave background is Ω_bh² = 0.02237 ± 0.00015.²⁶  The modern value from deuterium alone, using seven high-precision absorbers, is a one percent measurement that "agrees to within 2σ of the latest results from the Planck cosmic microwave background data."²⁸  Both sit above Rauch's floor.  The high-deuterium camp was wrong.

That is a real, dated, checkable success:  a measurement of intergalactic gas opacity, made with no microwave-background input at all, that picked the right side of an unsettled argument and has been vindicated by two later independent methods.

The one-dimensional power spectrum

Once you accept that the forest traces density, the transmitted flux along a sightline becomes a one-dimensional map of the matter distribution, and you can take its Fourier transform.  That statistic is called P_1D, and it is where most of the forest's modern cosmology lives.

The arc of the measurement:

The SDSS measurement was the first at survey scale, and Patrick McDonald's team spent most of the paper on systematics — noise, spectrograph resolution, sky subtraction, quasar continuum, and metal absorption — because with 3,035 spectra the statistical errors had dropped to about 0.6 percent on the amplitude and the systematics were what remained.²⁹  In a companion analysis they turned that measurement into a linear power spectrum and translated it:  "The result corresponds to σ₈ = 0.85, n = 0.94, for a ΛCDM model with Ω_m = 0.3, Ω_b = 0.04, and h = 0.7, but is most useful in a combined fit with the CMB."³¹  Those numbers came from hydrogen absorption at redshift 3, and they are within a few percent of what the microwave background gives from radiation at redshift 1100.

And this is a genuinely hard test, for a reason worth spelling out.  The microwave background measures the amplitude and tilt of the primordial fluctuation spectrum on large scales.  Extrapolating that down to the forest's scales requires the whole growth history in between — matter domination, dark energy taking over, gravity behaving as general relativity says.  The extrapolation spans a factor of about a thousand in wavenumber.  It could have failed.  It does not.

Where the forest disagrees, slightly

Honest reporting requires the disagreement too.  Nathalie Palanque-Delabrouille's 2020 analysis of the DR14 power spectrum found:

the latest SDSS DR14 BOSS and eBOSS Lyman-α forest data is in very good agreement with current weak lensing constraints on (Ω_m, σ₈) and has the same small level of tension with Planck.  We did not identify a systematic effect in the data analysis that could explain this small tension, but we show that it can be reduced in extended cosmological models where the spectral index is not the same on the very different times and scales probed by CMB and Lyman-α data.¹¹

So the forest prefers a slightly smoother universe than Planck does, at about the same level and in the same direction as the weak-lensing surveys did.  That is worth watching.  It is not a large discrepancy, the authors could not find a systematic explaining it, and it is the kind of thing that either grows into new physics or dissolves as calibration improves.  The weak-lensing version of the same tension has largely dissolved — see large-scale structure.

Three dimensions: tomography and the acoustic peak

A single sightline gives one dimension.  Many sightlines close together give three.

The CLAMATO survey built the first such map:  240 background sources in a 0.157 square degree patch of the COSMOS field, average transverse separation 2.37 h⁻¹ megaparsecs, reconstructed over 3.15 × 10⁵ h⁻³ cubic megaparsecs at 2.05 < z < 2.55, smoothed at 2.5 h⁻¹ megaparsecs.²³  What comes out is a picture of filaments and voids at a time when the universe was about three billion years old, made entirely from shadows.

At the other extreme of scale, BOSS and then DESI have used the forest to measure the baryon acoustic oscillation.  Busca's 2013 detection at z = 2.3 was the first BAO measurement anywhere above redshift 1, and it did something the low-redshift measurements could not:  it caught the universe while it was still decelerating.

This first detection of the BAO peak at high redshift, when the universe was strongly matter dominated, results in constraints on the angular diameter distance D_A and the expansion rate H at z = 2.3 that, combined with priors on H₀ and the baryon density, require the existence of dark energy. …  This demonstrates that the expansion was decelerating in the range 0.7 < z < 2.3, as expected from the matter domination during this epoch.¹²

DESI's second data release now measures the same ruler using the forest of 820,000 quasars at z > 2.09, alongside more than 30 million galaxies and quasars as discrete tracers.³

Weighing neutrinos and constraining dark matter

The physics in one paragraph

A particle that moves fast cannot be trapped by a small clump of gravity.  It streams out of it.  So any species of matter with significant thermal motion smooths out structure below a characteristic length — its free-streaming scale — while leaving larger structures alone.  Neutrinos are the known example.  They were relativistic in the early universe and slowed as it expanded, and the heavier they are the earlier they slowed and the less structure they erased.  So measuring how much small-scale structure survives is a way of weighing them.

Galaxy surveys are poorly placed for this, because their reliable scales are large and because galaxies are biased tracers whose relation to the underlying matter is uncertain.  The forest is well placed, because it reaches small scales and because the absorbing gas is only mildly overdense, so its relation to the matter is close to linear.  This is the forest's distinctive contribution to particle physics, and it is why particle physicists read intergalactic-medium papers.

Warm dark matter

If dark matter is a light particle — a keV-scale thermal relic, say, rather than a GeV-scale WIMP — it too would have been fast-moving early on, and would have erased structure below about a megaparsec.  That was once attractive, because it would have fixed the "small-scale crisis":  simulations of cold dark matter predicted more small satellite galaxies and cuspier galaxy centres than observations showed.

The forest closed that door.  Matteo Viel, George Becker, James Bolton and Martin Haehnelt analysed the flux power spectrum from 25 quasars at z > 4 observed with Keck's HIRES and Magellan's MIKE spectrographs:

we obtain a lower limit m_WDM ≳ 3.3 keV (2σ) for warm dark matter particles in the form of early decoupled thermal relics.  …  Thermal relics of masses 1 keV, 2 keV and 2.5 keV are disfavoured by the data at about the 9σ, 4σ and 3σ C.L., respectively.  …  There is thus very little room for a contribution of the free-streaming of WDM to the solution of what has been termed the small scale crisis of cold dark matter.¹⁰

Vid Iršič's 2017 analysis added the XQ-100 sample and pushed further:  XQ-100 alone gives 1.4 keV, the re-analysed HIRES/MIKE sample gives 4.1 keV, and the combination gives 5.3 keV, all at 2σ.³²

And then they said what would loosen it, which is the part that matters.  The forest's small-scale power depends on the temperature of the gas as well as on the dark matter, because hot gas smooths itself by pressure.  Iršič's team tested a more flexible thermal history and reported the cost:  allowing "temperature changes of up to 5000K reduces the lower limit for the combined analysis to 3.5 keV."³²

A limit that moves from 5.3 to 3.5 keV when you change an astrophysical prior is a limit with a real modelling dependence in it.  It is still a strong limit — every version of it kills the sterile-neutrino masses that were proposed to fix the small-scale crisis — but anyone quoting "5.3 keV" as though it were a laboratory number is overselling it.  See dark matter for where the rest of that case stands.

Neutrino mass

The forest's neutrino constraint comes from the same small-scale suppression.  Palanque-Delabrouille's 2020 analysis of the DR14 forest power spectrum, combined with Planck, gives:

In the ΛCDM model with running, we find Σm_ν < 0.11 eV at the 95% confidence level for combined Lyman-α and Planck (temperature and polarisation) data, or Σm_ν < 0.09 eV when adding CMB lensing and BAO data.  We further provide strong and nearly model-independent bounds on the mass of thermal warm dark matter.  For a conservative configuration consisting of SDSS data restricted to z < 4.5 combined with XQ-100 Lyman-α data, we find m_X > 5.3 keV (95%CL).¹¹

To see why 0.09 eV is a striking number, compare it with the laboratory.  Neutrino oscillation experiments measure the differences between the squared masses, and those differences set a floor:  the three masses must sum to at least about 0.059 eV if the ordering is "normal," and at least about 0.10 eV if it is "inverted."  A cosmological bound below 0.10 eV therefore excludes the inverted ordering — a statement about particle physics, derived from hydrogen absorption lines and microwave photons.

The bound has since tightened to the point of becoming a problem, and this should be reported rather than celebrated.  DESI's second data release, whose BAO measurements include the Lyman-alpha forest, combines with the microwave background to give Σm_ν < 0.064 eV at 95 percent confidence.³  That is barely above the oscillation floor.  Worse, the DESI collaboration says plainly what the posterior looks like when the physical requirement of positive mass is relaxed:

In the context of a model with effective neutrino masses that are allowed to assume negative values, the DESI+CMB likelihood peaks at Σm_ν,eff < 0, and the tension with the minimal mass bound from terrestrial experiments increases to 3.0σ.³

The data would prefer a negative neutrino mass, which is not a thing.  DESI relates this to the same discrepancy that shows up in Ω_m and H₀ r_d between their BAO and the microwave background.  Whatever it is — a systematic, an incomplete model of dark energy, or something else — it is a live problem, and it sits directly on the forest's most publicised result.

The forest as a chemistry sample

Metals in the intergalactic medium

Hydrogen is not the only thing in the way.  Alongside the Lyman-alpha lines, quasar spectra carry doublets from triply ionized carbon (C IV, at 1548 and 1551 ångströms) and triply ionized silicon (Si IV), each at the same redshift as some hydrogen absorber.  Because those elements are made in stars and nowhere else, finding them in intergalactic gas dates the first generation of stars against the gas they polluted.

Antoinette Songaila and Lennox Cowie established how common this is, in 1996:

The recent discovery of carbon in close to half of the low neutral hydrogen column density [N(H I) > 3 × 10¹⁴ cm⁻²] Lyman forest clouds toward z ∼ 3 quasars has challenged the widely held view of this forest as a chemically pristine population uniformly distributed in the intergalactic medium …  we now show that C IV can be found in 75% of clouds with N(H I) > 3 × 10¹⁴ cm⁻² and more than 90% of those with N(H I) > 1.6 × 10¹⁵ cm⁻².³³

They also measured how much:  "Carbon is seen to have a typical abundance of very approximately 10⁻² of solar and Si/C about three times solar, so that the chemical abundances of these clouds are very similar to those of Galactic halo stars."³³

Joop Schaye's group later did the measurement properly, using pixel statistics on 19 high-quality spectra rather than individual line fits, and correcting for ionization with a simulation.  Their median carbon abundance in gas at moderate overdensity is [C/H] = −3.47, which is about one part in 3,000 of the solar carbon fraction, with a spatial scatter of roughly a factor of six.³⁴

So the intergalactic medium at redshift 3 is polluted, but only slightly.  Roughly one atom of carbon for every few thousand the Sun has, spread very unevenly.  That is what you would expect if a first generation of stars had formed in the densest knots, exploded, and blown a small amount of processed material into the surrounding gas — and it is not what you would expect from a medium that had never seen a star, nor from one that had been through many generations.

The evolution question, which Worraker got half right

Worraker, following Morley Bell, argued that the forest supports local quasars because "the metallicity of the Lyα absorbers associated with quasars varies remarkably little with redshift; this is to be expected in a 'local' model for quasars, but is very puzzling if quasar redshifts are cosmological since the assumed intervening galaxies should evolve chemically with time."¹⁴

Half of that is a real observation and should be conceded.  Schaye's team, measuring carbon over 1.8 < z < 4.1, found "significant trends with overdensity, but no evidence for evolution" in redshift, giving a cosmic carbon abundance of [C/H] = −2.80 ± 0.13 with "no evidence for evolution."³⁴  That flatness is real and was known.

The inference from it does not work, for three reasons.

First, the premise is wrong.  The absorbers are not "intervening galaxies."  They are diffuse filaments at overdensities of a few, as the 1994-1996 simulations showed and as every subsequent measurement has confirmed.  A statement about how galaxies chemically evolve is not a statement about the intergalactic medium, which is enriched by outflows from galaxies rather than by star formation inside itself.

Second, flat C IV over that range is not flat carbon.  The C IV fraction depends on the ultraviolet background, which hardens as helium reionizes around z ≈ 3.  Songaila and Cowie saw exactly that:  "Si IV/C IV decreases rapidly with redshift from high values (> 0.1) at z > 3.1, a circumstance which we interpret as a change in the ionizing spectrum as the intergalactic medium becomes optically thin to He⁺ ionizing photons."³³  Ionization corrections are why Schaye's group ran a simulation instead of counting lines.

Third, and decisively, the flatness ends.  It ends exactly where a cosmological picture says it should:  at the redshifts where the first stars were still doing the enriching.  Valentina D'Odorico's X-shooter survey found the C IV column density distribution evolving above z ≈ 5.3, with the cosmic C IV mass density dropping by about a factor of 2 there, and rising by a factor of about 10 from z ≈ 6.2 down to z ≈ 1.5.³⁵  Rebecca Davies' 2023 analysis of 260 absorbers in 42 X-shooter spectra pinned the drop:

We find that Ω~C IV~ decreases by a factor of 4.8 ± 2.0 over the ∼ 300 Myr interval between z ∼ 4.7 and z ∼ 5.8.³⁶

A factor of five in 300 million years is not "varies remarkably little."  The observation Bell relied on was a real feature of a limited redshift range, and the wider range shows the evolution the cosmological picture predicts.

And there is a fourth problem, which is internal to Worraker's own paper.  He notes, correctly, that the z = 6.28 quasar SDSS J1030+0524 "contains material with metallicity equal to or exceeding solar values."¹⁴  Quasars are metal-rich.  If the forest absorbers were gas ejected by the quasar, they should be metal-rich too.  They are metal-poor by two to three orders of magnitude.  The ejection model predicts the wrong chemistry by a factor of a thousand.

Deuterium: the best baryometer there is

The forest also supplies the cleanest measurement of the cosmic baryon density that does not use the microwave background.

Deuterium is destroyed inside stars and made nowhere except the first few minutes after the Big Bang.  Its primordial abundance is therefore a direct read on how much ordinary matter there was — and it is steeply sensitive, so a good deuterium measurement is a good baryon measurement.  The trouble is finding gas that has not been contaminated.  A handful of extremely metal-poor absorbers in the forest, at redshifts 2 to 3, are the best candidates known.

Ryan Cooke's group has measured seven of them to high precision.  Their 2018 result:

we deduce that the primordial deuterium abundance is log₁₀(D/H)_P = −4.5974 ± 0.0052 or, expressed as a linear quantity, 10⁵(D/H)_P = 2.527 ± 0.030;  this value corresponds to a one percent determination of the primordial deuterium abundance.  Combining our result with a big bang nucleosynthesis (BBN) calculation that uses the latest nuclear physics input, we find that the baryon density derived from BBN agrees to within 2σ of the latest results from the Planck cosmic microwave background data.²⁸

That comparison is the whole nucleosynthesis argument in one line, and it belongs to big bang nucleosynthesis rather than here.  What matters for this article is that the measurement is made in the forest.  Absorption spectra of intergalactic gas at redshift 3 supply the sample.  The two-sigma residual disagreement with Planck, incidentally, comes almost entirely from the theoretical rate for one nuclear reaction, d(p,γ)³He, and shrinks when an empirical rate is used instead.²⁸

The forest is now the thing reionization has to fit, and it does not

The forest started as a puzzle to be explained.  It has become a constraint that other measurements have to satisfy.  In 2024 that constraint bit.

The logic of reionization accounting is simple.  Something ionized all the hydrogen between the galaxies.  Star-forming galaxies are the leading candidate.  To check whether they can do it you need three numbers:  how many galaxies there were, how many ionizing photons each one made per unit of ultraviolet light (written ξ_ion), and what fraction of those photons escaped the galaxy instead of being absorbed inside it (written f_esc).  Multiply the three and compare against the number of hydrogen atoms that had to be ionized, plus the ones that recombined along the way.

For twenty years the worry ran one direction.  There did not seem to be enough photons.  Julián Muñoz and colleagues put the history plainly:  "the situation has been reversed from the WMAP era, where the concern was producing enough photons to match τ_CMB, to the post-Planck and JWST era, where there may be too many photons."¹³

JWST changed all three numbers at once, and all three moved the same way.  There turned out to be more faint galaxies at z ≳ 9 than expected.  Those galaxies turned out to make more ionizing photons per unit ultraviolet luminosity than the value everyone had been assuming.  And separate low-redshift work on galaxies that resemble reionization-era galaxies suggested escape fractions near 5 to 15 percent rather than the smaller values often used.  Put the three together and the sum overshoots:

we show that the galaxies we have directly observed (M_UV < −15) not only can drive reionization, but would end it too early.  That is, our current galaxy observations, taken at face value, imply an excess of ionizing photons and thus a process of reionization in tension with the cosmic microwave background (CMB) and Lyman-α forest.¹³

Read what is doing the work in that sentence.  The galaxies are the observation.  The microwave background and the forest are the constraint.  Reionization ending at z ≈ 5.3, which is Bosman's forest measurement, and a microwave-background optical depth of 0.0544, are the two facts the photon budget now fails to reproduce.  Twenty years ago the forest was the thing being explained.  Now it is one of the two rulers a JWST result is being measured against, and the JWST result is the one in trouble.

Muñoz's team say what would fix it, and they do not pretend to know which:  the candidate resolutions are "systematics in either theory or observations."¹³  Possible outs include a turnover in the number of very faint galaxies that has not been seen down to M_UV ≈ −15, a lower escape fraction than the analogue galaxies suggest, or an error in how ξ_ion is inferred from photometry.  Adding still fainter galaxies makes it worse rather than better.¹³

This is an open problem and it should be counted as one.  It is not a problem for the forest measurement, which is a direct observation of quasar spectra.  It is a problem for the story about what did the ionizing.  But it is a real, current, unresolved mismatch inside the standard picture, and a skeptic is entitled to hear it named.

What a young-earth reader should make of the forest

Start with the honest part.  The forest is evidence against a small universe and against nearby quasars, and it is strong evidence.

Everything in the sections above follows from one assumption:  light from a quasar crosses a lot of structured gas on the way here, and the gas is carried away from us at speeds that grow with distance.  Nothing else in the article is needed.  From that assumption alone you get the absorption ceiling at the quasar's redshift, the thinning of the forest near the quasar, the shared absorbers in quasar pairs, the coherent three-dimensional maps, and the acoustic peak at 147 megaparsecs.  A model that denies the assumption owes an account of all five.

Three creationists have addressed it, and they disagree with each other

Bill Worraker, 2006, Journal of Creation.  Worraker followed Halton Arp's collaborator Morley Bell and proposed that quasars are relatively nearby, with redshifts that are intrinsic rather than cosmological.  On that model the forest is gas thrown out by the quasar itself:  "Quasars ejecting gas clouds that intersect our line of sight would produce series of absorption features at redshifts below their own, just as observed."¹⁴

That sentence is the whole proposal, and it does not survive contact with the 1980 data.  Sargent's team had already converted the forest redshifts into ejection velocities and found three things an ejection model must reproduce:  a number density flat in ejection velocity from zero to 0.2c, statistically identical in five different quasars, with no correlation between line strength and ejection speed.²  Worraker's paper does not mention that test.  Nor does it address the proximity effect, which had been published eighteen years earlier and runs the wrong way for ejection.²⁰  Nor the shared absorbers in quasar pairs, published in 1994.²¹  And his own paper supplies a fourth problem:  he notes that the z = 6.28 quasar SDSS J1030+0524 "contains material with metallicity equal to or exceeding solar values."¹⁴  Quasar gas is metal-rich.  Forest gas is metal-poor by a factor of a few thousand.³⁴  Ejected quasar gas would carry the quasar's chemistry, and it does not.

John Hartnett, 2011, Journal of Creation.  Hartnett is the most interesting of the three, because he states the difficulty against himself before answering it:

At first sight, the Lyα forest seems to be very good evidence that the quasars are at their large redshift distances.  It would seem to contradict the claim of Arp and others that some quasars have large intrinsic redshifts that are not due to cosmological expansion (figure 2).  The light from the quasar is uniformly redshifted.  If this is due to some intrinsic effect, it would not translate into a series of lines representing lower and lower redshift distances towards the observer from absorbing hydrogen clouds in the foreground of the quasar.¹⁵

That is a fair statement of the argument.  His counter has three parts, and none of them holds.

First, he points to a 2006 result by Gabriel Prochter's team, who found strong magnesium absorbers along nearly every gamma-ray-burst sightline they looked at, against about one quarter of quasar sightlines, and argues that this "adds doubt to the proposition that the Lyα lines represent neutral hydrogen clouds, absorbers, in the foreground of the quasars also."¹⁵  The inference does not follow.  The Prochter anomaly concerns Mg II absorbers, which are strong metal systems in galaxy halos, seen against a different kind of background source.  It says nothing about whether hydrogen absorption in quasar spectra is foreground, and it cannot, because the foreground question has been settled by measurements Hartnett does not engage:  the same absorbers seen in two separate quasars,²¹ the transverse correlation across quasar pairs at up to three arcminutes,²² and the tomographic map built from 240 background sources that lines up with an independently measured galaxy survey.²³

Second, he quotes Martín López-Corredoira at length to argue that the Gunn-Peterson trough appears at the wrong redshift compared with the microwave background's reionization epoch.  The number in that quoted passage is a WMAP reionization epoch of z_r = 20 (+10/−9) at 95 percent confidence, against a trough at z = 6.28, which López-Corredoira calls "a new inconsistency."¹⁵  The gap was real and it closed on its own.  Planck's final analysis puts the reionization midpoint at z_re = 7.68 ± 0.79 with a one-tail upper limit of z_re < 9.0, and says in the same paragraph that this "is consistent with observations of high-redshift quasars."²⁶  The early WMAP figure really was far too high, and a critic writing in 2011 was entitled to notice.  But it moved toward the forest, not away from it, and it moved because the large-angle polarization measurement improved.

Third, he cites Lyndon Ashmore on the spacing of hydrogen clouds with redshift, which Ashmore reads as a universe that expanded to z ≈ 0.5 and then stopped.  Hartnett states the problem with using it himself:  Ashmore "made the usual BB assumptions that quasars are at their redshift distances and that the Lyα absorption lines result from hydrogen clouds in the foreground of quasars."¹⁵  An argument that assumes the forest is foreground cannot be used to doubt that the forest is foreground.  The source is also a conference proceedings volume rather than a refereed journal paper.

Hartnett does not, in the end, offer an account of what the absorbers are.  His closing line on the point concedes the conditional:  if the absorption cannot be made to originate in a quasar's own atmosphere, "the standard model has a good argument in favour of cosmological expansion."¹⁵

Danny Faulkner, 2018, Answers Research Journal.  Faulkner is a young-earth creationist astronomer, and he simply accepts the forest.  His paper is an argument against fellow creationists who reject cosmological redshifts.  He lays out the physics correctly, including the point that the absorbing clouds cannot be near the quasar because the quasar's own ultraviolet light would ionize them:

Quasars typically have multiple Lyman-alpha absorption of various strengths and at various redshifts, but always with redshifts less than the quasars themselves. …  This is what we consistently see—Lyman-alpha absorption always is redshifted less than the Lyman-alpha emission of the quasar.  This is a key point, because the absorption is possible only if the absorbing regions are closer than the source of the continuum (Kirchoff's third law of spectroscopy).  This is a powerful argument that the Hubble relations holds for all sorts of extragalactic objects over a wide range of redshifts.¹⁶

Faulkner is right and this article sides with him.  On the narrow question the three creationists are arguing about, which is whether quasar redshifts track distance, the forest settles it, and the young-earth writer who says so is the one following the data.

What is actually missing

Accepting that quasar redshifts are cosmological is not the same as accepting an old universe, and Faulkner is careful about that.  Redshift measures how much the light has been stretched.  Converting that into elapsed time needs a further step, and the young-earth models are all attempts to supply a different further step.  See young universe cosmologies and the anisotropic synchrony convention.

But no young-earth cosmology has been asked to reproduce the forest, and none has tried.  A full-text search of the Creation Research Society Quarterly archive returns no article about it, and no article mentioning the Gunn-Peterson trough.¹⁷  Neither Jason Lisle's 220-post corpus nor Sarah Salviander's 371-post corpus mentions the forest at all; their only "Lyman" material is about the Lyman-break method for estimating galaxy distances.¹⁷

That gap matters, because the forest is a harder target than distant starlight in general.  A model that only has to get light here quickly has one thing to explain.  A model that has to reproduce the forest has to explain the arrangement of matter along every sightline.  Four questions, none of which any published young-earth model addresses:

1. What are the absorbers? Several hundred distinct absorption systems appear along a single z = 3 sightline. In the standard picture they are crossings of sheets and filaments at overdensities of a few, and that identification is not a guess: two independent simulation codes with opposite numerical methods reproduced the observed column-density distribution to within a factor of two.⁴⁵
2. Why is the ceiling never broken? Every absorber sits below the quasar's own redshift, in every quasar ever observed, now including the 820,000 in DESI's second data release.³ A model in which redshift is not distance has no reason for that.
3. Why does the statistical pattern match gravity acting on expanding gas? The forest's one-dimensional power spectrum, measured from 43,751 spectra, matches an extrapolation of the microwave background's primordial spectrum across a factor of about a thousand in scale.⁹³¹ And its three-dimensional correlation carries the acoustic peak at the length the microwave background predicts, to one percent.¹²
4. Why is the blackout confined to the highest redshifts? Complete Gunn-Peterson troughs appear in quasars above z ≈ 6 and not below.⁷²⁵ A model with no era of neutral gas has to produce that pattern some other way.

Until those are answered, the honest position is the one this article takes.  The forest is what light travelling a long way through structured, expanding gas looks like.  It is one of the strongest observational cases in cosmology, it was not designed to test a young universe, and it goes against one.

Objections and responses

"The forest is just a model.  Everything you quoted comes out of a simulation."

Half true, and the half that is true should be conceded.  The cosmological results do depend on simulations, because the observable is transmitted flux and the quantity of interest is density.  Converting one to the other needs the ultraviolet background, the gas temperature and the thermal history.  Iršič's team showed exactly how much that matters:  allowing "temperature changes of up to 5000K" moves the warm-dark-matter limit from 5.3 keV down to 3.5 keV.³²  A limit that moves by a third when an astrophysical prior is loosened is not a laboratory number.

But the structural facts are not model outputs.  That every absorber lies below the quasar's emission redshift is read straight off a spectrum.¹  That the forest thins toward the quasar is a count of lines.²⁰  That two quasars 9.5 arcseconds apart share eight absorbers is a comparison of two spectra.²¹  That the metals evolve above z ≈ 5 is a count of C IV systems.³⁶  No simulation is needed for any of them, and they are the ones that do the work against intrinsic redshift.

"You are assuming the redshift is a distance in order to prove that the redshift is a distance."

No.  The argument runs the other way.  Start with no assumption about what redshift means, and ask what a spectrum should look like under each hypothesis.

If redshift is intrinsic to the quasar, the intervening gas is unrelated to it, so absorbers should appear on both sides of the emission line.  If redshift tracks distance, absorbers can only appear on the blue side, because nothing in front of the quasar can be further away than the quasar.  The observation picks the second, in every quasar since 1971 and in 820,000 of them in DESI's second data release.³

Three further predictions separate the hypotheses, and all three were tested after the fact.  The proximity effect predicts fewer lines near the quasar under a distance interpretation, because the quasar's own ultraviolet light ionizes nearby gas;  ejection predicts more.  Fewer is what is seen.²⁰  A distance interpretation predicts that two nearby sightlines cross the same clouds;  ejection forbids it.  Shared absorbers are seen.²¹²²  And a distance interpretation predicts a preferred separation of about 147 megaparsecs in the absorbers' three-dimensional correlation, computed from microwave-background densities with no quasar data at all.  It is there, at (1.01 ± 0.03) times the predicted length.¹²

"Halton Arp found quasars physically connected to low-redshift galaxies.  Doesn't that beat all this?"

That case is handled on its own terms in discordant redshifts.  The point for this article is narrower.  Arp's evidence is a claim about alignment on the sky, which is a statistical argument about how often two objects land near each other by chance.  The forest is a claim about what is in front of what, which is not statistical at all.  Even granting every Arp alignment, the forest still has to be explained, and Arp's programme never explained it.  Nor did Worraker's borrowing of it,¹⁴ and Hartnett conceded the difficulty in print before attempting an answer.¹⁵

"The quasar's own outflowing gas could make the lines.  Quasars do have outflows."

They do, and those outflows are seen.  They are called broad absorption line systems, they sit within a few thousand kilometres per second of the quasar, and they are metal-rich because quasar gas is metal-rich.  Worraker's own paper notes that the z = 6.28 quasar SDSS J1030+0524 "contains material with metallicity equal to or exceeding solar values."¹⁴

Forest absorbers are none of those things.  They spread over the entire path length, not a few thousand kilometres per second.  Their carbon abundance is about one part in 3,000 of solar, measured over 1.8 < z < 4.1.³⁴  And an ejection model has to reproduce Sargent's three constraints, which no physical outflow does:  a flat number density in ejection velocity from zero to 0.2c, statistically identical across five quasars of different luminosity, with line strength uncorrelated with speed.²

"The Gunn-Peterson trough is supposed to show reionization, but Gunn and Peterson didn't find one."

Correct, and that is the point rather than an objection to it.  Gunn and Peterson predicted a black trough at z = 2 and found a 40 percent dip instead, which told them the intergalactic gas was ionized:  "only about one part in 5 × 10⁶ of the total mass at that time could have been in the form of intergalactic neutral hydrogen."⁶  The trough does appear, but only above z ≈ 6, where Becker's team measured a flux drop of more than a factor of 150.⁷  Two different answers at two different redshifts is not a contradiction.  It is the signal.

The genuinely weak version of this argument, which some popular accounts make, is that seeing a trough proves the gas was neutral.  It does not, and Becker's own abstract says so:  "the existence of the Gunn-Peterson trough by itself does not indicate that the quasar is observed prior to the reionization epoch."⁷  The real evidence is the rate of change:  the optical depth's growth index jumps from (1 + z)^4.3 to (1 + z)¹¹ or steeper above z ≈ 5.7, and the sightline-to-sightline scatter blows up.²⁵⁸

"The forest disagrees with Planck about σ₈, so one of them is wrong."

There is a mild disagreement and it is worth watching, but it is small and it is reported by the people who found it.  Palanque-Delabrouille's team say the forest agrees with weak lensing and "has the same small level of tension with Planck," that they "did not identify a systematic effect in the data analysis that could explain this small tension," and that a model with a running spectral index reduces it.¹¹  That is what an honest small discrepancy looks like.  The parallel weak-lensing tension has since largely dissolved;  see large-scale structure.

"Cosmologists keep changing the date of reionization.  z = 20, then z = 6, now z = 5.3."

They do, and the direction of travel is the interesting part.  WMAP's first estimates put reionization very early.  Planck's polarization brought the midpoint down to z_re = 7.68 ± 0.79.²⁶  The forest's end-of-reionization date moved the other way, from z ≈ 6 in 2006 to z ≈ 5.3 in 2022.²⁵⁸

That is two independent measurements converging rather than one being fudged toward the other.  A midpoint near 7.7 and an end near 5.3 describe a single drawn-out transition, and they come from different instruments measuring different physics.  Nothing forced them to agree.

"If the young-earth position is right, why does this article side with the standard reading?"

Because that is what the data show, and because pretending otherwise would be worse than useless.  The forest is not an interpretation looking for support.  It is a picket fence of absorption lines in a spectrum, and every structural feature of it follows from light crossing structured, expanding gas.

The young-earth question is not settled by the forest, because the forest measures redshift and structure, not elapsed time.  Converting redshift into elapsed time takes a further assumption, and that is where the argument actually lives:  see young universe cosmologies and the anisotropic synchrony convention.  But no young-earth model has yet been made to reproduce the forest, and until one is, this is a piece of evidence the creationist side owes an answer to rather than one it can use.  Danny Faulkner, writing in a young-earth journal, reached the same conclusion in 2018 and said so plainly.¹⁶

Sources