Measuring the Small-Scale Power Spectrum of Cosmic Density Fluctuations Through 21 cm Tomography Prior to the Epoch of Structure Formation

Abraham Loeb; Matias Zaldarriaga (Harvard Univ.)

REVIEW

Measuring the Small-Scale Power Spectrum of Cosmic Density Fluctuations Through 21 cm Tomography Prior to the Epoch of Structure Formation

Abraham Loeb, Matias Zaldarriaga (Harvard Univ.)

Astrophysics · Submitted 4 Dec 2003 · 20 references

Pith's verdict: The founding calculation of the dark-ages 21cm power spectrum: clean, standard physics, honest about the detection challenge, with the cosmological-constraint claims left qualitative rather than forecast.

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arXiv IDastro-ph/0312134 (version 2)

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CitationAbraham Loeb, Matias Zaldarriaga (Harvard Univ.). "Measuring the Small-Scale Power Spectrum of Cosmic Density Fluctuations Through 21 cm Tomography Prior to the Epoch of Structure Formation." arXiv:astro-ph/0312134 (2003). https://pith.science/paper/EEOETOY5

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Editor's note

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This is the paper that made dark-ages 21cm cosmology a quantitative subject, and it holds up. The new content is not the spin-flip physics (Field 1959) or the projection formalism (their own ref [6]) but the specific application to z ~ 30-200, before any stars, and the resulting angular power spectrum with its mode count. That is a real contribution and the derivation is clean: Eq. (2) for the spin temperature, Eqs. (3)-(4) for the brightness temperature and optical depth, Eqs. (5)-(7) for the fluctuation propagation, and Eq. (10) for C_l are all standard and correctly assembled. Fig. 1 showing the two contributions to dT_b/ddelta_H with the same sign is a nice, physically transparent result. The paper is also candid where it counts: it says outright that the predicted signal is ~1 mK and that a year of LOFAR integration or a larger covering fraction is needed [abstract:s4 acknowledges detection is challenging]. That is the right tone for a first paper in a hard field. On the thermal history, the stress-test concern is real but mild, and I would say so plainly: the paper asserts rather than quantifies how much early heating the signal tolerates, but the peak is at z ~ 50, comfortably above the likely first-star epoch, so the central claim survives. Where I part company with the reader's take is on where the overclaim lives. The body is careful; it is the abstract's 'orders of magnitude larger than any other cosmological probe' that outruns the evidence. The mode count N_21cm ~ 3e16 versus N_cmb ~ 2e7 is fair arithmetic, but it assumes you can reach l_max ~ 1e6 down to the Jeans scale, which the noise model of Eq. (11) does not deliver. Eq. (11) is a crude, LOFAR-specific sensitivity estimate with adopted numbers (f_cover = 0.016, l_max = 5000) that were optimistic even then. And Fig. 3 shows model power spectra side by side but gives no Fisher forecast, no error bars on n, alpha_r, f_nu, or m_WDM. The paper says these measurements 'could tightly constrain' these parameters; it never shows by how much. That is the gap a referee should press on, and it is a gap the authors could have closed with a page of algebra. None of this undermines the central result. This is for anyone working on the intergalactic medium, inflation, or neutrino mass, and it is required reading for anyone entering 21cm cosmology. Send it to referees; the questions above are exactly what a good report should ask.

Referee report

Significance

The paper is a forward prediction from standard cosmology and well-tested atomic physics: no parameter is fitted to the 21 cm signal, and the predicted amplitude and shape of Cl follow from the same density power spectrum that is constrained elsewhere. That makes the prediction falsifiable in a clean way, and the mode-counting argument (N21cm ~ 3e16 versus Ncmb ~ 2e7) is a concrete, checkable statement rather than a slogan. The identification of the redshift window in which the cosmological Jeans mass reaches its minimum (~3e4 Msun) is a genuinely useful observational target, since it is precisely the range that Ly-alpha forest studies cannot reach after reionization. The paper also correctly notes that the signal is shaped by gravity and adiabatic expansion rather than by complex astrophysics, which is the property that makes the proposed probe worth pursuing. These are substantial strengths and they are stated with appropriate caveats about detectability.

Major objections (3)

[Detectability of signal, Eq. (11)] The detectability argument rests entirely on Eq. (11), which is a single-number radiometer estimate, and the conclusion that 'a year of integration or an increase in the covering fraction are required to observe it with LOFAR' follows directly from it. The equation omits the two systematics that dominate at these frequencies: Galactic synchrotron foreground, which at ~28 MHz is orders of magnitude brighter than the ~1 mK signal and must be removed to high precision in the spectral direction, and ionospheric phase fluctuations. The paper mentions high sky noise and free-free absorption after reionization, but does not discuss foreground removal at all. Since the abstract's claim is that detection 'could tightly constrain' cosmology, the reader needs at least a sentence on whether the foreground problem is tractable, and the assumed values of Delta nu/nu, lmin, lmax, and fcover used to produce the quoted 0.4 mK should be stated explicitly rather than left implicit in the numerical substitution.
[The small scale power spectrum, Fig. 3, and abstract:s4] Fig. 3 shows ratios of power spectra for the tilted, running, warm dark matter, and massive neutrino models, and the text concludes that 'a precise measurement of the 21cm power spectrum will dramatically improve current constraints.' This is a qualitative statement attached to a quantitative claim in the abstract. Because Eq. (11) already supplies a noise level, a rough Fisher-matrix estimate of the achievable uncertainty on the running alpha_r, on f_nu, and on the WDM mass would be straightforward and would convert the figure into an actual forecast. If such an estimate is deferred to future work, the abstract and the closing sentence of that section should say so explicitly, so that the constraint claims are not read as demonstrated.
[Introduction and Eq. (2)] The entire calculation assumes the gas cools adiabatically as Tgas proportional to (1+z)^2 with no heating before z ~ 30, and the Introduction justifies this by asserting that the window 'precedes the appearance of collapsed objects.' That assertion is not quantified anywhere in the manuscript. The peak of dTb/delta_H is at z ~ 50, comfortably above the likely first-star epoch, so the peak is robust; but the low-redshift edge of the window is set by radiative decoupling, and modest early heating (X-rays from minihalos, decaying particles, or shock heating) would raise Tgas toward Tgamma and could weaken or erase the absorption at z ~ 30-40. A short statement of the tolerance, for example the maximum Tgas/Tgamma at z = 50 for which the signal remains in absorption, or a version of the lower panel of Fig. 1 computed with a modestly elevated gas temperature, would make the robustness of the predicted window explicit.

Minor objections (8)

[Eq. (10) and Fig. 2] The window function W_nu(r) is left unspecified, with the text noting only that its details depend on the experiment. Since Fig. 2 must assume a particular band shape and width, the assumed Delta nu/nu or top-hat width should be stated in the caption so that the plotted amplitudes can be reproduced.
[Paragraph following Eq. (10)] The statement that peculiar-velocity and gravitational-potential distortions are suppressed by factors of order H/ck and (H/ck)^2 is correct at high l, but Fig. 2 extends to low l where H/ck is not small; at l of a few hundred the redshift-space distortion is comparable to or larger than the density term. The claim should be explicitly restricted to the high-l range, or the low-l portion of Fig. 2 should be flagged as not including these terms.
[Unprecedented information] The mode count N21cm ~ 3e16 is quoted at lmax = 10^6, which is far beyond any planned instrument and beyond the scales where the gas Jeans mass suppresses power. The text should state the fiducial lmax and k range used for the 'orders of magnitude' comparison, and note explicitly that the accessible mode count is limited by the Jeans scale rather than by the hypothetical lmax.
[Final comments] At z = 50 the redshifted 21 cm line falls at about 28 MHz, close to the ionospheric cutoff, yet the discussion of space-based instruments is confined to z > 70 (nu < 20 MHz). A sentence on the ionospheric and radio-frequency-interference environment at the peak redshift would help the reader judge the practical difficulty.
[Fig. 1, lower panel] The curve labeled dTb/delta_H times delta_H is described as having an 'arbitrary normalization' but the normalization actually used is not given; state it in the caption so the relative size of the two contributions can be read off.
[References] Reference [11] (Tegmark & Zaldarriaga 2002) does not appear to be cited anywhere in the body text; either cite it where the noise formalism is introduced or remove it from the list.
[Abstract and Introduction] The observed wavelength is quoted as 10.56[(1+z)/50] m in the abstract and as 21.12[(1+z)/100] m in the Introduction. The two are numerically consistent, but using a single form throughout would avoid the appearance of a discrepancy.
[Typesetting] There are several typographical artifacts in the current version: 'tansform' in the text below Eq. (8), 'thats' in the description of Eq. (11), 'and and' in the Jeans mass paragraph, and broken spacing in the title and in '10 .56'. These should be cleaned up in the final version.

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The paper

The paper claims

Before the first stars, cosmic hydrogen absorbed the microwave background at 21 cm, and the resulting blotchy sky maps density ripples on scales no other probe can reach.

The reading

Between the epoch when the cosmic gas stopped tracking the microwave background (redshift $z$ around 200) and the birth of the first stars, the neutral hydrogen filling the universe resonantly absorbed microwave photons at its 21 cm spin-flip line. Loeb and Zaldarriaga compute how the spin temperature of that hydrogen evolves, and then how small density ripples turn into brightness-temperature ripples on the sky during this interval. Their claim is that these ripples, at an observed wavelength near $10.56[(1+z)/50]$ metres, carry orders of magnitude more independent samples of the underlying density field than the primary microwave background does, because the microwave background is damped on small scales while the 21 cm maps are not. If the signal can be detected, the same data would test whether the primordial power spectrum bends with scale as some fits to the microwave background suggest, whether it deviates from Gaussianity, and how much mass sits in neutrinos or in warm dark matter. The authors are explicit that the measurement is hard: the predicted signal is about a milliKelvin against a bright low-frequency sky.

What carries the argument

The load-bearing object is the 21 cm spin temperature $T_s$, defined by the ratio of excited to ground hyperfine populations, $n_1/n_0 = 3 exp(-T_star/T_s)$ with $T_star = 0.068$ K. Its evolution is followed through a single differential equation for the ground-state fraction $Upsilon = n_0/n_H$, balancing collisional and radiative rates against the expansion. The observable is the brightness temperature $T_b = au(T_s - T_gamma)/(1+z)$, where the optical depth $au$ is proportional to $n_H/(T_s H(z))$. Fluctuations in $T_b$ follow from a linearised equation for $delta Upsilon$ driven by the density contrast, converted into $delta T_s/T_s$ and thence into $dT_b/ddelta_H$. That derivative is what weights the density power spectrum inside the angular power spectrum integral, so the whole prediction rests on one number per redshift, plotted in the paper's lower panel of Figure 1.

Extended reading notes

Core claim

The paper establishes that the cosmic dark ages are a measurable epoch rather than a blank. The authors integrate the rate equation for the population of the two hyperfine levels of neutral hydrogen from $z=200$ downward, using collisional de-excitation rates and the radiative couplings to the microwave background. They find the spin temperature tracks the gas temperature down to $z$ around 70 because collisions are still fast, then re-couples to the radiation background at lower redshift as expansion dilutes the collisions. In between, roughly $30 < z < 200$, the spin temperature sits below the radiation temperature and the gas absorbs. Density fluctuations change the absorption in two ways that add with the same sign: more hydrogen means more optical depth directly, and more hydrogen also raises the collision rate, pushing the spin temperature closer to the gas temperature. The authors turn this into a derivative $dT_b/dH$ of brightness temperature with respect to density contrast, then into an angular power spectrum $C_ell$ written as an integral of the three-dimensional density power spectrum against a window function and spherical Bessel functions. The predicted signal peaks near $z$ around 50 at roughly a milliKelvin, and the paper argues that a full-sky survey over a range of frequencies would yield of order $3 imes 10^{16}$ independent samples at $l_{max} = 10^6$, against about $2 imes 10^{7}$ for the microwave background.

Load-bearing premise

The calculation assumes the cosmic gas simply cools with expansion and is not heated by anything, such as early stars, quasars, or particle decays, before redshift 30; if that is wrong the absorption is weaker or absent and the predicted anisotropies shrink.

Editorial extensions

If this is right

A measured 21 cm power spectrum at $z$ around 50 would extend the density power spectrum to wavenumbers far beyond the microwave background's damping tail, reaching down to the cosmological Jeans mass of about $3 imes 10^4$ solar masses.
The shape of that spectrum would discriminate a running spectral index from a plain tilt, and would show or exclude a cut-off from a keV-scale warm dark matter particle.
The same data would tighten the allowed fraction of mass in massive neutrinos below the roughly ten percent level that galaxy surveys allow, and would probe non-Gaussianity to a precision set by the square root of the number of independent modes.
Because the signal comes from the bulk of the cosmic gas rather than the trace neutral fraction surviving after reionization, it avoids the astrophysical complications that limit the Lyman-alpha forest.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The prediction is sharpest exactly where it is least protected: the absorption window depends on the gas staying colder than the radiation, so a single unmodelled heating channel, such as decaying particles or an early X-ray background, would shrink the trough without changing the density field, and the two effects would be hard to separate with the anisotropy alone.
A global (all-sky average) spectrum measurement at these frequencies is a cheaper first test than a tomography survey, since it needs only the absorption trough's depth and shape rather than the angular power; a null result there would already constrain the epoch's thermal history.
Because the same physical window function applies to any tracer of the gas at these redshifts, cross-correlating 21 cm maps with the microwave background's large-angle polarization would isolate the density contribution from foreground and instrumental systematics.
The claim that the number of modes is orders of magnitude larger than the microwave background's depends on the maximum multipole an interferometer can reach, which is set by the longest baseline; the practical ceiling may be instrumental rather than cosmological.

Original abstract

The thermal evolution of the cosmic gas decoupled from that of the cosmic microwave background (CMB) at a redshift z~200. Afterwards and before the first stars had formed, the cosmic neutral hydrogen absorbed the CMB flux at its resonant 21cm spin-flip transition. We calculate the evolution of the spin temperature for this transition and the resulting anisotropies that are imprinted on the CMB sky due to linear density fluctuations during this epoch. These anisotropies at an observed wavelength of 10.56[(1+z)/50] meters, contain an amount of information that is orders of magnitude larger than any other cosmological probe. Their detection, although challenging, could tightly constrain any possible running of the spectral index from inflation (as suggested by WMAP), small deviations from Gaussianity, or any significant contribution from neutrinos or warm dark matter to the cosmic mass budget.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,413 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.62 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.44 · compares with prior results 0.29 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

The thermal evolution of the cosmic gas decoupled from that of the cosmic microwave background (CMB) at a redshift z~200. Afterwards and before the first stars had formed, the cosmic neutral hydrogen absorbed the CMB flux at its resonant 21cm spin-flip transition. We calculate the evolution of the spin temperature for this transition and the resulting anisotropies that are imprinted on the CMB sky due to linear density fluctuations during this epoch. These anisotropies at an observed wavelength of 10.56[(1+z)/50] meters, contain an amount of information that is orders of magnitude larger than any other cosmological probe. Their detection, although challenging, could tightly constrain any possible running of the spectral index from inflation (as suggested by WMAP), small deviations from Gaussianity, or any significant contribution from neutrinos or warm dark matter to the cosmic mass budget.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The thermal evolution of the cosmic gas decoupled from that of the cosmic microwave background (CMB) at a redshift z~200.	background 1.00	0.06	0.02	asserted 1.00
s1	Afterwards and before the first stars had formed, the cosmic neutral hydrogen absorbed the CMB flux at its resonant 21cm spin-flip transition.	background 1.00	0.04	0.03	asserted 1.00
s2	We calculate the evolution of the spin temperature for this transition and the resulting anisotropies that are imprinted on the CMB sky due to linear density fluctuations during this epoch.	contribution 0.81	0.93	0.09	asserted 0.96
s3	These anisotropies at an observed wavelength of 10.56[(1+z)/50] meters, contain an amount of information that is orders of magnitude larger than any other cosmological probe.	interpretation 0.72	0.32	0.41	asserted 1.00
s4	Their detection, although challenging, could tightly constrain any possible running of the spectral index from inflation (as suggested by WMAP), small deviations from Gaussianity, or any significant contribution from neutrinos or warm dark matter to the cosmic mass budget.	interpretation 0.96	0.11	0.51	hedged possibility 1.00

What kind of paper the classifier reports this is: theoretical result 0.93 · evidence from simulation or computation 0.67.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 2.** FIG. 2. Angular power spectrum of 21cm anisotropies

Showing 1 of the paper's 3 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:astro-ph/0312134 by the authors.

References

Works cited (20)

[6]

M. Zaldarriaga, S. Furlanetto, & L. Hernquist, Astro- phys. J., submitted, preprint [astro-ph/0311514] (2003)

View on Pith Pith review arXiv 2003
[1]

P. J. E. Peebles, Principles of Physical Cosmology , Princeton U. Press: Princeton, (1993), pp. 176, 177

View on Pith 1993
[2]

R. Barkana, & A. Loeb, Phys. Rep. 349, 125 (2001)

View on Pith 2001
[3]

G. B. Field, Astrophys. J. 129, 536 (1959)

View on Pith 1959
[4]

D. Scott, & M. J. Rees, Mon. Not. R. Astr. Soc. 247, 510 (1990)

View on Pith 1990
[5]

P. Tozzi, P. Madau, A. Meiksin, & M. J. Rees, Astrophys. J. 528, 597 (2000); N. Y. Gnedin & P. A. Shaver, Astro- phys. J., submitted, preprint [astro-ph/0312005] (2003)

View on Pith Pith review arXiv 2000
[7]

D. N. Spergel, et al., Astrophys. J. Suppl. 148, 175 (2003)

View on Pith 2003
[8]

P. Bode, J. P. Ostriker & N. Turok, Astrophys. J., 556, 93 (2001); R. Barkana, Z., Haiman, & J. P. Ostriker, Astrophys. J., 558, 482 (2001)

View on Pith 2001
[9]

G. B. Rybicki, & A. P. Lightman, Radiative Processes in Astrophysics, Wiley: New York, (1979), pp. 29-32

View on Pith 1979
[10]

A. C. Allison, & A. Dalgarno, Astrophys. J., 158, 423 (1969); B. Zygelman, & A. Dalgarno, in preparation

View on Pith 1969
[11]

M. Tegmark, & M. Zaldarriaga, Phys.Rev. D 66,103508, (2002)

View on Pith 2002
[12]

U-L. Pen, preprint [astro-ph/0305387] (2003)

View on Pith Pith review arXiv 2003
[13]

X. Chen, & J. Miralda-Escud´ e, Astrophys. J., submitted, preprint [astro-ph/0303395] (2003)

View on Pith Pith review arXiv 2003
[14]

A. R. Liddle & D. H. Lyth, Cosmological Inﬂation and Large-Scale Structure, Cambridge U. Press: Cambridge, (2000)

View on Pith 2000
[15]

M. Kamionkowski & A. R. Liddle, Phys.Rev.Lett. 84, 4525 (2000)

View on Pith 2000
[16]

E. T. Kearns, Frascati Phys.Ser. 28 413 (2002); J. N. Bahcall & C. Pena-Garay, JHEP 0311, 004 (2003)

View on Pith 2002
[17]

M. Tegmark et al , preprint [astro-ph/0310723] (2003)

View on Pith Pith review arXiv 2003
[18]

N. E. Kassim & K. W. Weiler, Low Frequency Astro- physics from Space, Springer-Verlag: New-York, (1990); R. G. Stone et al. , Radio Astronomy at Long Wavelengths , American Geophysical Union: Washington DC, (2000); see also, http://rsd-www.nrl.navy.mil/7213/weiler/lfraspce.html

View on Pith 1990
[19]

U. Seljak & M. Zaldarriaga, Phys.Rev.Lett. 82, 2636, (1999) ; W. Hu, Astrophys. J. 556, 93 (2001); C.M. Hi- rata & U. Seljak, Phys.Rev. D 67, 043001(2003)

View on Pith 1999
[20]

J. M. Maldacena, JHEP 0305, 013 (2003) 4

View on Pith 2003

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The Pesky Power Asymmetry
astro-ph.CO 2013-03 conditional novelty 5.0 of 10

Only four proposed explanations for the CMB hemispherical power asymmetry survive the homogeneity and quasar constraints, and each leaves a distinct multipole-dependent signature that Planck polarization data can test.
Towards a measurement of the spectral runnings
astro-ph.CO 2016-11 conditional novelty 4.0 of 10

Fisher forecasts give a Stage-4 CMB experiment sigma(alpha_s) = 0.0025 and sigma(beta_s) = 0.0045, enough to test primordial-black-hole scenarios but not the slow-roll predictions of 10^-3 and 10^-5.
Bell violation in the Sky
hep-th 2016-07 reject novelty 4.0 of 10

A time-dependent heavy-field mass during inflation is used to define a new curvature observable claimed to fix the inflation scale and bound the heavy-particle mass, though the Bell-violation link is not derived.
Features and New Physical Scales in Primordial Observables: Theory and Observation
astro-ph.CO 2015-05 accept novelty 4.0 of 10

Features in primordial correlation functions, if they exist, would let cosmologists infer new mass scales and partially discriminate between inflationary models that otherwise predict identical power spectra.
Signals of Inflationary Models with Cosmic Strings
astro-ph.CO 2011-06 accept novelty 3.0 of 10

A review of the observational signatures of cosmic strings produced at the end of inflation, concluding that CMB data already bound the string tension G-mu below roughly 10^-6, while the loop population and hence the ...
TASI Lectures on Primordial Cosmology
hep-th 2018-07 accept novelty 2.0 of 10

Lecture notes showing that CMB damping, acoustic phase shifts, and inflationary squeezed-limit bispectra constrain new particles, with a target sensitivity of Delta Neff around 0.027 and axion-photon couplings three o...

How the literature uses it

83 arXiv papers cite this in 123 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 93 sentences without a confident label

Uses its data or values 3 papers

As shown in Fig. 2 in Ref. [ref] , the 21-cm power spectrum extends without suppression out to $l≳10^6$, and values of $l_max∼10^7$ are perhaps achievable with a bit more effort.

Lensing of 21-cm Fluctuations by Primordial Gravitational Waves · Introduction · 0.83
Something like $10^7$ pixels of data on this exist [ref] , with estimates as high as $10^16$ potentially recoverable from highly redshifted 21 centimeter radiation [ref] .

Don't Throw the Baby Out with the Bath Water · A Thought-Provoking Question · 0.86
Such a precision is controlled only by the number of modes $N_21-cm$ and is given by, [equation] Thus using the estimate $N_21-cm∼10^16$ [ref] , one has very roughly $σ_∼10^-4-10^-3$.

Cosmological Collider Physics and the Curvaton · Observables and cosmological collider physics · 0.95

Cites it as background 24 papers

Mapping 21-cm fluctuations can assess the aggregate impact of the first emitting sources on the IGM [ref] , constrain reionization properties [ref] and the growth of cosmic structure [ref] , and probe fundamental physics [ref] .

21-cm fluctuations from primordial magnetic fields · Introduction · 0.86
The subject of 21 cm absorption and its fluctuations during the dark ages has been treated extensively by multiple authors [ref] .

A new light on 21 cm intensity fluctuations from the dark ages · Basic equations · 1.00
Recent work has explored the 21 cm signal that may arise during reionization [ref] from variations in the flux [ref] , X-ray heating [ref] , gas density [ref] or peculiar velocities [ref] .

Evolution of the 21 cm signal throughout cosmic history · Introduction · 0.98

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [6]

M. Zaldarriaga, S. Furlanetto, & L. Hernquist, Astro- phys. J., submitted, preprint [astro-ph/0311514] (2003)

View on Pith Pith review arXiv 2003

[2] [1]

P. J. E. Peebles, Principles of Physical Cosmology , Princeton U. Press: Princeton, (1993), pp. 176, 177

View on Pith 1993

[3] [2]

R. Barkana, & A. Loeb, Phys. Rep. 349, 125 (2001)

View on Pith 2001

[4] [3]

G. B. Field, Astrophys. J. 129, 536 (1959)

View on Pith 1959

[5] [4]

D. Scott, & M. J. Rees, Mon. Not. R. Astr. Soc. 247, 510 (1990)

View on Pith 1990

[6] [5]

P. Tozzi, P. Madau, A. Meiksin, & M. J. Rees, Astrophys. J. 528, 597 (2000); N. Y. Gnedin & P. A. Shaver, Astro- phys. J., submitted, preprint [astro-ph/0312005] (2003)

View on Pith Pith review arXiv 2000

[7] [7]

D. N. Spergel, et al., Astrophys. J. Suppl. 148, 175 (2003)

View on Pith 2003

[8] [8]

P. Bode, J. P. Ostriker & N. Turok, Astrophys. J., 556, 93 (2001); R. Barkana, Z., Haiman, & J. P. Ostriker, Astrophys. J., 558, 482 (2001)

View on Pith 2001

[9] [9]

G. B. Rybicki, & A. P. Lightman, Radiative Processes in Astrophysics, Wiley: New York, (1979), pp. 29-32

View on Pith 1979

[10] [10]

A. C. Allison, & A. Dalgarno, Astrophys. J., 158, 423 (1969); B. Zygelman, & A. Dalgarno, in preparation

View on Pith 1969

[11] [11]

M. Tegmark, & M. Zaldarriaga, Phys.Rev. D 66,103508, (2002)

View on Pith 2002

[12] [12]

U-L. Pen, preprint [astro-ph/0305387] (2003)

View on Pith Pith review arXiv 2003

[13] [13]

X. Chen, & J. Miralda-Escud´ e, Astrophys. J., submitted, preprint [astro-ph/0303395] (2003)

View on Pith Pith review arXiv 2003

[14] [14]

A. R. Liddle & D. H. Lyth, Cosmological Inﬂation and Large-Scale Structure, Cambridge U. Press: Cambridge, (2000)

View on Pith 2000

[15] [15]

M. Kamionkowski & A. R. Liddle, Phys.Rev.Lett. 84, 4525 (2000)

View on Pith 2000

[16] [16]

E. T. Kearns, Frascati Phys.Ser. 28 413 (2002); J. N. Bahcall & C. Pena-Garay, JHEP 0311, 004 (2003)

View on Pith 2002

[17] [17]

M. Tegmark et al , preprint [astro-ph/0310723] (2003)

View on Pith Pith review arXiv 2003

[18] [18]

N. E. Kassim & K. W. Weiler, Low Frequency Astro- physics from Space, Springer-Verlag: New-York, (1990); R. G. Stone et al. , Radio Astronomy at Long Wavelengths , American Geophysical Union: Washington DC, (2000); see also, http://rsd-www.nrl.navy.mil/7213/weiler/lfraspce.html

View on Pith 1990

[19] [19]

U. Seljak & M. Zaldarriaga, Phys.Rev.Lett. 82, 2636, (1999) ; W. Hu, Astrophys. J. 556, 93 (2001); C.M. Hi- rata & U. Seljak, Phys.Rev. D 67, 043001(2003)

View on Pith 1999

[20] [20]

J. M. Maldacena, JHEP 0305, 013 (2003) 4

View on Pith 2003