Looking for $\Lambda$ with the Rees-Sciama Effect

Neil Turok (Princeton University); Robert G. Crittenden

REVIEW

Looking for $\Lambda$ with the Rees-Sciama Effect

Robert G. Crittenden, Neil Turok (Princeton University)

Astrophysics · Submitted 13 Oct 1995 · 10 references

Pith's verdict: This is the paper that turned the ISW effect into a measurable cross-correlation, and the estimator it derives is still the standard one; the one soft spot is the uncomputed SW×RS cross term used to simplify Eq. (9).

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arXiv IDastro-ph/9510072 (version 1)

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CitationNeil Turok (Princeton University), Robert G. Crittenden. "Looking for $\Lambda$ with the Rees-Sciama Effect." arXiv:astro-ph/9510072 (1995). https://pith.science/paper/BFZJX3U3

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Editor's note

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Short version: this is the paper that turned the integrated Sachs-Wolfe effect from a nuisance into a measurement. The estimator it introduces — cross-correlate a low-redshift density tracer with a CMB map using a real-space filter f_l(r) proportional to g-dot(tau_0 - r) — is the one people still use, and it is derived cleanly. What is new is not the RS/ISW physics (Kofman and Starobinskii 1985 is cited) but the observable: Eqs. (4)-(7) show the RS multipoles are a convolution of the local density contrast with a filter that depends only on the growth rate, not on P(k). That is the whole trick, and it is why the prediction is essentially parameter-free. The delta-function reduction in Eq. (7) is checked numerically down to l = 2, which is the right check to run. The likelihood-ratio argument behind Eq. (9) is a reasonable Fisher estimate, and the bias-independence for constant b is correct. Soft spots, in order of how much they matter. First, the step just below Eq. (9) — that the RS contribution is almost uncorrelated with the rest of the anisotropy, so that the cross term equals C_l^RS — is asserted, not computed. Both terms are linear in the same delta_M(k), so the SW times RS cross term is a k-space overlap integral and is not zero by any symmetry; g-dot negative against a positive SW kernel makes it negative, and it could be a fair fraction of C_l^RS. That is the one place where the quoted 5.5, 7.4, 7.9 could move. Second, the ROSAT forecast assumes constant b and F(z) and ignores shot noise from unresolved AGN; the authors write 'barring other sources of noise' and leave it there. Minor. On the beam: I would push back on the worry that the signal sits at l of 50 to 100. Figure 3 peaks around l of 10 to 20 and the text says the sum converges quickly beyond l of 50, so a 7-degree COBE beam keeps most of it. The paper should have convolved with a beam anyway, but that does not sink the forecast. Who should read it: anyone doing CMB-tracer cross-correlations, which is now a large slice of the field. Worth a serious referee, and worth citing.

Referee report

Significance

If the forecast holds, this is a genuinely useful and falsifiable probe of Λ that is orthogonal in its systematics to lensing and q0 measurements. The strongest element is the derivation of the filter f_l(r): it depends only on the rate of change of the growth factor, not on P(k) or on the bias, so the predicted cross-correlation is parameter-free given a tracer map. The delta-function reduction of Eq. (7) is checked numerically down to l = 2, which is the right kind of check, and the truncation analysis of Fig. 4 shows the signal degrades gracefully with survey depth. The paper is also commendably explicit that the effect should exist in open models and defect models, i.e. that flat matter domination is the special case. The weaknesses are in the quantitative forecast rather than the method: the headline S/N values rest on an unproven decorrelation assumption and on an idealised, beam-free experiment.

Major objections (3)

[§III, sentence immediately following Eq. (9)] The reduction of Eq. (9) to the plotted quantity rests on the assertion that 'the Rees-Sciama contribution is almost uncorrelated with the remainder of the anisotropy, so that ⟨a^RS_lm a^tot*_lm⟩ ≈ C^RS_l'. This is asserted, not shown, and it is load-bearing: it is what makes the summand in Eq. (9) equal to l(2l+1)C^RS_l/C^tot_l, which is what Fig. 3 plots and what produces 5.5, 7.4 and 7.9. Both a^RS_lm and the dominant last-scattering (Sachs-Wolfe) term are linear functionals of the same primordial δ_M(k), so their cross term is a k-space overlap integral of the RS kernel ∫dτ ġ(τ) j_l(kΔτ) with the SW kernel, not zero by any symmetry. Because ġ < 0 while the SW kernel is positive, the cross term is negative and could be a non-negligible fraction of C^RS_l. The authors should compute ⟨a^RS_lm a^SW*_lm⟩/√(C^RS_l C^SW_l) explicitly and either demonstrate that it is small or replace C^RS_l in the numerator of Eq. (9) by the actual cross term. The '≥' in Eq. (9) should also be justified, since it too follows only under this approximation.
[§III–IV, Eq. (9) and Fig. 3] The quoted signal-to-noise values are for an ideal full-sky, noiseless experiment with every multipole measured, and the paper does not state what survives a realistic beam. The proposed instrument, COBE, has a beam of roughly 7° FWHM, corresponding to l ≲ 20, whereas the text states the sum 'converges quickly beyond l ∼ 50' and Fig. 3 shows the cumulative contribution still rising through l ∼ 30–50. The paper should convolve the summand with a Gaussian beam of the relevant FWHM (and, ideally, add a detector-noise term) and report the retained fraction of (S/N)² for each Ω_Λ. My expectation is that the qualitative conclusion survives, since the signal peaks at l ∼ 10–20, but the numbers 5.5, 7.4 and 7.9 should not be presented as achievable with COBE without this step.
[§IV, Eq. (14) and the ROSAT forecast] The estimated suppression factor of ∼0.8 for Ω_Λ = 0.8 assumes b(z) and F(z) constant and, in the authors' own words, holds only 'barring other sources of noise'. Two contaminants are left unquantified and are relevant to the proposed test: Poisson shot noise from unresolved AGN in the ROSAT map, and the significant ROSAT autocorrelation on θ < 6° reported in ref. [9], which the authors themselves note may indicate a new clustered source population. A clustered X-ray component correlated with large-scale structure would contribute to the measured cross-correlation in a way that is not the Rees-Sciama signal. At minimum the authors should add a shot-noise term to the denominator of the correlation estimator and bound its effect on the forecast; otherwise the claim that 'a substantial signal should be visible in the COBE-ROSAT correlation' is not supported at the stated confidence.

Minor objections (6)

[Abstract and §I–II] Several typographical errors should be corrected: 'aquire' in the abstract, 'amout' in §I, and 'gravitional', 'signifcant' and 'instantanous' in §II. In the reference list, 'Trumper' in ref. [9] should read 'Trümper'.
[Eqs. (11)–(12)] The symbol f_l is used both for the real-space filter f_l(r) and for its Fourier transform f_l(k) in Eq. (12), with f̃_l(k) denoting the truncated version. This is confusing; a distinct symbol for the transform (e.g. F_l(k)) would make Eqs. (11)–(12) much easier to follow.
[Figs. 1 and 3] Although f_l(r) is correctly stated to be independent of the primordial power spectrum, the plotted quantities C^RS_l and C^tot_l are not: they require a P(k) and a normalisation. The paper does not state which spectrum and normalisation were assumed (COBE-normalised scale-invariant?). This should be specified so that the numbers in Figs. 1 and 3 and the S/N values can be reproduced.
[§IV, paragraph on bias] The statement that the cross-correlation is 'fairly insensitive' to variation of b(z) is supported by Fig. 4 only for the case of a redshift cutoff z_c, not for a redshift-dependent bias. Either add a figure showing the effect of, say, a linearly varying b(z), or soften the claim to indicate that it is an expectation rather than a demonstrated result.
[Fig. 1 caption] The caption should state explicitly that the curves labelled z > 0.5, z > 1 and z > 2 are cumulative contributions from z_c to the present, not contributions from a redshift shell, so that the reader does not misread the figure as a differential redshift distribution.
[Eq. (7)] The normalisation convention for g(τ) and Φ should be stated explicitly at the point where Eq. (7) is introduced (i.e. Φ(k,τ) = g(τ)δ_M(k,τ0)/k² with the stated units), so that the amplitude of f_l(r) and hence of the predicted a^RS_lm can be reproduced without reverse-engineering Eqs. (3)–(6).

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The paper

The paper claims

If the universe has a cosmological constant, the microwave sky should be correlated with the nearby matter distribution, and that correlation can be predicted without knowing the primordial power spectrum.

The reading

In a flat, matter-dominated universe the gravitational potential is frozen, so photons crossing it gain and lose exactly the same energy and nothing is left over. The authors point out that a cosmological constant breaks this: the potential starts to decay at late times, at redshifts below about one, and photons crossing that decaying potential emerge with a net frequency shift. This is the Rees-Sciama, or integrated Sachs-Wolfe, contribution to the microwave background. Because the potential is generated by matter we can actually map, the resulting anisotropy should be spatially correlated with the local density field rather than being a pure random sky. The paper's aim is to turn that fact into a measurement: derive the optimal weighting of a density survey against a microwave map, forecast how much signal survives cosmic variance and finite survey depth, and argue that an X-ray survey compared with COBE could detect the effect.

What carries the argument

The load-bearing object is the radial filter $f_l(r)$ of Eq. (6), and its large-$l$ approximation $f_l(r) �approx ġ(τ_0-r)/(2π l(l+1))$. It converts a map of local density into a predicted microwave multipole, and it does so without reference to the primordial spectrum, which is what makes the test a measurement of $Ω_Λ$ rather than a consistency check with a free amplitude. The second piece of machinery is the likelihood ratio of Eq. (8) and its signal-to-noise sum of Eq. (9), which converts the overlap between predicted and observed multipoles into a single number for how strongly a correlation would be detected.

Extended reading notes

Core claim

The central claim is that the Rees-Sciama contribution to each microwave multipole can be written as a convolution of the present-day matter density with a single radial filter, $a^{RS}_{lm} = 5.5pt plus 1.0fill$, and that for $l>2$ this filter collapses to a simple closed form proportional to the local rate of change of the potential, $f_l(r) �approx 1/(2π l(l+1)) · ġ(τ_0 - r)$. The filter contains no information about the primordial power spectrum — only the growth history, which is fixed once $Ω_Λ$ is chosen — so the predicted cross-correlation is a parameter-free prediction for each value of the cosmological constant. Summing the per-multipole signal-to-noise over an ideal full-sky survey gives $S/N ≥ 5.5$, $7.4$ and $7.9$ for $Ω_Λ = 0.6$, $0.8$ and $0.9$. The authors then show that truncating the density survey at a modest redshift costs surprisingly little, and that a weighting function modelled on the observed redshift distribution of X-ray AGN retains about $0.8$ of the ideal signal, so a ROSAT–COBE comparison is a plausible first test.

Load-bearing premise

The forecast assumes an ideal full-sky, noiseless microwave map with all multipoles measured and assumes the Rees-Sciama anisotropy is uncorrelated with the last-scattering anisotropy, even though the paper's own Figure 3 shows the signal accumulating out to $l$ of order 50 to 100 while the COBE beam it proposes to use reaches only $l$ of order 20.

Editorial extensions

If this is right

A measured cross-correlation between a low-redshift density tracer and the large-angle microwave sky would constitute direct evidence that the gravitational potential is decaying today, which in the simplest models means a nonzero cosmological constant.
Because the predicted filter is independent of the primordial power spectrum, the amplitude of the detected correlation is a direct handle on $Ω_Λ$ rather than a degenerate combination with the perturbation amplitude.
Surveys need not be extremely deep: cutting the density survey off at $z_c �approx 1$ still leaves a substantial fraction of the signal, so shallow wide-field catalogues are useful for this test.
The same logic applies beyond the cosmological constant — any model in which the potential evolves at late times, including open universes and models with cosmic defects, should produce a density–microwave correlation.
A null result at the forecast sensitivity would bound the late-time evolution of the potential and hence constrain $Ω_Λ$ from a direction completely independent of gravitational lensing statistics.

Reading between the lines

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

The forecast numbers assume every multipole is measured; a real microwave experiment with a finite beam samples only the low-$l$ part of the sum, so the quoted $S/N$ should be read as an upper bound and the realistic figure is smaller by an amount the paper does not compute.
The claim that the Rees-Sciama and last-scattering contributions are essentially uncorrelated is what allows the cross term to be replaced by $C_l^{RS}$; if there were any correlation, for example through a late-time or reionization contribution, the forecast would shift and the test would need the full covariance.
Cross-correlating a density tracer with the microwave sky is a cheap measurement in the sense that it needs no new instrument, only archival maps, which suggests the same statistic could be applied retrospectively to any pair of existing all-sky catalogues.
Because the filter is proportional to $ġ$, a detection would also measure the shape of the growth history, so the test could in principle distinguish a cosmological constant from modified gravity scenarios that produce a similar late-time decay.

Original abstract

In models with a cosmological constant, a significant component of the large scale cosmic microwave background (CMB) anisotropy is produced at rather low redshifts, z < 1. In these models, the gravitational potential perturbations begin to evolve at late times. Photons passing through these time varying potentials aquire frequency shifts, an effect first noted by Rees and Sciama. Since the gravitational potential is associated with matter at observable redshifts, the local matter density (or some tracer thereof) is correlated with the CMB anisotropy on the sky. We outline the optimal method of measuring this correlation, and discuss the prospects for using an X-ray/COBE comparison to detect a cosmological constant.

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.

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What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.09 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.11 · compares with prior results 0.13 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

In models with a cosmological constant, a significant component of the large scale cosmic microwave background (CMB) anisotropy is produced at rather low redshifts, z < 1. In these models, the gravitational potential perturbations begin to evolve at late times. Photons passing through these time varying potentials aquire frequency shifts, an effect first noted by Rees and Sciama. Since the gravitational potential is associated with matter at observable redshifts, the local matter density (or some tracer thereof) is correlated with the CMB anisotropy on the sky. We outline the optimal method of measuring this correlation, and discuss the prospects for using an X-ray/COBE comparison to detect a cosmological constant.

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	In models with a cosmological constant, a significant component of the large scale cosmic microwave background (CMB) anisotropy is produced at rather low redshifts, z < 1.	background 0.99	0.10	0.12	asserted 1.00
s1	In these models, the gravitational potential perturbations begin to evolve at late times.	background 1.00	0.06	0.04	asserted 1.00
s2	Photons passing through these time varying potentials aquire frequency shifts, an effect first noted by Rees and Sciama.	background 1.00	0.04	0.05	asserted 1.00
s3	Since the gravitational potential is associated with matter at observable redshifts, the local matter density (or some tracer thereof) is correlated with the CMB anisotropy on the sky.	background 0.65	0.10	0.23	asserted 0.99
s4	We outline the optimal method of measuring this correlation, and discuss the prospects for using an X-ray/COBE comparison to detect a cosmological constant.	contribution 0.80	0.67	0.26	asserted 0.37

What kind of paper the classifier reports this is: method or tool 0.92 · evidence from argument 0.91.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

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

levels run

P abstract

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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 1.** FIG. 1. The large scale anisotropy power spectrum,

**Figure 2.** FIG. 2. The ideal filter function, ˙g

**Figure 3.** FIG. 3. We plot the signal to noise squared as a function of

**Figure 4.** FIG. 4. We plot the reduction of the signal to noise ratio if th

Figures reproduced from arXiv:astro-ph/9510072 by the authors.

References

Works cited (10)

[9]

A. M. Soltan, G. Hasinger, R. Egger, S. Snowden and J. Trumper , Max Planck preprint (1995)

View on Pith 1995
[1]

A. Einstein, Sitz. Preuss. Akad. Wiss., 142 (1917)

View on Pith 1917
[2]

J.P. Ostriker and P.J. Steinhardt, Penn preprint UPR-0659T, as tro-ph/9505066; L.M. Krauss and M.S. Turner, CWRU-P6-95, astro-ph/9504003; G. Ef stathiou, W.J. Suther- land and S.J. Maddox, Nature 348 705 (1990); and P.J.E. Peebles, Ap. J. 284, 439 (1984)

View on Pith Pith review arXiv 1990
[3]

L.A. Kofman and A.A. Starobinskii, Sov. Astron. Lett. 11, 271 (1985)

View on Pith 1985
[4]

D. Maoz and H. Rix, Ap. J. 416, 425 (1993)

View on Pith 1993
[5]

For a recent review, see S.M. Carroll, W.H. Press and E.L. Turner, Annu. Rev. Astron. Astrophys. 30, 499 (1992)

View on Pith 1992
[6]

M.J. Rees and D.W. Sciama, Nature 217 511 (1968)

View on Pith 1968
[7]

U. Seljak, MIT-CSR-95-13, astro-ph/9506048

View on Pith Pith review arXiv
[8]

A. Comastri, G. Setti, G. Zamorani and G. Hasinger, Astron. As trophys. 296, 1 (1995)

View on Pith 1995
[10]

K. Ganga et al , Ap. J. Lett. 410, L57 (1993). 11 Lo oking for / with the Rees/-Sciama E/ ect Rob ert G/. Crittenden and Neil T urok Joseph Henry L ab or atory/, Princ eton University/, Princ eton NJ/, /0/8/5/4/4/. /(/1/0///1/2///9/5/) In mo dels with a cosmological constan t/, a signi/ can t comp onen t of the large scale cosmic micro w a v e bac kground...

View on Pith 1993

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How the literature uses it

51 arXiv papers cite this in 62 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 · 40 sentences without a confident label

Uses its method or tool 1 paper

In the Limber approximation [ref] , the spherical harmonic power spectrum between CMB temperature anisotropies and a tracer $i$ of the LSS becomes: [ref] [equation] where $T_CMB$ denotes the mean temperature of the CMB today, $i ∈{δ_g, γ}$ and $W^i(χ(z))$ represents the window functions defined in Equations [ref] and [ref].

Integrated approach to cosmology: Combining CMB, large-scale structure and weak lensing · Theoretical predictions · 0.94

Cites it as background 18 papers

The residual $𝒪(f_NL^2)$ variance is a result of the late-time, large-scale integrated Sachs-Wolfe (ISW) effect, in which CMB anisotropies are generated by gravitational potential decay along the line-of-sight [ref] .

An improved estimator for non-Gaussianity in cosmic microwave background observations · Introduction · 0.83
A CMB photon traveling through time-varying gravitational potentials $Φ$ and $Ψ$ in the metricmetric will suffer a change in energy, resulting in a change in the observed CMB temperature: the so-called Integrated Sachs-Wolfe (ISW) effect ( [ref] , see [ref] for a review).

Galaxy-CMB Cross-Correlation as a Probe of Alternative Models of Gravity · Integrated Sachs-Wolfe Effect · 1.00
The seminal work by [ref] proposed to use a galaxy catalogue as LSS tracer, and the first positive detection following this approach was done by [ref] using data and radio and $X$-ray tracers.

Planck 2015 results. XXI. The integrated Sachs-Wolfe effect · CMB correlation with tracers of the gravitational potential · 0.97

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] [9]

A. M. Soltan, G. Hasinger, R. Egger, S. Snowden and J. Trumper , Max Planck preprint (1995)

View on Pith 1995

[2] [1]

A. Einstein, Sitz. Preuss. Akad. Wiss., 142 (1917)

View on Pith 1917

[3] [2]

J.P. Ostriker and P.J. Steinhardt, Penn preprint UPR-0659T, as tro-ph/9505066; L.M. Krauss and M.S. Turner, CWRU-P6-95, astro-ph/9504003; G. Ef stathiou, W.J. Suther- land and S.J. Maddox, Nature 348 705 (1990); and P.J.E. Peebles, Ap. J. 284, 439 (1984)

View on Pith Pith review arXiv 1990

[4] [3]

L.A. Kofman and A.A. Starobinskii, Sov. Astron. Lett. 11, 271 (1985)

View on Pith 1985

[5] [4]

D. Maoz and H. Rix, Ap. J. 416, 425 (1993)

View on Pith 1993

[6] [5]

For a recent review, see S.M. Carroll, W.H. Press and E.L. Turner, Annu. Rev. Astron. Astrophys. 30, 499 (1992)

View on Pith 1992

[7] [6]

M.J. Rees and D.W. Sciama, Nature 217 511 (1968)

View on Pith 1968

[8] [7]

U. Seljak, MIT-CSR-95-13, astro-ph/9506048

View on Pith Pith review arXiv

[9] [8]

A. Comastri, G. Setti, G. Zamorani and G. Hasinger, Astron. As trophys. 296, 1 (1995)

View on Pith 1995

[10] [10]

K. Ganga et al , Ap. J. Lett. 410, L57 (1993). 11 Lo oking for / with the Rees/-Sciama E/ ect Rob ert G/. Crittenden and Neil T urok Joseph Henry L ab or atory/, Princ eton University/, Princ eton NJ/, /0/8/5/4/4/. /(/1/0///1/2///9/5/) In mo dels with a cosmological constan t/, a signi/ can t comp onen t of the large scale cosmic micro w a v e bac kground...

View on Pith 1993