{"id":"5a92252e-db25-40eb-8743-dacd2e70793a","arxiv_id":"2411.12594","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"A new measurement of the gravitational potential decay rate at z=0.2-1.4, detected at 3.1 sigma, helps sharpen dark energy constraints when combined with BAO and supernova data.","lead":"This paper measures how fast gravitational potential wells decay as the universe accelerates, using galaxy maps from DESI Legacy Surveys DR9 and Planck CMB data out to redshift 1.4, detecting the signal at 3.1 sigma. It then combines the decay-rate measurement with BAO and supernova data to tighten dark energy constraints, including the w0-wa model.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"High-z DR bins are 'possibly caused by a mixture of galaxies' per Fig. 3; photo-z leakage bias is not modeled and propagates into the improved w0-wa constraints.","rationale":"I read the paper as a careful extension of the Dong et al. (2022) ratio method. The imaging-systematics weighting, the magnification-bias calibration with q=3, the cross-check of q through galaxy-shear correlations, and the consistency between fixed-cosmology and cosmology-dependent magnification calibration in Fig. 11 are genuine strengths. The low-z DRf3z measurement is consistent with the earlier result once the smaller DR9 footprint is accounted for. My concern is not that the individual cross-powers are wrong; it is that the redshift assignment of the new constraining power, the z4-z6 bins, relies on an unmixed-bin assumption that is explicitly questioned by the manuscript itself in Fig. 3. The covariance matrix in Fig. 3 handles noise correlations; it cannot turn a leakage-induced shift of the effective redshift into a correct DR value. Because the purpose of the high-z extension is the steeply growing sensitivity of DR to w, this is the point where the cosmological conclusions are least secure. I agree with the reader's weakest_assumption, so the verdict stays conditional: the paper should either demonstrate with calibrated n_i(z) that leakage changes the z4-z6 DR values by less than their error bars, or incorporate leakage into the likelihood and systematic budget. If the proposed forward-model test shows no significant shift, the central claim stands and the conditional can be relaxed.","tokens_in":20521,"tokens_out":8554,"duration_ms":89941,"concrete_test":"Forward-model the six-bin DR likelihood of Sec. 3.1 using the actual PRLS per-galaxy photo-z PDFs (or a spectroscopic-calibrated n_i(z)) instead of top-hat bin windows: for each bin i compute C^{Xg}_l,i = ∫ dz n_i(z) W_X(z) C^{Xg}(z) and refit the DR_i values and the wCDM/w0wa posteriors. If the z4-z6 DR_i shift by more than about 0.03 (roughly one third of the quoted 1σ errors in Table 1) or the w/wa posteriors in Tables 3-4 shift by more than about 0.1, photo-z leakage is a leading systematic and the 3.1σ significance and improved DE constraints require re-evaluation.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing step is identifying each photometric bin with a single effective redshift z_m in Sec. 3.1. Eq. (1) yields C^{Ig}=DR(z_m)C^{phi g} only if the galaxy window is effectively monochromatic. For a finite photo-z distribution n_i(z), the measured ratio is C^{Ig}_i/C^{phi g}_i = [∫ n_i(z) W_ISW(z) C^{Ig}(z) dz] / [∫ n_i(z) W_lens(z) C^{phi g}(z) dz], a weighted average whose effective redshift differs from z_m and depends on n_i(z); this dependence is not in P(DR|z_i) used in Eq. (5). The paper's own Fig. 3 shows strong cross-correlations between z4/z5 and z5/z6, 'possibly caused by a mixture of galaxies due to the lower accuracy in the photo-z estimation for higher redshifts.' The simultaneous fit with the full covariance accounts for statistical correlations between bins, not for the deterministic bias from this leakage. Since the sensitivity of DR to w increases steeply with redshift (factor 2.4 at z=1.4 relative to z=0.8, Sec. 3.2.1), a small leaked fraction from adjacent bins shifts the effective redshift of the z4-z6 DR points and can bias w0 and wa, especially wa which enters weighted by z/(1+z). The DR_l3z and DR6z posteriors, and therefore the quoted improvements for BAO+DR and SNe+DR in Tables 3 and 4, inherit this bias.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper measures the gravitational potential decay rate DR(z) through the ratio of ISW-galaxy and lensing-galaxy cross-power spectra in six photometric redshift bins from z=0.2 to z=1.4, using DESI DR9 galaxy catalogs and Planck CMB products. It reports a total significance of 3.1 sigma, extends the earlier DR measurement of Dong et al. (2022) to higher redshift, and uses the DR measurements to constrain flat wCDM and w0-waCDM models, both alone and in combination with SDSS/DESI BAO and PantheonPlus supernovae. The paper claims that adding DR significantly improves dark-energy constraints relative to SNe alone or SDSS BAO alone, while the improvement over DESI BAO is modest.","tokens_in":20820,"tokens_out":4595,"duration_ms":47927,"significance":"If the high-redshift DR measurements are unbiased, this work provides a genuinely new and independent cosmological probe at z~0.9-1.3, where the sensitivity of DR to the dark-energy equation of state is substantially higher than at z<0.8. The treatment of imaging systematics with Random Forest weights, the use of full covariance matrices for the DR estimates, and the explicit magnification-bias consistency checks are strengths, as is the reliance on public data. However, the central claim of improved dark-energy constraints from the z4-z6 bins depends on the assumption that each photometric redshift bin is effectively unmixed, and the paper's own Fig. 3 indicates that this assumption is questionable at high redshift.","major_comments":[{"comment":"The identification C^Ig_i/C^phi g_i = DR(z_m) is only valid if each galaxy bin has an effectively monochromatic redshift selection. For a realistic photometric redshift distribution n_i(z), the measured ratio is an n_i-weighted ratio of integrals involving the ISW and lensing kernels, so the effective redshift of the ratio can differ from the nominal z_m and depends on the photo-z tails. Figure 3 itself reports strong cross-correlations between z4/z5 and z5/z6, which the text attributes to 'a mixture of galaxies due to the lower accuracy in the photo-z estimation for higher redshifts.' The full covariance matrix accounts for statistical correlations between bins, but not for the deterministic bias produced by this leakage. Because the sensitivity of DR to w increases steeply with redshift (Sec. 3.2.1), even a modest leaked fraction can shift the z4-z6 DR values and bias the w0 and wa constraints in Tables 3 and 4. Please quantify the leakage using the photo-z error distribution or a spec-z cross-match, propagate it into the DR values and the final posteriors, or otherwise demonstrate that this effect is negligible.","section":"Sec. 3.1, Eq. (1)"},{"comment":"The parameter likelihood multiplies the per-bin PDFs P_i(DR|theta,z_i) as if the six DR measurements were independent, but Sec. 3.1 emphasizes that the cross-correlations between bins are non-negligible and states that the DR values are measured simultaneously using the full covariance matrix. Marginalizing the joint DR posterior to skew-normal PDFs and then multiplying them discards the cross-bin covariance information that motivated the simultaneous measurement. This independence assumption is contradictory to the evidence in Fig. 3 and can bias the quoted error bars and best-fit shifts in Tables 3 and 4. Please construct the theta likelihood directly from the joint data vector and covariance, or provide a quantitative justification that the cross-bin covariance is negligible for the parameter combination considered here.","section":"Sec. 3.2.1, Eq. (5)"},{"comment":"The baseline magnification-bias correction adopts q=3, but the galaxy-shear cross-correlation measurements in Fig. 10 estimate q in the range of roughly 1.4 to 2.7, generally below 3. A factor-of-two error in q changes the magnification correction by a factor of two, and the paper states that the resulting impact on DR is approximately 20% at ell>10; however, the uncertainty in q is not propagated into the DR values in Table 1 or into the final wCDM and w0waCDM constraints in Tables 3 and 4. Please propagate the measured q uncertainty, or vary q within its measured range, and show the corresponding shifts in DR and in the derived dark-energy parameters.","section":"Sec. 4 and Sec. 2.3"}],"minor_comments":[{"comment":"The table caption refers to columns for <DR> and sigma(DR), but the table only shows the best-fit DR value and its 68% uncertainties; the caption should be updated to match the actual columns.","section":"Table 1"},{"comment":"The sentence 'the addition of DR can significantly improves DE constraints' has a subject-verb agreement error and should read 'can significantly improve.'","section":"Abstract"},{"comment":"The note contains the typo 'the first there redshifts'; it should be 'the first three redshifts.'","section":"Table 3 note"},{"comment":"The choice of (ell_min, ell_max) ~ (9,117) is stated without a detailed discussion of how sensitive the DR measurement is to this window; a short robustness test or a reference to the earlier analysis would help.","section":"Sec. 3.1"},{"comment":"The color bar for the covariance matrices is labeled from 0 to 1, but cross-covariances can be negative or exceed unity in normalized units; please clarify the normalization or use a symmetric color scale.","section":"Fig. 3"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a real new measurement, not a rehash. The authors extend the gravitational potential decay-rate probe from z<0.8 to z<1.4 with six tomographic bins, add random-forest imaging systematics weights, and calibrate magnification bias with several consistency checks. Total detection significance is 3.1 sigma. I buy the low-redshift part; the high-z extension is the interesting but fragile part.\n\nWhat's genuinely new: the z=0.9-1.3 bins are new, and the simultaneous six-bin likelihood with full covariance is a step beyond Dong et al. (2022). The magnification-bias treatment is careful: they measure q via galaxy-shear cross-correlation, find it below 3, and test cosmology-dependent calibration with negligible change. The imaging systematics weighting is standard but appropriate. These are real improvements.\n\nThe soft spot is the one the paper itself flags. Fig. 3 shows strong cross-correlations between z4/z5 and z5/z6, attributed to photo-z leakage, and the analysis does not model the bias this induces. The ratio method in Eq. (1) assumes each bin's galaxy window is effectively monochromatic; with a finite photo-z distribution n_i(z), the measured ratio is a weighted average over redshift, and the effective redshift shifts. The full covariance handles statistical correlations, not this deterministic shift. Since DR sensitivity to w grows steeply with redshift (about a factor of 2.4 from z=0.8 to 1.4), a small leaked fraction in the z4-z6 bins can move the DR points and bias w0 and wa. The quoted improved constraints from DR+l3z and the DR+SNe w0-wa results inherit that risk.\n\nA second, minor issue: the paper shows different systematics treatments (imaging weights vs. mask-only, fixed vs. varying magnification calibration) side by side but does not fold them into a systematic error budget. That leaves the reader to judge how much the answer moves.\n\nThe circularity worry is mild. The measured DR is constructed from observed cross-spectra, not from a w-containing model; the magnification correction uses a fiducial Planck cosmology, but the consistency checks they run (varying the calibration cosmology) suggest this is not driving the result.\n\nBottom line: this paper deserves a serious referee. The measurement is a genuine addition to the cosmological dataset, the analysis is careful, and the main flaw is addressable. I would ask the authors to propagate photo-z distribution uncertainties and add a systematic covariance before final acceptance, but I would not desk-reject it.","headline":"Genuine new DR measurement to z=1.4 with careful systematics, but photo-z leakage in the high-z bins is unmodeled and can bias the improved w constraints.","tokens_in":21410,"tokens_out":3517,"would_cite":true,"duration_ms":35458,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper reports a direct measurement of the gravitational potential decay rate DR(z), the quantity behind the integrated Sachs–Wolfe effect, in six tomographic redshift bins over $0.2\\le z<1.4$, using Planck CMB temperature and lensing…","keywords":["gravitational potential decay rate","integrated Sachs-Wolfe effect","CMB lensing","dark energy equation of state","cosmic acceleration","photometric redshift tomography","DESI DR9 galaxy catalog","magnification bias"],"falsifier":"Take the stacked photometric-redshift distribution in each of the three highest bins, recalculate the effective redshift and the expected DR, and compare with the quoted values; if the inferred DR shifts by more than the error bars, the clean-bin assumption is falsified. A complementary test is to redo the measurement using only galaxies with the most reliable photo-z estimates and see whether the $w$ posterior changes.","tokens_in":20292,"feed_emoji":"🌌","tokens_out":10831,"duration_ms":91163,"temperature":0.7,"pith_summary":"This paper reports a direct measurement of the gravitational potential decay rate $\\mathrm{DR}(z)$, the quantity behind the integrated Sachs–Wolfe effect, in six tomographic redshift bins over $0.2\\le z<1.4$, using Planck CMB temperature and lensing maps together with DESI DR9 photometric galaxies. The detection is quoted at a total significance of $3.1\\sigma$. Because the decay rate is caused by cosmic acceleration, it is a direct probe of dark energy, and the paper shows that adding $\\mathrm{DR}$ to baryon acoustic oscillation and supernova data tightens equation-of-state constraints. In the flat $w$CDM model the three probes all favor $w=-1$; in the $w_0w_a$CDM model, $\\mathrm{DR}$ plus supernovae give $w_0=-0.94^{+0.11}_{-0.13}$ and $w_a=-0.22^{+0.57}_{-0.97}$, so the data show no preference for dynamical dark energy over a cosmological constant.","feed_headline":"Gravitational potential decay measured at 3.1σ out to z=1.4","feed_subtitle":"The ratio of ISW to lensing signals probes dark energy and, with BAO and SNe data, favors w = -1.","key_machinery":"The load-bearing identity is $C^{Ig}_\\ell \\simeq \\mathrm{DR}(z_m)\\,C^{\\phi g}_\\ell$: the ISW–galaxy and lensing–galaxy cross-spectra share the same galaxy window and matter-clustering factors, so their ratio isolates $\\mathrm{DR}(z)=(-d\\ln D_\\phi/d\\ln a)(aH/c)/W_L(z)$, where $D_\\phi$ is the linear growth factor of the potential and $W_L$ is a lensing weight. This removes the usual galaxy-bias and sampling-variance limitations of ISW measurements. The measurement uses a Bayesian likelihood for $P(\\mathrm{DR})$ evaluated from these cross-spectra over $(\\ell_{\\min},\\ell_{\\max})\\simeq(9,117)$, with the full covariance across all six redshift bins treated simultaneously, random-forest imaging weights, and a magnification-bias correction.","core_discovery":"The central claim is that the ratio of the CMB temperature–galaxy cross-power spectrum $C^{Ig}_\\ell$ to the CMB lensing–galaxy cross-power spectrum $C^{\\phi g}_\\ell$ isolates the gravitational potential decay rate $\\mathrm{DR}(z_m)$ at the effective redshift of each galaxy slice, with galaxy bias and matter clustering cancelling out. Using six equally spaced redshift bins in $0.2\\le z<1.4$, a full covariance matrix across bins, imaging-systematics weights from a random-forest calibration, and a magnification-bias correction with $q=3$, the paper obtains $\\mathrm{DR}$ values at $z_m\\simeq0.31$, $0.51$, $0.70$, $0.91$, $1.09$ and $1.28$, with a combined significance of about $3.1\\sigma$. These measurements are then used to constrain flat $w$CDM and flat $w_0w_a$CDM cosmologies. The paper finds that $\\mathrm{DR}$ agrees with DESI BAO, improves dark-energy constraints from SDSS BAO or PantheonPlus supernovae substantially, and that $\\mathrm{DR}$ plus DESI BAO gives $\\Omega_m=0.292^{+0.014}_{-0.014}$ and $w=-1.019^{+0.112}_{-0.120}$, while $\\mathrm{DR}$ plus supernovae in the $w_0w_a$ model gives $w_0=-0.94^{+0.11}_{-0.13}$, $w_a=-0.22^{+0.57}_{-0.97}$.","pith_inferences":["If photometric redshift leakage mixes the high-redshift bins, the DR values at $z\\simeq0.9$–$1.3$ are weighted mixtures rather than single-redshift measurements, and the $w$ constraints built from them could be biased because DR sensitivity to $w$ increases steeply with redshift; a spectroscopic or better-calibrated photo-z sample could test this.","The same ratio method should become much more powerful with lower-noise CMB lensing and larger galaxy samples, since CMB temperature noise dominates the ISW term and currently limits the total significance.","The observable could also serve as a modified-gravity test: because DR measures the evolution of the potential directly, residuals relative to the $\\Lambda$CDM prediction would signal physics beyond smooth dark energy even if the expansion history were fixed."],"forward_implications":["DR at $z\\simeq1.3$ is roughly twelve times more sensitive to $w$ than $H(z)$, so the high-redshift bins carry real weight in equation-of-state fits.","Adding DR to DESI BAO shrinks the $w$ error bar by about 18 percent and leaves $\\Omega_m$ essentially unchanged.","Because the degeneracy directions of DR, SDSS BAO, and PantheonPlus SNe are nearly orthogonal, adding DR to those probes improves the dark-energy constraints substantially.","All three probes — DR, DESI BAO, and PantheonPlus SNe — favor $w=-1$ within $1\\sigma$ in the $w$CDM model, while SDSS BAO alone favors $w<-1$ at the $2\\sigma$ level.","In the $w_0w_a$ model, DR plus supernovae has no preference for dynamical dark energy over $\\Lambda$CDM."],"supporting_citations":[{"why":"Proposes the ratio relation between ISW-galaxy and lensing-galaxy cross-spectra that defines DR and removes galaxy bias.","marker":"Zhang (2006)"},{"why":"Previous DR measurement at low redshift and the Bayesian likelihood and covariance treatment that this work extends to z=1.4.","marker":"Dong et al. (2022)"},{"why":"DESI DR1 BAO measurements used for the combined dark-energy constraints.","marker":"DESI Collaboration et al. (2024a)"},{"why":"SMICA CMB temperature map used to measure the ISW-galaxy cross-correlation.","marker":"Planck Collaboration et al. (2016b)"},{"why":"Planck lensing potential map used to measure the lensing-galaxy cross-correlation.","marker":"Planck Collaboration et al. (2020)"},{"why":"Random-forest imaging systematics mitigation method adopted to weight galaxy density maps.","marker":"Chaussidon et al. (2022)"},{"why":"PantheonPlus likelihood with full covariance used for the supernova constraints.","marker":"Brout et al. (2022)"},{"why":"PantheonPlus supernova compilation that supplies the SNe data combined with DR.","marker":"Scolnic et al. (2022)"}],"fun_headline_variants":["Gravitational decay rate weighs dark energy at 3.1σ","Cosmic potential decay probes dark energy to z=1.4","Gravitational decay measurement bolsters dark energy with 3.1σ","Gravitational potential decay reaches z=1.4 in dark energy test","Gravitational decay hints at w=-1 from deep cosmic data"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The high-redshift bins are treated as if each contains galaxies at one effective redshift; if photometric-redshift errors blend the bins, the measured DR values at $z\\simeq0.9$–$1.3$ are mixtures and the dark-energy constraints drawn from them could be biased.","fun_headline_variants_meta":{"raw":{"variants":["Gravitational decay rate weighs dark energy at 3.1σ","Cosmic potential decay probes dark energy to z=1.4","Gravitational decay measurement bolsters dark energy with 3.1σ","Gravitational potential decay reaches z=1.4 in dark energy test","Gravitational decay hints at w=-1 from deep cosmic data"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000958,"raw_usage":{"total_tokens":4234,"prompt_tokens":1252,"completion_tokens":2982,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":868,"completion_tokens_details":{"reasoning_tokens":2886}},"tokens_in":868,"tokens_out":2982,"duration_ms":21087,"temperature":1.0,"reasoning_tokens":2886,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T17:22:18.935725+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take the stacked photometric-redshift distribution in each of the three highest bins, recalculate the effective redshift and the expected DR, and compare with the quoted values; if the inferred DR shifts by more than the error bars, the clean-bin assumption is falsified. A complementary test is to redo the measurement using only galaxies with the most reliable photo-z estimates and see whether the $w$ posterior changes.","supporting_citations":[],"review_version":1}