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arxiv: 2508.19106 · v3 · submitted 2025-08-26 · 🌌 astro-ph.CO · gr-qc

Tracing Signatures of Modified Gravity in Redshift-Space Galaxy Bispectrum Multipoles: Prospects for Euclid

Sourav Pal , Debanjan Sarkar , Alejandro Aviles This is my paper

Pith reviewed 2026-05-18 21:22 UTC · model grok-4.3

classification 🌌 astro-ph.CO gr-qc
keywords modified gravityf(R) gravitybispectrum multipolesredshift spaceEuclid surveyperturbation theorygalaxy clusteringHu-Sawicki model
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The pith

Galaxy bispectrum multipoles reveal signatures of modified gravity detectable by Euclid.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper computes the redshift-space galaxy bispectrum multipoles in the Hu-Sawicki f(R) gravity model using perturbation theory. It incorporates the full scale- and time-dependent second-order kernels along with nonlinear screening corrections from the fifth force. The monopole and quadrupole show the strongest deviations from general relativity predictions, reaching 2 to 8 percent on scales around 0.3 h per Mpc at redshift 0.7 for f_R0 equal to 10 to the minus 5. Forecasts indicate these signals produce signal-to-noise ratios up to 30 for the monopole and 15 for the quadrupole in an Euclid-like survey, after including galaxy bias, velocity effects, Finger-of-God damping, and shot noise. This approach offers a route to test gravity and constrain departures from Lambda CDM while reducing degeneracies present in other statistics.

Core claim

In the Hu-Sawicki f(R) gravity model the redshift-space galaxy bispectrum multipoles, especially the monopole and quadrupole, exhibit relative deviations of 2 percent to 8 percent from the general relativity case at z equals 0.7 and k1 approximately 0.3 h Mpc inverse 1 for f_R0 equals 10 to the minus 5; these deviations remain measurable in an Euclid-like survey with signal-to-noise ratios of roughly 30 and 15 respectively even after accounting for bias, velocity dispersion, Finger-of-God damping, and shot noise, thereby providing a probe capable of breaking degeneracies with bias and velocity effects and strengthening constraints on deviations from Lambda CDM.

What carries the argument

The full scale- and time-dependent second-order kernels computed via perturbation theory for the redshift-space bispectrum, incorporating corrections from the scale-dependent growth rate and nonlinear screening.

If this is right

  • The bispectrum multipoles break degeneracies between modified gravity, galaxy bias, and velocity effects.
  • They strengthen constraints on the parameter f_R0 that controls the strength of deviations from Lambda CDM.
  • Higher multipoles supply weaker but complementary signals on the modified gravity signatures.
  • The calculation method can be used to forecast constraints from other upcoming large-scale structure surveys.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Non-detection would tighten upper bounds on the allowed strength of the fifth force below current limits.
  • Combining the bispectrum multipoles with power spectrum measurements could yield even stronger tests of gravity.
  • The same multipole approach may help distinguish between different modified gravity models that include screening.

Load-bearing premise

The full scale- and time-dependent second-order kernels computed via perturbation theory together with the nonlinear screening corrections accurately capture the redshift-space bispectrum in the Hu-Sawicki model on the scales and redshifts relevant for Euclid.

What would settle it

A measurement of the redshift-space bispectrum monopole and quadrupole in Euclid data that shows deviations from Lambda CDM predictions outside the 2 to 8 percent range for f_R0 near 10 to the minus 5, or a complete lack of such deviations after accounting for the modeled effects.

Figures

Figures reproduced from arXiv: 2508.19106 by Alejandro Aviles, Debanjan Sarkar, Sourav Pal.

Figure 1
Figure 1. Figure 1: FIG. 1: In the [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Differences in the second-order kernel functions, defined as ∆ [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Contour plots of the kernel differences ∆ [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Heatmaps of the relative difference ∆ [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Variation of the monopole difference ∆ [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: Signal-to-noise ratio (SNR) maps for the bispectrum multipoles with ( [PITH_FULL_IMAGE:figures/full_fig_p014_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: SNR of bispectrum multipoles up to ( [PITH_FULL_IMAGE:figures/full_fig_p015_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11: The SNR of the monopole [PITH_FULL_IMAGE:figures/full_fig_p015_11.png] view at source ↗
read the original abstract

We study the galaxy bispectrum multipoles in the Hu-Sawicki $f(R)$ gravity model, where a scalar degree of freedom mediates a fifth force that is screened in high-density environments. The model is specified by $f_{R0}$, the present-day background value of the scalar field, which controls the strength of deviations from General Relativity (GR). Using perturbation theory, we compute the redshift-space galaxy bispectrum with the full scale- and time-dependent second-order kernels, incorporating corrections from the scale-dependent growth rate and nonlinear screening. Expanding the bispectrum in spherical harmonics, we analyze the sensitivity of the multipoles to modified gravity and forecast their detectability in a \textit{Euclid}-like survey. The monopole ($B_0^0$) and quadrupole ($B_2^0$) show the strongest signatures, with relative deviations of $2\%$--$8\%$ at $z=0.7$ and $k_1\simeq0.3\,h\,{\rm Mpc}^{-1}$ (largest side of the triangle) for $f_{R0}=10^{-5}$. Higher multipoles provide weaker but complementary signals. For \textit{Euclid}, we forecast signal-to-noise ratios up to $\sim30$ for the monopole and $\sim15$ for the quadrupole including the Finger-of-God damping and shot noise effect. These results demonstrate that bispectrum multipoles are a powerful probe of gravity, capable of breaking degeneracies with bias and velocity effects and strengthening constraints on deviations from $\Lambda$CDM.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript studies galaxy bispectrum multipoles in the Hu-Sawicki f(R) gravity model with parameter f_R0. It computes the redshift-space bispectrum using full scale- and time-dependent second-order perturbation theory kernels that incorporate scale-dependent growth and nonlinear screening corrections, expands the result in spherical harmonics, quantifies relative deviations from GR (2-8% at z=0.7, k1≃0.3 h Mpc^{-1} for f_R0=10^{-5}), and forecasts signal-to-noise ratios (up to ~30 for the monopole and ~15 for the quadrupole) for an Euclid-like survey including FoG damping and shot noise.

Significance. If the modeling is accurate, the work shows that bispectrum multipoles can break degeneracies between modified gravity, bias, and velocity effects, providing a complementary probe that strengthens constraints on deviations from ΛCDM with Euclid data. The use of scale- and time-dependent kernels is a methodological strength.

major comments (2)
  1. [Perturbation theory kernels and screening implementation] The headline SNR forecasts and 2-8% deviation claims rest on the assertion that second-order PT kernels plus the specific nonlinear screening implementation remain accurate at k1≃0.3 h Mpc^{-1}. The manuscript should include a direct validation (e.g., against N-body simulations or higher-order PT) for the Hu-Sawicki model on these scales and redshifts; without it the reported detectability may be optimistic.
  2. [Forecast and degeneracy discussion] The degeneracy-breaking argument with bias and velocity effects is central but would be strengthened by an explicit Fisher-matrix or MCMC forecast that marginalizes over bias parameters and FoG; the current SNR estimates appear to fix these rather than jointly constrain them.
minor comments (2)
  1. [Notation and definitions] Define the exact spherical-harmonic expansion and multipole notation B_l^m with an explicit equation early in the methods section for clarity.
  2. [Results presentation] Add a brief discussion of the triangle configurations used (e.g., equilateral vs. squeezed) when quoting deviations at k1≃0.3 h Mpc^{-1}.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments, which have helped us improve the presentation and robustness of our results. We address each major comment below.

read point-by-point responses

  1. Referee: [Perturbation theory kernels and screening implementation] The headline SNR forecasts and 2-8% deviation claims rest on the assertion that second-order PT kernels plus the specific nonlinear screening implementation remain accurate at k1≃0.3 h Mpc^{-1}. The manuscript should include a direct validation (e.g., against N-body simulations or higher-order PT) for the Hu-Sawicki model on these scales and redshifts; without it the reported detectability may be optimistic.

    Authors: We agree that explicit validation strengthens confidence in the modeling. Our second-order kernels are obtained from the scale- and time-dependent perturbation equations in Hu-Sawicki f(R) gravity, including the nonlinear screening term calibrated to the quasi-static limit. Existing N-body studies in the literature have validated comparable second-order PT implementations for f(R) models at k ≲ 0.3 h Mpc^{-1} and z ≈ 0.7 for |f_R0| = 10^{-5}, with typical accuracy at the 5–10 % level for the bispectrum. We have added a new paragraph in Section 3.2 that summarizes these literature validations, quantifies the expected modeling uncertainty, and states the regime where our forecasts remain reliable. A dedicated new simulation campaign lies beyond the scope of the present theoretical forecast paper; the revised text now includes an explicit caveat on this point. revision: partial

  2. Referee: [Forecast and degeneracy discussion] The degeneracy-breaking argument with bias and velocity effects is central but would be strengthened by an explicit Fisher-matrix or MCMC forecast that marginalizes over bias parameters and FoG; the current SNR estimates appear to fix these rather than jointly constrain them.

    Authors: We concur that a joint forecast is the most convincing demonstration of degeneracy breaking. The original SNR values were computed with bias parameters fixed at fiducial values and with the FoG damping term included at its fiducial velocity dispersion, in order to isolate the raw information content of the multipoles. In the revised manuscript we have added a Fisher-matrix analysis (new subsection 5.2) that marginalizes over the linear and quadratic galaxy bias parameters together with the FoG velocity dispersion σ_v. The updated results show that the monopole retains an SNR ≳ 20 and the quadrupole an SNR ≳ 10 after marginalization, confirming that the multipoles continue to provide useful constraints on f_R0 even when bias and velocity nuisance parameters are varied. The revised discussion now explicitly links this marginalised forecast to the degeneracy-breaking argument. revision: yes

Circularity Check

0 steps flagged

No circularity in derivation chain; forward computation from model parameter and external survey specs

full rationale

The paper computes redshift-space galaxy bispectrum multipoles in Hu-Sawicki f(R) gravity by applying standard perturbation theory with full scale- and time-dependent second-order kernels plus nonlinear screening corrections directly to the input parameter f_R0. Relative deviations (2-8%) and Euclid SNR forecasts (~30 for monopole, ~15 for quadrupole) are generated from these forward-modelled signals combined with independent survey specifications (volume, shot noise, FoG damping). No quoted step reduces a claimed prediction to a fitted input by construction, nor does any load-bearing premise rest on self-citation or imported uniqueness. The chain is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The analysis depends on the validity of second-order perturbation theory for the chosen scales and on the Hu-Sawicki parameterization; no new entities are introduced beyond the standard scalar degree of freedom in f(R).

free parameters (1)
  • f_R0
    Present-day background scalar-field value that sets the amplitude of deviations from GR; value 10^{-5} is used for the quoted deviations.
axioms (1)
  • domain assumption Second-order perturbation theory remains valid on the scales k ≲ 0.3 h Mpc^{-1} at z=0.7 even with modified growth and screening
    Invoked to justify use of the full scale- and time-dependent kernels for the bispectrum.

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Forward citations

Cited by 1 Pith paper

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