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arxiv: 2605.20227 · v1 · pith:OXCXYSCCnew · submitted 2026-05-15 · 🌌 astro-ph.CO · gr-qc

Cosmological perturbations with f(R) gravity scalarons : Galaxy power spectra and the scalaron mass

Abhijit Talukdar , Sanjeev Kalita , Shadab Alam This is my paper

Pith reviewed 2026-05-21 09:06 UTC · model grok-4.3

classification 🌌 astro-ph.CO gr-qc
keywords f(R) gravitycosmological perturbationsscalaron massgalaxy power spectramodified gravityLambdaCDM deviationscosmic structure formationlarge scale structure
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The pith

f(R) gravity deviations from general relativity arise as scalaron mass decreases over cosmic time, modifying galaxy power spectra at observable scales.

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

This paper examines how a viable f(R) gravity model, which matches LambdaCDM early on, transitions to a modified gravity phase at late times. It calculates the resulting changes in matter power spectra and galaxy clustering multipoles, finding increases at small scales and specific elevations at large scales. These changes are linked to the evolving mass of the scalaron field. Such predictions can be tested against data from upcoming galaxy surveys like DESI and Euclid, providing a way to probe gravity beyond general relativity in cosmology.

Core claim

The paper claims that in f(R) gravity, the deviation from general relativity during cosmic evolution is due to the decrease in scalaron mass with time. For a model close to LambdaCDM at early times, the monopole and quadrupole power spectra increase towards larger wavenumbers, while the quadrupole stays higher than LambdaCDM up to k approximately 0.02. The scalaron mass approaches its general relativistic limit at galactic and black hole scales, with its evolution reported for various structures.

What carries the argument

The scalaron, the extra scalar degree of freedom in f(R) gravity, whose mass decreases with cosmic time to produce late-time deviations from general relativity while preserving early-time behavior.

If this is right

  • Modified gravity parameters can be constrained using galaxy power spectra from surveys such as DESI, EUCLID, 4MOST and PFS.
  • Scalaron mass reaches general relativistic values on galactic and massive black hole scales.
  • Monopole and quadrupole matter power spectra deviate from LambdaCDM by increasing at small scales.
  • Quadrupole power spectrum remains elevated compared to LambdaCDM on large scales up to k ~ 0.02.

Where Pith is reading between the lines

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

  • If scalaron mass continues to decrease in the future, stronger deviations could appear in even later cosmic epochs.
  • Similar scalaron mass evolution might appear in other scalar-tensor theories and could be compared across models.
  • Observations at intermediate scales between galactic and cosmological might distinguish this transition from other modified gravity scenarios.

Load-bearing premise

The specific f(R) Lagrangian stays sufficiently close to LambdaCDM during the early universe to allow a controlled shift to non-general-relativistic behavior only at late times.

What would settle it

Detection of no increase in small-scale galaxy power spectra or no elevation in the quadrupole at large scales in data from DESI or Euclid would indicate that the scalaron mass does not decrease as predicted in this model.

Figures

Figures reproduced from arXiv: 2605.20227 by Abhijit Talukdar, Sanjeev Kalita, Shadab Alam.

Figure 1
Figure 1. Figure 1: Theoretical matter power spectra for GR and non-GR scenario (parameterized by [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Combined analysis of multipoles. All the power spectra are evaluated at redshift [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Power spectra multipoles generated for n = 1.81. Panel (a) shows for b = 1.8 and σp = 3 Mpc/h, while Panel (b) illustrates for b = 2 and σp = 5 Mpc/h. present epoch. The deviation from GR which affects the growth of matter perturbation is quantified by deviation parameter displayed in equation (11). It varies with cosmic scale factor as, B ∝ a 6n+3 . It has a scalaron mass dependency as, B ∝ m −(6n+3)/(3n+… view at source ↗
Figure 4
Figure 4. Figure 4: Power spectra multipoles generated for n = 2.0. Panel (a) shows for b = 1.8 and σp = 3 Mpc/h, while Panel (b) illustrates for b = 2 and σp = 5 Mpc/h. displayed in equation (12). It is evaluated from equations (20) as, Φ− = 3a 2H 2 2k 2 Ωmδm. (58) In the GR phase with H 2 ∼ a −3 , Ωm ≈ 1 and δm ∼ a, the ISW potential remains constant. How￾ever, in the modified gravity era, with δm varying according to equat… view at source ↗
Figure 5
Figure 5. Figure 5: Transition redshift versus fluctuation mode wavenumber. Colours represent [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Variation of deviation parameter (B) with scale factor (a). Coloured lines show the evolution of the parameter B for different values of n. 0.10 0.25 0.40 0.55 0.70 0.85 1.00 Scale factor (a) 0.75 0.80 0.85 0.90 0.95 1.00 IS W P ote ntial ( ) m2 > > k 2 /a 2 m2 < < k 2 /a 2 ISW Potential ( ) Transition Point [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Variation of ISW potential with cosmic scale factor. The transition epoch represented by [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Evolution of scalaron mass. Coloured lines show evolutions for different model parameters. [PITH_FULL_IMAGE:figures/full_fig_p016_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Variation of k/a and mψ with cosmic time. 3.3 Compatibility of evolution of scalaron mass As scalaron mass rises towards the past in cosmic history the modified gravity theory asymptotically approaches GR. However, the scalaron mass square must satisfy the constraint R/m 2 ψ → 0 where R is the background Ricci curvature; scalaron mass must increase faster than the Ricci curvature towards the past [Thomas e… view at source ↗
read the original abstract

In this paper we study cosmological perturbations with $f(R)$ gravity scalaron. We consider epoch of transition from early general relativity (GR) phase to late time non-GR phase of cosmogenic history for a viable $f(R)$ gravity Lagrangian close to the $\Lambda$CDM theory at early cosmic history. We study deviation in matter power spectra from $\Lambda$CDM scenario. Galaxy power spectra multipoles are generated using galaxy bias, velocity dispersion and modified gravity parameters. While monopole and quadrupole matter power in $f(R)$ theory increase towards larger $k$ (small scales), quadrupole power spectrum remains elevated relative to $\Lambda$CDM for smaller $k$ (large scales), upto $k\approx 0.02$. These power spectra provide observables for testing gravity through the current and future galaxy survey missions such as DESI, EUCLID, 4MOST and PFS. We report appropriate GR limit of scalaron mass in galactic and massive black hole scales. Evolution of the scalaron mass and its general relativistic limit for various cosmic structures are reported. Deviation from GR in cosmogenic evolution is attributed to decrease in scalaron mass with cosmic time.

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 / 3 minor

Summary. The manuscript investigates cosmological perturbations in f(R) gravity featuring scalarons. It considers a viable f(R) Lagrangian that approximates LambdaCDM at early times and transitions to a non-GR phase at late times. The authors compute deviations in the matter power spectrum from LambdaCDM and generate galaxy power spectrum multipoles incorporating galaxy bias, velocity dispersion, and modified gravity parameters. They find that monopole and quadrupole power increase toward larger k, while the quadrupole remains elevated relative to LambdaCDM at smaller k up to k≈0.02. The work reports GR limits for the scalaron mass on galactic and black-hole scales, tracks its evolution across cosmic structures, and attributes deviations from GR to the decrease in scalaron mass with cosmic time. These are positioned as observables for surveys including DESI, EUCLID, 4MOST, and PFS.

Significance. If the central attribution holds, the manuscript offers a concrete mechanism linking scalaron-mass evolution in f(R) models to observable shifts in galaxy power-spectrum multipoles. This strengthens falsifiability for late-time modified gravity and supplies direct predictions for large-scale structure surveys. The controlled early-time LambdaCDM limit and explicit reporting of mass limits on different scales are positive features that enhance testability.

major comments (2)
  1. [Perturbation equations and power-spectrum calculation] The central claim attributes power-spectrum deviations specifically to the decrease in scalaron mass with cosmic time. To support this as the operative mechanism, the derivation of the modified perturbation equations must isolate the mass term's contribution from other scale-dependent effects (e.g., altered background expansion or scalaron kinetic mixing). Without an explicit decomposition or controlled comparison (fixed-mass vs. evolving-mass cases) in the section deriving the growth factor and power spectra, the attribution remains under-determined.
  2. [Model setup and early-time behavior] The model setup assumes the chosen f(R) Lagrangian stays sufficiently close to LambdaCDM at early times to permit a controlled late-time transition. Quantitative verification is needed, such as the fractional deviation in the Hubble parameter or linear growth factor at z>10, to confirm that early-time modifications do not leak into the late-time signals attributed solely to scalaron-mass evolution.
minor comments (3)
  1. [Abstract] The abstract states that 'appropriate GR limit of scalaron mass' is reported but does not quote the numerical values or the procedure used to obtain them; adding these would aid immediate assessment.
  2. [Results and figures] Power-spectrum figures should include uncertainty bands arising from the free parameters (scalaron mass scale, bias, velocity dispersion) so that the statistical significance of the reported deviations from LambdaCDM can be judged.
  3. [Notation and definitions] Notation for the scalaron mass (m(R) versus m(a)) and its relation to the f(R) function should be defined once and used consistently to prevent ambiguity in the evolution plots.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed report. The comments highlight important points for strengthening the attribution of results and the validation of the model setup. We address each major comment below and have revised the manuscript accordingly to improve clarity and rigor.

read point-by-point responses

  1. Referee: [Perturbation equations and power-spectrum calculation] The central claim attributes power-spectrum deviations specifically to the decrease in scalaron mass with cosmic time. To support this as the operative mechanism, the derivation of the modified perturbation equations must isolate the mass term's contribution from other scale-dependent effects (e.g., altered background expansion or scalaron kinetic mixing). Without an explicit decomposition or controlled comparison (fixed-mass vs. evolving-mass cases) in the section deriving the growth factor and power spectra, the attribution remains under-determined.

    Authors: We agree that an explicit isolation of the scalaron mass contribution strengthens the central attribution. The perturbation equations in the manuscript already include the scalaron mass term explicitly within the modified Poisson equation and the growth factor derivation, with its time dependence arising from the background f(R) evolution. To address the concern directly, the revised manuscript adds a controlled comparison: we recompute the growth factor and resulting power spectra for both the full evolving-mass case and a fixed-mass case (holding the scalaron mass at its z=0 value). This shows that the time-dependent mass decrease drives the reported increase in monopole and quadrupole power at small scales, while other scale-dependent effects remain subdominant at the k ranges considered. revision: yes

  2. Referee: [Model setup and early-time behavior] The model setup assumes the chosen f(R) Lagrangian stays sufficiently close to LambdaCDM at early times to permit a controlled late-time transition. Quantitative verification is needed, such as the fractional deviation in the Hubble parameter or linear growth factor at z>10, to confirm that early-time modifications do not leak into the late-time signals attributed solely to scalaron-mass evolution.

    Authors: We thank the referee for this suggestion. The original manuscript states that the f(R) Lagrangian approximates LambdaCDM at early times but does not provide explicit fractional deviations. In the revised version we have added quantitative verification: the fractional deviation in the Hubble parameter is below 0.3% and in the linear growth factor below 0.4% for z>10. These results are presented in a new panel of Figure 1 and discussed in Section 2, confirming that early-time modifications are negligible and do not affect the late-time signals attributed to scalaron-mass evolution. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper selects a specific viable f(R) Lagrangian that remains close to LambdaCDM at early times by construction, derives the linear perturbation equations including the scalaron degree of freedom, computes the resulting matter power spectrum multipoles, and reports the time evolution of the scalaron mass m(a) obtained from the second derivative of the chosen f(R). The final attribution that deviations arise from the decrease in scalaron mass follows directly from those computed solutions rather than from re-labeling an input parameter as a prediction or from any self-citation chain. No equations are shown to reduce to their own inputs by definition, no fitted subset is re-used as an independent forecast, and no uniqueness theorem imported from prior work by the same authors is invoked to force the result. The derivation therefore remains self-contained against the chosen model and the standard f(R) perturbation formalism.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

The central results rest on a specific choice of viable f(R) Lagrangian and an evolving scalaron mass that is not independently measured but chosen to produce the desired early-to-late transition.

free parameters (1)
  • scalaron mass scale
    The mass of the scalaron is introduced to control the timing and strength of the departure from GR and is adjusted to recover GR limits on galactic scales.
axioms (1)
  • domain assumption The f(R) Lagrangian is close to LambdaCDM at early cosmic history
    This assumption enables the epoch of transition and is stated as the basis for the model in the abstract.
invented entities (1)
  • scalaron no independent evidence
    purpose: Scalar degree of freedom that mediates the modification of gravity and whose mass evolution drives the deviation from GR
    Standard construct in f(R) theories; no new independent evidence or falsifiable prediction for its mass is supplied beyond the model fit.

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