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arxiv: 2606.03729 · v1 · pith:Z6AZF4P3new · submitted 2026-06-02 · 🌌 astro-ph.CO · gr-qc

Constraining Scale-Dependent Growth in f(R) Gravity with Future 21 cm Surveys

Apurba Samanta , Bhuwan Joshi , Jess Worsley , Peter Dunsby , Saikat Chakraborty This is my paper

Pith reviewed 2026-06-28 08:30 UTC · model grok-4.3

classification 🌌 astro-ph.CO gr-qc
keywords f(R) gravity21 cm surveysgrowth indexscale-dependent growthHI biasmodified gravitycosmic accelerationintensity mapping
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The pith

Future 21 cm surveys can constrain the scale-dependent growth index in f(R) gravity models.

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

The paper examines whether upcoming 21 cm intensity mapping surveys can measure the growth of cosmic structure in modified gravity theories known as f(R). In these models the growth rate changes with the scale of observation and with time, unlike in standard cosmology. By forecasting the precision on the growth index and on the product of neutral hydrogen bias and growth rate, the authors show that such surveys can give moderate but useful limits on f(R) scenarios that produce late-time acceleration without a separate dark energy field. This matters because recent data have hinted that dark energy may not be a simple constant, so independent tests from structure growth are needed to decide between explanations.

Core claim

In f(R) gravity the linear matter density contrast evolves in a scale-dependent way, so the growth index becomes a function of both wavenumber and redshift. Viable f(R) models reproduce LambdaCDM at high redshift yet drive acceleration at late times. Forthcoming 21 cm surveys can measure this scale-dependent growth index together with the combined HI bias and growth-rate parameter, thereby supplying moderate constraints that support these modified gravity models.

What carries the argument

The scale-dependent growth index gamma(k,z) in f(R) gravity, extracted from 21 cm power spectrum measurements of the HI bias-growth-rate product.

If this is right

  • The growth index can be measured at different scales to test for scale dependence predicted by f(R).
  • Moderate constraints on viable f(R) functional forms become possible from the data.
  • The combined HI bias and growth-rate parameter can be jointly constrained alongside the growth index.
  • 21 cm observations provide an independent probe of late-time acceleration in modified gravity.

Where Pith is reading between the lines

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

  • Combining 21 cm constraints with galaxy surveys such as DESI could produce tighter limits on f(R) parameters.
  • The forecasts assume a particular form for the f(R) model; relaxing that assumption would require checking whether the extraction remains stable.
  • If unmodeled systematics in the 21 cm signal prove larger than expected, the moderate support claimed for modified gravity would weaken.

Load-bearing premise

The assumption that the scale-dependent growth index and combined HI bias-growth-rate parameter can be extracted from 21 cm data without being dominated by unmodeled systematics or by the specific choice of f(R) functional form.

What would settle it

A measurement showing the growth index is constant with scale and matches general relativity within survey errors would falsify the claim that 21 cm data supports f(R) scenarios.

Figures

Figures reproduced from arXiv: 2606.03729 by Apurba Samanta, Bhuwan Joshi, Jess Worsley, Peter Dunsby, Saikat Chakraborty.

Figure 1
Figure 1. Figure 1: Evolution of the transition redshift (solid blue line) under the quasi￾static approximation, given the initial conditions in equation (13). This curve delineates the GR (blue) and 𝑓 (𝑅) gravity (light orange) regimes. At 𝑧 = 0, the transition occurs at a Fourier wave number 𝑘0 ≃ 0.031 Mpc−1 . Dotted lines highlight specific scales at 𝑘 = 0.01 Mpc−1 (grey), 0.05 Mpc−1 (green), and 0.1 Mpc−1 (red), which are… view at source ↗
Figure 2
Figure 2. Figure 2: In these plots, we show the evolution of different modes and the variation of the growth index within the full quasi-static approximation (9) using the initial conditions discussed above. The plots also highlight the relevant modes probed by 21 cm surveys, which are important for understanding the modes responsible for galaxy formation. 0 1 2 3 4 5 6 z 0.2 0.4 0.6 0.8 1.0 D(z) k = 0.012 Mpc 1 k = 0.034 Mpc… view at source ↗
Figure 3
Figure 3. Figure 3: In these plots, we show the evolution of different modes and the variation of the growth index within the exact equation (8) using the initial conditions discussed above. The plots also highlight the relevant modes probed by 21 cm surveys, which are important for understanding the modes responsible for galaxy formation. 0 1 2 3 4 5 6 z 0.0 0.1 0.2 0.3 0.4 0.5 0.6 |(D(z)e x a ct D(z)full)| × 1 0 0 k = 0.012… view at source ↗
Figure 4
Figure 4. Figure 4: Absolute percentage difference between the exact solutions and the full QS (solid) solutions for: (a) the normalised perturbation D(z), and (b) the growth index, 𝛾(𝑘, 𝑧). MNRAS 000, 1–9 (2026) [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Relative percentage difference between the exact solutions and the full QS (solid) solutions for: (a) the normalised perturbation D(z), and (b) the growth index, 𝛾(𝑘, 𝑧). (21) Here the system temperature 𝑇sys is taken from Bacon et al. (2020), 𝜒 and 𝐻(𝑧) are respectively the co-moving distance and Hubble param￾eter. For SKA-Mid, which is the only SD mode survey considered in this paper, we take efficiency … view at source ↗
Figure 6
Figure 6. Figure 6: Relative error of the full QS approximation across different Fourier scales. Panels (b,c,e,f) illustrate the 𝑓 (𝑅) regime (𝑘 = 0.05 and 0.1 Mpc−1 ), where the relative error deviates significantly from the GR prediction. Panels (a,d) represent the GR-dominated regime, showing nearly identical relative errors and confirming theoretical consistency with survey expectations on these scales. These results rema… view at source ↗
Figure 7
Figure 7. Figure 7: Relative error of the Exact equation across different Fourier scales. Panels (b,c,e,f) illustrate the 𝑓 (𝑅) regime (𝑘 = 0.05 and 0.1 Mpc−1 ), where the relative error deviates significantly from the GR prediction. Panels (a,d) represent the GR-dominated regime, showing nearly identical relative errors and confirming theoretical consistency with survey expectations on these scales. These results remain cons… view at source ↗
read the original abstract

Recent observations, particularly from DESI, have provided intriguing hints of dynamical behaviour in late-time dark energy. Modified gravity theories offer a compelling framework for interpreting such phenomena, with $f(R)$ gravity emerging as one of the most extensively studied examples. A central challenge in these models, however, lies in determining the precise functional form of $f(R)$. Nevertheless, several viable models have been proposed that successfully reproduce the standard $\Lambda$CDM cosmology at high red shifts while generating late-time cosmic acceleration without an explicit dark energy component. Within this framework, the evolution of the linear matter density contrast becomes scale dependent, leading to a growth index that varies with both scale and redshift. In this work, we explore the capability of forthcoming 21 cm observations to constrain the growth index, as well as the combined neutral hydrogen (HI) bias and growth-rate parameter. Our results indicate that future 21 cm surveys can provide meaningful, though moderate, support for these modified gravity scenarios.

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 forecasts the ability of future 21 cm intensity-mapping surveys to constrain the scale-dependent growth index γ(k,z) in viable f(R) gravity models (which reproduce ΛCDM at high redshift while driving late-time acceleration) together with the combined HI bias–growth-rate parameter. It concludes that these surveys can deliver meaningful though moderate support for the modified-gravity scenarios relative to GR.

Significance. If the forecast assumptions prove robust, the work would usefully inform survey design for testing gravity on cosmological scales with intensity mapping. The identification of scale dependence in the growth index as a distinguishing feature of f(R) is correctly noted. The result remains a forecast rather than a data-driven constraint, so its significance is moderate and contingent on the realism of the covariance modeling and systematics treatment.

major comments (2)
  1. [§3] §3 (Fisher-matrix setup): the central claim that γ(k,z) and the HI bias–growth-rate combination can be recovered with errors small enough to yield moderate support for f(R) rests on the unquantified assumption that foreground residuals, instrumental noise, and nonlinear bias evolution remain sub-dominant at the relevant k and z; no explicit error budget or end-to-end simulation is shown to demonstrate that these systematics do not inflate the forecasted errors by the factors of 2–5 commonly reported in 21 cm literature.
  2. [§4] §4 (results and model comparison): the statement that results are insensitive to the specific f(R) functional form is not demonstrated; the growth-index parametrization is introduced as a fitted function of scale and redshift, so the claimed support for f(R) over GR may depend on the chosen parametrization and on the particular f(R) model used to generate the mock data.
minor comments (2)
  1. Notation for the combined HI bias–growth-rate parameter is introduced without an explicit equation; adding a numbered definition would improve clarity.
  2. Figure captions should state the exact survey specifications (redshift range, k-range, noise model) used for each forecast curve.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. We address the two major comments point by point below, indicating the revisions that will be incorporated in the next version of the manuscript.

read point-by-point responses

  1. Referee: [§3] §3 (Fisher-matrix setup): the central claim that γ(k,z) and the HI bias–growth-rate combination can be recovered with errors small enough to yield moderate support for f(R) rests on the unquantified assumption that foreground residuals, instrumental noise, and nonlinear bias evolution remain sub-dominant at the relevant k and z; no explicit error budget or end-to-end simulation is shown to demonstrate that these systematics do not inflate the forecasted errors by the factors of 2–5 commonly reported in 21 cm literature.

    Authors: We agree that the Fisher-matrix analysis is performed under the assumption that the listed systematics remain sub-dominant and that no explicit error budget or end-to-end simulation is provided. This is a standard limitation of many forecast papers, but the referee is correct that it should be stated more explicitly. In the revised manuscript we will add a new subsection in §3 that (i) summarizes the dominant 21 cm systematics, (ii) cites the literature reporting typical error inflation factors, and (iii) clarifies that the quoted constraints represent the statistical floor under idealized conditions. We will also add a short paragraph in the conclusions noting that realistic systematics could degrade the forecasted precision. revision: yes

  2. Referee: [§4] §4 (results and model comparison): the statement that results are insensitive to the specific f(R) functional form is not demonstrated; the growth-index parametrization is introduced as a fitted function of scale and redshift, so the claimed support for f(R) over GR may depend on the chosen parametrization and on the particular f(R) model used to generate the mock data.

    Authors: The referee correctly notes that we did not demonstrate insensitivity to the choice of f(R) functional form or to the precise parametrization of γ(k,z). The manuscript employs one representative viable f(R) model to generate the mock data and adopts a specific scale- and redshift-dependent parametrization for γ. We will revise the text in §4 (and the abstract) to remove the claim of insensitivity, to state explicitly that the results apply to the class of viable f(R) models that produce scale-dependent growth, and to note that the scale dependence itself is the generic distinguishing feature relative to GR. This will make the interpretation of the model-comparison results more precise. revision: yes

Circularity Check

0 steps flagged

No circularity: standard forecast based on independent perturbation theory and survey modeling

full rationale

The paper performs a forecast of parameter constraints from future 21 cm intensity mapping on the scale-dependent growth index in f(R) models. The derivation relies on established linear perturbation equations in modified gravity (yielding scale-dependent growth) combined with standard Fisher-matrix forecasting on the HI power spectrum; neither step reduces to a self-definition, a fitted quantity renamed as a prediction, or a load-bearing self-citation chain. The growth-index parametrization is an input modeling choice drawn from the literature, not derived from the forecast results themselves. The analysis remains self-contained against external cosmological codes, survey specifications, and independent f(R) model implementations.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Abstract-only review prevents exhaustive extraction; the work implicitly relies on standard assumptions about linear perturbation theory in f(R) and on the functional forms of viable f(R) models that recover LambdaCDM at high redshift.

free parameters (1)
  • growth index gamma(k,z)
    Scale- and redshift-dependent growth index introduced to capture modified-gravity effects; its functional form is fitted or parametrized rather than derived from first principles.
axioms (1)
  • domain assumption Linear matter density contrast evolution remains valid on the scales probed by 21 cm surveys
    Standard assumption in cosmological forecasts; invoked when translating survey sensitivity into constraints on growth.

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