Euclid: Constraints on f(R) cosmologies from the spectroscopic and photometric primary probes
Pith reviewed 2026-05-24 08:01 UTC · model grok-4.3
The pith
Euclid spectroscopic and photometric data together constrain the Hu-Sawicki f(R) parameter log f_R0 to 1 percent precision.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
In an optimistic setting, Euclid alone constrains log f_R0 at the 1 percent level using the combination of spectroscopic and photometric observations for the fiducial value f_R0 = 5 times 10 to the minus 6; this corresponds to a 1-sigma error of order 6 times 10 to the minus 7 on f_R0 itself. Spectroscopic data alone reach 3 percent, photometric data alone reach 1.4 percent. The same forecasts distinguish the models with f_R0 = 5 times 10 to the minus 5 and 5 times 10 to the minus 7 from Lambda-CDM at more than 3 sigma.
What carries the argument
The Hu-Sawicki f(R) model whose extra parameter f_R0 sets the amplitude of a scale-dependent fifth force, together with the phenomenological scale-dependent growth model for baryon acoustic oscillations and redshift-space distortions in the spectroscopic probe and the fitting formula for the modified nonlinear matter power spectrum in the photometric probes.
If this is right
- Spectroscopic galaxy clustering alone yields a 3 percent constraint on log f_R0.
- The combination of photometric probes alone yields a 1.4 percent constraint on log f_R0.
- For fiducial values f_R0 = 5 times 10 to the minus 5 and 5 times 10 to the minus 7, Euclid data separate the model from Lambda-CDM at more than 3 sigma.
- The quoted precisions assume an optimistic survey configuration with no additional systematics beyond those already modeled.
Where Pith is reading between the lines
- If the forecast is realized, Euclid data would exclude most of the f(R) parameter space still allowed by current observations if no deviation is detected.
- The same methodology could be applied to other scale-dependent modified-gravity models whose effects on growth and lensing can be captured by similar fitting functions.
- A null result at the forecasted precision would tighten the requirement that any viable f(R) model must mimic general relativity on the scales probed by Euclid to within roughly one part in a thousand.
Load-bearing premise
The phenomenological modeling of scale-dependent growth for BAO and RSD together with the fitting formula for the non-linear matter power spectrum accurately captures the f(R) modifications without introducing significant systematic bias.
What would settle it
A future Euclid data release that returns an uncertainty on log f_R0 larger than 1 percent, or a best-fit f_R0 inconsistent with the forecasted precision around the fiducial value 5 times 10 to the minus 6, would show the forecast does not hold.
Figures
read the original abstract
$\textit{Euclid}$ will provide a powerful compilation of data including spectroscopic redshifts, the angular clustering of galaxies, weak lensing cosmic shear, and the cross-correlation of these last two photometric observables. In this study we extend recently presented $\textit{Euclid}$ forecasts into the Hu-Sawicki $f(R)$ cosmological model, a popular extension of the Hilbert-Einstein action that introduces an universal modified gravity force in a scale-dependent way. Our aim is to estimate how well future $\textit{Euclid}$ data will be able to constrain the extra parameter of the theory, $f_{R0}$, for the range in which this parameter is still allowed by current observations. For the spectroscopic probe, we use a phenomenological approach for the scale dependence of the growth of perturbations in the terms related to baryon acoustic oscillations and redshift-space distortions. For the photometric observables, we use a fitting formula that captures the modifications in the non-linear matter power spectrum caused by the $f(R)$ model. We show that, in an optimistic setting, and for a fiducial value of $f_{R0} = 5 \times 10^{-6}$, $\textit{Euclid}$ alone will be able to constrain the additional parameter $\log f_{R0}$ at the $3\%$ level, using spectroscopic galaxy clustering alone; at the $1.4\%$ level, using the combination of photometric probes on their own; and at the $1\%$ level, using the combination of spectroscopic and photometric observations. This last constraint corresponds to an error of the order of $6 \times 10^{-7}$ at the $1\sigma$ level on the model parameter $f_{R0} = 5 \times 10^{-6}$. We report also forecasted constraints for $f_{R0} = 5 \times 10^{-5}$ and $f_{R0} = 5 \times 10^{-7}$ and show that in the optimistic scenario, $\textit{Euclid}$ will be able to distinguish these models from $\Lambda\mathrm{CDM}$ at more than 3$\sigma$. (abridged)
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper forecasts Euclid constraints on the Hu-Sawicki f(R) parameter f_R0 using spectroscopic galaxy clustering (with phenomenological scale-dependent growth for BAO/RSD) and photometric probes (weak lensing, galaxy clustering, cross-correlations, with a fitting formula for modified non-linear P(k)). For fiducial f_R0 = 5×10^{-6} in an optimistic setting, it claims 3% precision on log f_R0 from spectroscopy alone, 1.4% from photometry alone, and 1% (σ(f_R0) ≈ 6×10^{-7}) from the combination, with >3σ distinction from ΛCDM for f_R0 = 5×10^{-5}, 5×10^{-6}, and 5×10^{-7}.
Significance. If the modeling holds, the results provide useful forecasts for Euclid's ability to test f(R) gravity with combined probes, extending prior ΛCDM forecasts. The work is strengthened by its use of multiple observables and reporting across several fiducials, but the lack of quantified validation for the approximations limits immediate applicability.
major comments (2)
- [Abstract; spectroscopic probe section] Abstract and spectroscopic probe modeling: the 1% combined constraint on log f_R0 (and >3σ distinction from ΛCDM) rests on the phenomenological scale-dependent growth model for BAO and RSD terms; no direct residuals or accuracy tests against exact linear MG solvers (e.g., MGCLASS) or N-body results are shown at the relevant k and z, so any few-percent systematic bias would directly shift the reported error on f_R0 = 5×10^{-6}.
- [Photometric observables modeling] Photometric probes section: the fitting formula for the non-linear matter power spectrum modifications is used to derive the 1.4% constraint from photometry alone, but without reported comparisons to full f(R) simulations the systematic accuracy at the precision needed for the forecast remains unquantified and load-bearing.
minor comments (2)
- [Abstract and results tables] Clarify whether the optimistic setting assumptions (e.g., no systematics beyond the model) are applied uniformly across all three fiducial values when reporting the >3σ distinctions.
- [Abstract] Ensure consistent notation for log f_R0 versus f_R0 errors when translating the 1% constraint to the absolute error of 6×10^{-7}.
Simulated Author's Rebuttal
We are grateful to the referee for the detailed comments, which help improve the presentation of our forecasting results for Euclid in f(R) models. Below we provide point-by-point responses to the major comments.
read point-by-point responses
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Referee: [Abstract; spectroscopic probe section] Abstract and spectroscopic probe modeling: the 1% combined constraint on log f_R0 (and >3σ distinction from ΛCDM) rests on the phenomenological scale-dependent growth model for BAO and RSD terms; no direct residuals or accuracy tests against exact linear MG solvers (e.g., MGCLASS) or N-body results are shown at the relevant k and z, so any few-percent systematic bias would directly shift the reported error on f_R0 = 5×10^{-6}.
Authors: The phenomenological model for the scale-dependent growth is introduced in the spectroscopic probe section and is based on prior work. We did not include new validation tests in this manuscript. We will revise the text to include a discussion of the model's accuracy as reported in the literature and add a note on potential systematic uncertainties in the forecasted constraints. This will be a partial revision. revision: partial
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Referee: [Photometric observables modeling] Photometric probes section: the fitting formula for the non-linear matter power spectrum modifications is used to derive the 1.4% constraint from photometry alone, but without reported comparisons to full f(R) simulations the systematic accuracy at the precision needed for the forecast remains unquantified and load-bearing.
Authors: We note that the fitting formula is from a cited reference where it was tested against simulations. To address the referee's point, we will add text in the photometric section referencing the validation performed in the original paper and discussing the implications for our forecasts. This constitutes a partial revision to the manuscript. revision: partial
Circularity Check
No circularity: forecasts rely on external models and fiducials
full rationale
The paper presents forecasted constraints on f_R0 using a phenomenological model for scale-dependent growth (spectroscopic) and a fitting formula for the nonlinear power spectrum (photometric). These are described as extensions of prior published approaches applied to external fiducial cosmologies; the reported 1% precision on log f_R0 is a simulated forecast, not a quantity that reduces by the paper's own equations to a fit performed on the same data. No self-definitional loop, fitted-input-as-prediction, or load-bearing self-citation chain is present in the derivation chain. The central result remains independent of the paper's own outputs.
Axiom & Free-Parameter Ledger
axioms (2)
- domain assumption The Hu-Sawicki f(R) model can be adequately described by the chosen phenomenological growth rate and fitting formula for the non-linear power spectrum across the relevant scales and redshifts.
- domain assumption Optimistic survey specifications and systematic control levels assumed in prior Euclid forecasts remain valid when extended to f(R).
Forward citations
Cited by 4 Pith papers
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Fourth-order galaxy-galaxy-lensing: Theoretical framework and direct estimation
The authors derive the fourth-order galaxy-galaxy lensing 4PCF and aperture statistics, implement a numerical pipeline and FFT estimator, and detect the connected ⟨N³ M_ap⟩ signal at SNR ~9 in stage IV mock data over ...
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Euclid preparation. CosmoPostProcess: A simulation calibrated framework for weak lensing selection bias in richness-selected galaxy clusters
CosmoPostProcess delivers simulation-calibrated radial corrections for projection-induced selection bias (20-40% amplitude near 1 h^{-1} Mpc) and baryonic effects in Euclid richness-selected cluster weak lensing profiles.
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Euclid preparation. XCVI. Cosmology Likelihood for Observables in Euclid (CLOE). 3. Inference and Forecasts
CLOE pipeline produces forecasts showing Euclid can reach FoM >400 for dark energy w0 and wa by combining primary probes on synthetic data.
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Euclid preparation. XCVIII. Cosmology Likelihood for Observables in Euclid (CLOE). 5: Extensions beyond the standard modelling of theoretical probes and systematic effects
CLOE has been extended to model magnification bias, massive neutrinos, and modified gravity for Euclid probes and validated via posterior sampling on synthetic data.
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