Decoupling perturbations from background in $f(Q)$ gravity: the square-root correction and the alleviation of the $σ_8$ tension

TL;DR

This work analyzes a perturbation-level modification of symmetric teleparallel gravity, f(Q)=F(Q)+M√Q, which leaves the background expansion H(z) unchanged while altering the growth of structure through an effective gravitational coupling G_eff = G_N/f_Q. By fitting to redshift-space distortion data including DESI DR1 Full-Shape, the authors explore three backgrounds (Model A: ΛCDM-like, Model B: H0-tension–alleviating, Model C: Quintom dark energy) and constrain both M and σ8. A key finding is that a positive M suppresses growth, enabling σ8 to align with Planck in Model B (and, to a lesser extent, in Model A), with Model C showing no strong need for M. However, a residual degeneracy between M and σ8 remains, indicating that breaking it will require multi-probe analyses (lensing, full-shape clustering, CMB lensing) in future surveys. Overall, the square-root correction provides a theoretically economical way to mitigate the S8 tension across backgrounds, particularly when the background already addresses the H0 tension, and highlights the necessity of combined probes to decisively test the modification’s physical relevance.

Abstract

We investigate a perturbation-level modification of symmetric teleparallel gravity of the form $f(Q)=F(Q)+M\sqrt{Q}$ and assess its ability to ease the $σ_8$ tension. The square-root term leaves the background expansion unchanged while modifying the effective gravitational coupling, providing a pure decoupling between background cosmology and structure-growth evolution. Using the latest redshift-space distortion data, including DESI DR1 Full-Shape measurements, we constrain $M$ and $σ_8$ across three representative backgrounds: $Λ$CDM, an $H_0$-tension-reducing model, and a DESI-motivated dynamical dark energy scenario. In all cases, the square-root correction suppresses growth and can reconcile $σ_8$ with Planck at the $1σ$ level, with the strongest improvement occurring in the $H_0$-tension-oriented background. A residual degeneracy between $M$ and $σ_8$ remains, indicating that future multi-probe analyses combining lensing and full-shape clustering will be required to determine whether the $\sqrt{Q}$ term represents a genuine signal of modified gravity.

Figures (1)

• Figure 1: Upper panel: Constrains for $\sigma_8$ values when $M=0$; Lower panel: Marginalised constraints for $\sigma_8$ and $M$ values at 68% and 95% C.L. The gray dashed line represents the value $\sigma_8=0.81$, which aligns with the Planck 2018 results.