Decoupling perturbations from background in $f(Q)$ gravity: the square-root correction and the alleviation of the $\sigma_8$ tension

TL;DR

This paper explores a modification to symmetric teleparallel gravity with a square-root term that leaves background expansion unchanged but suppresses structure growth, helping to resolve the $\sigma_8$ tension in cosmology.

Contribution

It introduces a novel $f(Q)$ gravity model with a square-root correction that decouples background evolution from structure growth, providing a new approach to address the $\sigma_8$ tension.

Findings

The square-root term suppresses structure growth, aligning $\sigma_8$ with Planck data.

The model fits observational data well across different background scenarios.

A degeneracy between the correction parameter and $\sigma_8$ suggests need for multi-probe analysis.

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 $\sigma_8$ 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 $\sigma_8$ across three representative backgrounds: $\Lambda$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 $\sigma_8$ with Planck at the $1\sigma$ level, with the strongest improvement occurring in the $H_0$-tension-oriented background. A residual degeneracy between $M$ and $\sigma_8$ 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.