Decoupling perturbations from background in $f(Q)$ gravity: the square-root correction and the alleviation of the $σ_8$ tension
Authors
Chunyu Li
Xin Ren
Yuhang Yang
Emmanuel N. Saridakis
Yi-Fu Cai
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.
