Decoupling perturbations from background in $f(Q)$ gravity: the square-root correction and the impact on the $sigma_8$ tension
Chunyu Li, Xin Ren, Yuhang Yang, Emmanuel N. Saridakis, Yi-Fu Cai
arXiv:2512.16551v3 Announce Type: replace
Abstract: We investigate a perturbation-level modification of symmetric teleparallel gravity of the form $f(Q)=F(Q)+Msqrt{Q}$ and assess its potential to ease the $sigma_8$ tension. The square-root term leaves the background expansion unchanged at the level of FLRW cosmology, while modifying the effective gravitational coupling and thereby providing a decoupling between background evolution and structure-growth. Using the latest redshift-space distortion data, including DESI DR1 Full-Shape measurements, we constrain the model through its impact on the growth observable $fsigma_8(z)$ 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 the growth of structure and induces a degeneracy with $sigma_8$, leading to weaker constraints from current data. This allows for a wider range of $sigma_8$ values consistent with Planck, with the effect being most pronounced in the $H_0$-tension-oriented background model. However, because RSD data constrain $fsigma_8$ rather than $sigma_8$ directly, 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.arXiv:2512.16551v3 Announce Type: replace
Abstract: We investigate a perturbation-level modification of symmetric teleparallel gravity of the form $f(Q)=F(Q)+Msqrt{Q}$ and assess its potential to ease the $sigma_8$ tension. The square-root term leaves the background expansion unchanged at the level of FLRW cosmology, while modifying the effective gravitational coupling and thereby providing a decoupling between background evolution and structure-growth. Using the latest redshift-space distortion data, including DESI DR1 Full-Shape measurements, we constrain the model through its impact on the growth observable $fsigma_8(z)$ 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 the growth of structure and induces a degeneracy with $sigma_8$, leading to weaker constraints from current data. This allows for a wider range of $sigma_8$ values consistent with Planck, with the effect being most pronounced in the $H_0$-tension-oriented background model. However, because RSD data constrain $fsigma_8$ rather than $sigma_8$ directly, 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.