Structure growth in <i>f</i> (<i>Q</i>) cosmology

ABSTRACT We take into account redshift space distortion measurements to investigate the growth of cosmological large-scale structures within the framework of generalized symmetric teleparallel – $f(Q)$ – gravity. After comparing the predictions of the $f(Q)$-gravity expansion history with Hubble parameter data and SNIa Pantheon + sample data sets and constraining the pertinent cosmological parameters $\Omega _{m}$ and $H_0$, together with the exponent n for $f(Q)$ power-law models, we derive the full system of equations governing linear cosmological perturbations to study matter fluctuations using the $1 + 3$ covariant formalism when applied to $f(Q)$ gravity. Thus, we resort to both the usual redshift-space distortion data $f\sigma _8$ and some recent separate measurements of the growth rate f and the amplitude of matter fluctuations $\sigma _8$ from the VIPERS (VIMOS Public Extragalactic Redshift Survey) and SDSS (Sloan Digital Sky Survey) collaborations to find the best-fitting cosmological parameters $\Omega _m$, $\sigma _{8}$, and n. We also apply a collective analysis of such growth-structure data together with the aforementioned cosmic expansion measurements to constrain these parameters through Monte Carlo Markov Chain simulations. As a result, our analysis is capable of determining the statistical significance for the best-fitting parameter values through the AIC and BIC Bayesian selection criteria.