A designer approach to $f(Q)$ gravity and cosmological implications

TL;DR

This paper explores the evolution of linear perturbations in $f(Q)$ gravity, designing specific functions to match various dark energy behaviors and predicting observable signatures to distinguish it from standard cosmology.

Contribution

It introduces a method to tailor $f(Q)$ functions for specific expansion histories and analyzes their impact on structure growth and cosmological observables.

Findings

Patterns in effective gravitational coupling identified

Predictions for $ ilde{f}\sigma_8$ and cross-correlation spectra provided

Potential to distinguish $f(Q)$ gravity from standard cosmology

Abstract

We investigate the evolution of linear perturbations in the Symmetric Teleparallel Gravity, namely $f(Q)$ gravity, for which we design the $f(Q)$ function to match specific expansion histories. We consider different evolutions of the effective dark energy equation of state, $w_Q(a)$, which includes $w_Q=-1$, a constant $w_Q \neq -1$ and a fast varying equation of state. We identify clear patterns in the effective gravitational coupling, which accordingly modifies the linear growth of large scale structures. We provide theoretical predictions for the product of the growth rate $\tilde{f}$ and the root mean square of matter fluctuations $\sigma_8$, namely $\tilde{f}\sigma_8$ and for the sign of the cross-correlation power spectrum of the galaxy fluctuations and the cosmic microwave background radiation anisotropies. These properties can be used to distinguish the $f(Q)$ gravity from the standard cosmological model using accurate cosmological observations.