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

Understand

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.