Self-similar Cosmological Solutions in Symmetric Teleparallel theory: Friedmann-Lema\^itre-Robertson-Walker spacetimes

TL;DR

This paper investigates self-similar solutions in symmetric teleparallel $f(Q)$-theory for FLRW cosmologies, reconstructing the functional form of $f(Q)$ and analyzing their relation to general relativity's asymptotic behavior.

Contribution

It introduces the reconstruction of $f(Q)$ functions for self-similar FLRW solutions in symmetric teleparallel gravity, extending understanding of cosmological models in this framework.

Findings

Reconstructed $f(Q)$ functions for four connection families.

Analyzed the asymptotic behavior of $f(Q)$ solutions.

Established connections with classical GR solutions.

Abstract

The existence of self-similar solutions is discussed in symmetric teleparallel $f(Q)$-theory for a Friedmann-Lema\^itre-Robertson-Walker background geometry with zero and non-zero spatial curvature. For the four distinct families of connections which describe the specific cosmology in symmetric teleparallel gravity, the functional form of $f(Q)$ is reconstructed. Finally, to see if the analogy with General Relativity holds, we discuss the relation of the self-similar solutions with the asymptotic behaviour of more general $f(Q)$ functions.