Insights in $f(Q)$ cosmology: the relevance of the connection

TL;DR

This paper investigates how different affine connections in $f(Q)$ gravity influence cosmological dynamics, showing that connection choice can resolve singularities and significantly alter universe evolution.

Contribution

It demonstrates that multiple compatible connections in $f(Q)$ gravity lead to distinct cosmological behaviors, emphasizing the importance of connection selection in the theory.

Findings

Certain connections resolve cosmological singularities

Different connections produce varied cosmic evolution

Some models replace Big Bang with de Sitter phases

Abstract

We explore the role of the affine connection in $f(Q)$ gravity, a modified theory where gravity is governed by non-metricity within the symmetric teleparallel framework. Although the connection is constrained to be flat and torsionless, it is not uniquely determined by the metric, allowing for multiple physically distinct formulations. We analyze three such connections compatible with a homogeneous and isotropic universe to show that they yield markedly different cosmological dynamics, even under the same functional form of $f(Q)$. Using both analytical and numerical methods, including a Born-Infeld type model of $f(Q)$, we demonstrate that specific connections can resolve cosmological singularities like the Big Bang and Big Rip, replacing them with smooth de Sitter phases. Others retain singularities but with notable modifications in their behavior. These findings highlight the physical relevance of connection choice in $f(Q)$ gravity and its potential to address fundamental cosmological questions.