Exploring the stability of $f(Q)$ cosmology near general relativity limit with different connections

TL;DR

This paper investigates the stability of different symmetric teleparallel connections in $f(Q)$ gravity near the general relativity limit across various cosmological eras, revealing stability conditions and potential singularities.

Contribution

It analyzes the stability of cosmological solutions in $f(Q)$ gravity with different connections, identifying conditions for viability and issues like sudden singularities.

Findings

Standard connection set 1 is stable throughout all epochs.

Alternative connection set 2 has stable trivial limit but issues with nontrivial configurations.

Certain $f(Q)$ models can lead to sudden singularities even near GR regime.

Abstract

In this work, we study cosmological spacetime configurations in $f(Q)$ gravity with nonvanishing symmetric teleparallel connections. It is known that the spatially flat, homogeneous and isotropic connections can be classified into three sets. Focusing on two of those, we explore the stability of cosmological background evolution near the general relativity regime across radiation, matter, dark energy, and geometric dark energy dominated eras. Our results show that for the standard connection set 1 the general relativity regime can be realized in two ways and both exhibit stable behavior throughout all evolutionary epochs. Conversely, for the alternative connection set 2 the trivial general relativity limit is stable, while the nontrivial option exhibits stability during the radiation era and marginal stability during the matter era, but for the dark energy and geometric dark energy eras our results are inconclusive. Furthermore, we discuss the general conditions on the function $f(Q)$ that physically viable models should obey, and point out that for a generic $f(Q)$ the alternative connection sets 2 and 3 are prone to trigger a sudden singularity. This can happen even near the otherwise good looking general relativity regime, as we demonstrate by an explicit numerical example. Hence the alternative configurations could be problematic already on the background level.