Correction to Lagrangian for Bouncing Cosmologies in $f(Q)$ Gravity

TL;DR

This paper explores bouncing cosmologies within symmetric teleparallel gravity, reconstructing Lagrangians for various bounce models and analyzing their implications for dark energy and deviations from general relativity.

Contribution

It introduces reconstructed Lagrangians for multiple bouncing cosmologies in $f(Q)$ gravity, highlighting additional terms that modify general relativity to support bounce scenarios.

Findings

Reconstructed Lagrangians for different bounce models.

Additional terms modify GR to enable bouncing cosmologies.

Dark energy profiles analyzed in reconstructed models.

Abstract

Symmetric teleparallel gravity offers to reformulate the gravitational formalism without the presence of curvature and torsion with the help of non-metricity tensors. Interestingly, Symmetric teleparallel gravity can be formulated equivalently to teleparallel gravity or general relativity for an appropriate setup. In this study, our aim lies in exploring the bouncing cosmologies as an alternative to the initial singularity of the Universe in the background of modified symmetric teleparallel gravity. To explore this, we adopt the reconstruction technique to present the possible reconstructed Lagrangian for various cosmological bouncing solutions in a flat Friedmann-Lema\^itre-Robertson-Walker spacetime with a perfect fluid matter distribution. We study the reconstructed gravitational Lagrangians, which are capable of reproducing analytical solutions for \textit{symmetric bounce}, \textit{super-bounce}, \textit{oscillatory bounce}, \textit{matter bounce}, and \textit{exponential bouncing} model settings. Further, we examine the dark energy profiles of the models using reconstructed Lagrangians. In addition, we found that an additional term arises in each reconstructed Lagrangian compared to general relativity (GR). That extra term corrected the background GR to present bouncing cosmology in modified gravity. These newly motivated cosmological models may have an effect on gravitational phenomena at other cosmological scales.