A Non-Singular Cosmic Bounce in $\mathcal{F}(Q)$ Gravity: A Reconstruction and Phase Space Analysis

Abstract

The key focus of this research work is the analysis of a non-singular cosmic bounce in the context of $\mathcal{F}(Q)$ gravity, with $Q$ representing the non-metricity scalar. We consider the gravitational Lagrangian $\mathcal{F}(Q)=Q+ψQ^n$ in the presence of a modified Chaplygin-type matter source with a flat Friedmann-Robertson-Walker spacetime and a perfect matter distribution. In order to proceed, we adopt two approaches: a reconstruction approach using scale-factor ansatz and analysis of a two-dimensional autonomous dynamical system. Our results imply that the geometry coupling parameter $ψ$ plays an important role and causes geometrical repulsion for violating the null energy condition. A numerical scan of the $(ρ_0,ψ)$ parameter space suggests that there is a critical energy density for the bounce to take place, below which the universe evolves towards the standard singular cosmological solution. Moreover, the effective equation of state slowly evolves towards the de Sitter value ($ω_{eff}\rightarrow -1$) and the squared sound speed is bounded by the stability and causality condition ($0\leq C_s^2\leq1$). It is found that $\mathcal{F}(Q)$ gravity provides a coherent geometric picture of the non-singular bouncing universe in accordance with the cosmic accelerated expansion.