Study of Non-Static Plane Symmetric Universe with Exponential Scale Factor and Perfect Fluid in f(Q)-gravity

Abstract

In this study, we analyze the cosmological evolution of a non-static plane symmetric universe with an exponential scale factor, which drives the phase transition of the universe from deceleration to acceleration, within the framework of f(Q)-gravity, incorporating a perfect fluid. We assume a proportionality condition between the shear scalar \(\sigma \left( t\right) \) and the expansion scalar \(\Theta \left( t\right) \) in order to obtain a determinate cosmological solution of the field equations, leading to a specific relationship between the metric potentials, expressed as \(e^h=s^m\), where m is an arbitrary constant. In the present work, we have studied two \(f\left( Q\right) \)-gravity models: the first \(f\left( Q\right) =\alpha Q+\beta \) is a linear model with free parameters \(\alpha \) and \(\beta \) while the second \(f\left( Q\right) =\left( \alpha Q+\beta \right) e^{-\left( \alpha Q+\beta \right) }\) is a non-linear exponential form with the same free parameters influencing the cosmic behavior. We analyze the physical behavior of both models by examining key cosmological quantities, including the density, pressure, equation of state parameter, deceleration parameter, and jerk parameter. Furthermore, we also analyze the energy conditions to assess the validity of both models, ensuring that they align with the physical requirements of the cosmological framework. We discuss the non-metricity scalar and its physical interpretation. Finally, our models reveal that the universe is in a phase of expansion and acceleration, displaying characteristics similar to a quintessence dark energy model.