Exploring the evolution of a non-static plane symmetric universe with cosmic strings and LVDP in f(Q) gravity

Abstract

In this study, we have investigated the non-static plane symmetric space–time with perfect fluid containing cosmic string in the frame work of $f\left(Q\right)$ gravity in which the non-metricity scalar $Q$ describes the gravitational interaction. To find exact solutions for the field equations, we assume the metric potentials relation as $e^h=s^m$, where $m\ne \frac{1}{2}$ is an arbitrary constant and the linearly varying deceleration parameter $q\left(t\right)=-kt+n-1$, where $k\ge 0$ and $n\ge 0$ are constants. We estimate the best-fit values of the model parameters using the Observational Hubble Data (OHD) comprising 31 data points of Cosmic Chronometers (CC) and the Pantheon+SHOES dataset comprising 1701 data points, employing the minimum chi-square method and the Markov Chain Monte Carlo (MCMC) technique, yielding ${n=2.08}_{-0.10}^{+0.09}$ and $H_0={74.07}_{-2.32}^{+2.30}$ for OHD, and ${n=2.80}_{-0.07}^{+0.07}$ and $H_0={74.63}_{-0.22}^{+0.21}$ for Pantheon+SHOES dataset. The evolution of the deceleration parameter indicates transition from an early decelerating phase to the current accelerating expansion phase of the universe in our model. Furthermore, the evolution of the deceleration parameter predicts a future transition into a super-acceleration phase of the universe. Moreover, to explore some key cosmological quantities such as energy density, pressure, equation of state parameter, the string tension density, we consider the quadratic form of the $f\left(Q\right)$ gravity model, specifically $f\left(Q\right)=\alpha Q^2+\beta Q+\gamma$, where $\alpha$, $\beta$, $\gamma$ represent the model parameters. The equation of state parameter $\omega$ in our model exhibits a smooth transition from the radiation-dominated era to the matter-dominated era, and eventually to the dark energy era. The present-day values of ${\omega }_0=-0.9037$ for the OHD dataset and ${\omega }_0=-0.6632$ for the Pantheon+SHOES dataset suggest that the universe is currently in a quintessence phase,where dark energy behaves as a dynamical component rather than a simple cosmological constant $\left(\omega =-1\right)$. This behavior of equation of state parameter supports the physical viability of our model and confirms that the universe is undergoing accelerated expansion. Additionally, we further evaluate the physical validity of the model by analyzing the energy conditions and assessing its stability through the squared speed of sound test.