Exploring cosmological effects of a constant jerk parameter in FLRW universe within \(f(T)\) gravity

Abstract

In this paper, we investigate the evolution of the FLRW universe by analyzing the constant jerk parameter \(j\) within the framework of \(f(T)\) gravity. Using a model-independent parametrization approach, we assume \(j\) as constant and derive an expression for the Hubble parameter as

$$\begin{aligned} H(z)=H_{0}\left [\xi _{1}\left (z+1\right )^{\frac{3+\sqrt{8j+1}}{2}}+ \left (1{-\xi }_{1}\right )\left (z+1\right )^{\frac{3-\sqrt{8j+1}}{2}} \right ]^{\frac{1}{2}} \end{aligned}$$

We estimate model parameters via a Chi-square test coupled with Markov Chain Monte Carlo (MCMC) simulations, based on 52 Observational Hubble Data (OHD) points and 1701 Pantheon+SHOES data points. This method yields the best fit values: \(\xi _{1}={0.39}_{-0.08}^{+0.12}\), \(j={0.67}_{-0.19}^{+0.19}\), \(H_{0}={66.08}_{-2.78}^{+2.83} \; km/s/Mpc\) for OHD dataset and \(\xi _{1}={0.37}_{-0.03}^{+0.03}\), \(j={0.67}_{-0.38}^{+0.40}\), \(H_{0}={72.80}_{-0.29}^{+0.31}\) \(km/s/Mpc\) for Pantheon+SHOES dataset. The value of \(H_{0}\) obtained in our analysis closely resembles the value estimated by the Planck Collaboration in 2018, \(H_{0}=67.4\pm 0.5\; km/s/Mpc\). Our analysis of the deceleration parameter \(q\) reveals a transition from an early decelerating phase to a present accelerating expansion, with \(q_{0}\approx -0.3887\) \((OHD)\) and \(q_{0}\approx -0.4139\) \((Pantheon+SHOES)\). Additionally, we examine dynamic parameter such as energy density, pressure, and equation of state parameter within the model \(f\left (T\right )=T+\eta T^{\beta }\), where \(\eta \) and \(\beta \) are an arbitrary real constant. The equation of state parameter \(\omega \) in our model demonstrates a smooth transition from the radiation-dominated era to the matter-dominated era and finally to the dark energy era. The present-day values of \(\omega _{0} \approx -0.6196\) \((OHD)\) and \(\omega _{0} \approx -0.6548\) \((Pantheon+SHOES)\) suggests that the universe is currently in a quintessence phase, where dark energy behaves as a dynamical component rather than a cosmological constant \(\omega = -1\). This behavior indicates that our model is physically acceptable and aligns with the general features of cosmic evolution. Notably, the strong energy condition (SEC) is violated at present \(\left (z =0\right )\) and is projected to remain violated in the future \(\left (z < 0\right )\), driving the observed accelerated expansion of the universe. Also, this study offers insights into the impact of a constant jerk parameter on cosmic evolution and expansion dynamics within the framework of modified gravity, with a specific focus on the \(f\left (T\right )\) gravity model.