Constraining Parameters for the Accelerating Universe in $f(R,\mathcal{L}_{m})$ Gravity

TL;DR

This paper develops a cosmological model within $f(R, ext{L}_m)$ gravity, constrains its parameters using observational data, and finds it exhibits late-time acceleration consistent with dark energy characteristics.

Contribution

It introduces a specific $f(R, ext{L}_m)$ gravity model inspired by Starobinsky and power law forms, and constrains its parameters with observational data to explain cosmic acceleration.

Findings

Model shows early deceleration and late-time acceleration.

Current deceleration parameter $q_0 \\approx -0.63$.

Model favors quintessence behavior and converges to \\Lambda CDM.

Abstract

In the paper, we present an accelerating cosmological model in $f(R,\mathcal{L}_{m})$ gravity with the parameter constrained through the cosmological data sets. At the beginning, we have employed a functional form of $f(R,\mathcal{L}_{m}) =\frac{R}{2}+\alpha R^2+\mathcal{L}_{m}^\beta$, where $\alpha$ and $\beta$ are model parameters. This model is well motivated from the Starobinsky model in $f(R)$ gravity and the power law form of $f(\mathcal{L}_{m})$. The Hubble parameter has been derived with some algebraic manipulation and constrained by Hubble data and Pantheon$^{+}$ data. With the constraint parameters, present value of deceleration parameter has been obtained to as $q_{0}\approx-0.63$ with the transition at $z_{t}\approx0.7$. It shows the early deceleration and late time acceleration behaviour. The present value of other geometric parameters such as the jerk and snap parameter are obtained to be $j_{0}\approx0.78$ and $s_{0}\approx 0.1$ respectively. The state finder diagnostic test gives the quintessence behaviour at present and converging to $\Lambda$CDM at late times. Moreover the $Om(z)$ diagnostics gives negative slope which shows that the model favours the state finder diagnostic result. Also the current age of Universe has been obtained as, $t_{0} = 13.64~~Gyrs$. The equation of state parameter also shows the quintessence behaviour. Based on the present analysis, it indicates that the $f(R,\mathcal{L}_{m})$ gravitational theory may be another alternative to study the dark energy models.