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

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 $z_t\approx 0.7$. 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 $j_0\approx 0.78$ 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, $t_0=13.64Gyrs$. 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.

12 pages, 10 figures

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