Exact Cosmological Models in Modified $$\boldsymbol{f(R,L_{m})}$$ Gravity with Observational Constraints
Dinesh Chandra Maurya
Abstract
This study is an investigation of exact cosmological models in modified $$f(R,L_{m})$$ gravity with observational constraints, where $$R$$ is the Ricci scalar, and $$L_{m}$$ is the matter Lagrangian for a perfect fluid. We have obtained the field equations using a flat FLRW metric with matter Lagrangian $$L_{m}=-p$$ and $$f(R,L_{m})=R/2+\alpha L_{m}^{n}-\beta$$ , where $$\alpha$$ , $$\beta$$ , $$n$$ are positive parameters. We have solved the field equations for the scale factor $$a(t)$$ with the equation of state (EoS) $$p=\omega\rho$$ , where $$p$$ is the isotropic pressure and $$\rho$$ is the energy density. We have obtained the scale factor $$a(t)=k_{0}[\sinh(k_{1}t+k_{2})]^{[2(n+\omega-n\omega]/[3n(1+\omega)]}$$ , where $$k_{1}=\frac{\sqrt{3\beta}}{2}\frac{n(1+\omega)}{n+\omega-n\omega}$$ , and $$k_{0}$$ , $$k_{2}$$ are integration constants. Using this scale factor, we have analyzed various cosmological parameters $$\{H_{0},q_{0},j_{0},s_{0},t_{0}\}$$ with observational constraints by applying the $$\chi^{2}$$ test with four observational datasets $$H(z)$$ , Union 2.1, JLA and Bined datasets. Also, we have analyzed the Om diagnostic parameter.