Constraining Parameters for the Accelerating Universe in f(R,Lₘ) Gravity

In the paper, we present an accelerating cosmological model in f(R,Lₘ) gravity with the parameter constrained through the cosmological data sets. At the beginning, we have employed a functional form of f(R,Lₘ) =R/2+α R²+Lₘ^β, where α and β are model parameters. This model is well motivated from the Starobinsky model in $f(R)$ gravity and the power law form of f(Lₘ). 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 q₀≈-0.63 with the transition at zₜ≈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 j₀≈0.78 and s₀≈ 0.1 respectively. The state finder diagnostic test gives the quintessence behaviour at present and converging to ΛCDM 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, t₀ = 13.64~~Gyrs. The equation of state parameter also shows the quintessence behaviour. Based on the present analysis, it indicates that the f(R,Lₘ) gravitational theory may be another alternative to study the dark energy models.