Constrained transit cosmological models in f(R,L_(m),T)-gravity

In the present paper, we investigate constrained transit cosmological models in the most recent proposed modified gravity theory, $f(R,L_{m},T)$-gravity. We obtain the modified field equations for a flat homogeneous and isotropic Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) spacetime metric. We constrain the equation of continuity by imposing the equation of state for the perfect fluid source $p=-\frac{1}{3}\rho+p_{0}$ so that we get energy conservation equation as $\dot{\rho}+3H(\rho+p)=0$, (because generally, energy conservation law is not satisfied in $f(R,L_{m},T)$-gravity). Using this constraint, we establish a relation between the energy density parameters $\Omega_{m0}$, $\Omega_{r0}$, and $\Omega_{f0}$ and the Hubble function. After that, we made observational constraints on $H(z)$ to obtain the best-fit present values of $\Omega_{m0}$, $\Omega_{r0}$, and $H_{0}$. Then, we use these best-fit values of energy parameters to investigate cosmological parameters such as the deceleration parameter, the effective equation of state $\omega_{eff}$, and the energy density parameters $\Omega_{m}$, $\Omega_{r}$, and $\Omega_{f}$ to learn more about the components and history of the expanding universe. We found an effective EoS parameter in the range $-1\le \omega_{eff}\le\frac{1}{3}$ with a deceleration-acceleration transition redshift value of $z_{t}=0.6377, 0.6424$ along two datasets cosmic chronometer (CC) and Pantheon SNIa, respectively.