Role of modified Chaplygin gas in Little Rip phenomena from interaction between dark energy and dark matter

In this article, an interacting dark energy (DE)- dark matter (DM) scenario has been considered in a flat Friedmann–Lemaitre–Robertson–Walker (FLRW) cosmological model, where DE has a variable equation-of-state that follows the modified Chaplygin-like equation of state (Eq. (1)) characterized by two time dependent parameters $\Lambda \left(t\right)$ and $\omega \left(t\right)$ and DM has a non-zero equation of state $p_{DM}=\tilde{\omega }{\rho }_{DM}$. Gravitational equations of motion for dark matter have been solved for two different cases of thermodynamic parameter $\tilde{\omega }$ as $\tilde{\omega }=constant$ and $\tilde{\omega }\ne$ constant. Also, it has been found that $\Lambda \left(t\right)\to -\infty$ as $t\to \infty$, it shows that the fate of our universe depends on specific model parameters for the coupled dark energy and dark matter, and experiences Little Rip behavior. Also, it is observed that coupled dark energy and dark matter may inflate and expand the universe after the Big Bang in the far future.