Exploring a Universe Model by Gravitational Decoupling in a Modified Gravity

This work presents an anisotropic cosmological model constructed within the framework of Rastall gravity by applying the gravitational decoupling method to a time-dependent spherically symmetric spacetime. Utilizing the minimal deformation approach, we decouple the field equations corresponding to an extended matter distribution into two separate systems: one governing the original (seed) source and the other describing the additional source introduced through decoupling. The seed sector is solved by adopting a specific EoS that establishes a relationship between energy density and isotropic pressure, consistent with the anisotropic Bianchi-I cosmology. The equations for the additional source are then addressed under a prescribed density condition, with the decoupling parameter playing a key role. The integration of these solutions leads to an anisotropic cosmological extension. To assess the physical viability of the model, we analyze its dynamical behavior across three cosmological epochs, each defined by distinct EoS parameter values and fixed choices of Rastall and decoupling parameters. Our findings indicate that the model remains stable and physically plausible during the matter- and radiation-dominated periods but does not meet these standards in the dark energy-dominated era.