LAUSR

In this article, we present and analyze cosmological models with an anisotropic variable parameter. We have set up the field equations with the space time in the form of Bianchi I metric with an f ( R ,  T ) gravity. The functional form for the f ( R ,  T ) gravity has been assumed to be $$f(R,T)=R+2f(T)$$ f ( R , T ) = R + 2 f ( T ) , where R and T are, respectively, the Ricci scalar and trace of the energy–momentum tensor. Two different models are constructed with respect to the scale factors, such as power law scale factor and hybrid scale factor. Moreover, the anisotropic parameter taken here in the form of hyperbolic function further gives clarity on the behavior of equation of state parameter. It is to note that when the values of the coefficient constant vanish, the model yields the isotropic universe. For both the cases, the deceleration parameter, state finder diagnostic pair and energy conditions have been obtained and analyzed which provide physical plausibility of the models.