Cosmological aspects of anisotropic chameleonic Brans-Dicke gravity

We study the cosmological implications of non-minimal coupling of a scalar field with matter sector in the Brans-Dicke gravity. In particular, in the context of locally rotationally symmetric Bianchi-I (LRS BI) metric, we derived the field equations and used these equations to find a relation between scale factor and scalar field. We use this relation to find two different solutions, namely an eternally accelerating universe and a transit universe. By the power-law solutions for scalar field and coupling function, we find the allowed range of exponents for an accelerating universe. We further explore the direction and magnitude of energy transfer between scalar field and matter sector. We show by using the second law of thermodynamics that the direction and magnitude of energy transfer are closely related to the behavior of coupling function. In the transit universe, we investigate the dependence of the effective equation of state parameter and the effective energy density on the anisotropy parameter. The model explains the late-time accelerating universe evolution.