Scalar-tensor gravity from thermodynamic and fluid-gravity perspective

Out of several possible extensions of general relativity, the scalar-tensor theory is the most popular for several reasons. Since the quantum description of gravity is yet to be formulated properly, the understanding of a gravitational theory remains incomplete until the study of thermodynamic and fluid-gravity aspects, which provides an alternative viewpoint to understand the gravitational theory. In this review, we study these features (thermodynamics and the fluid gravity analogy) in a rigorous and yet in a concise manner for the scalar-tensor gravity, which has been revealed in our recent works. In addition, the issue of conformally connected frames (\textit{i.e.} whether the two frames, which are conformally related are physically equivalent) has been explored in an explicit manner at the action level as well as from the viewpoint of thermodynamics and fluid-gravity correspondence.