Theoretical study of interaction between matter and curvature fluid in the theory of f(R)-gravity: Diffusion and friction

Abstract

The relativistic diffusion process and friction have been studied, especially in the framework of [Formula: see text]-gravity theory. The study of relativistic diffusion and friction processes based on [Formula: see text]-gravity is an alternative solution to solve the incompatibility problem emerging in the attempt to couple between the Fokker–Planck equation [FPE] to the Einstein field equation [EFE] encountered by Calogero. The energy–momentum tensor of the cosmological scalar field as proposed by Calogero is replaced by the presence of additional terms in the field equation of [Formula: see text]-gravity. The additional energy–momentum tensor in the field equation of [Formula: see text]-gravity in this context is regarded to compensate for the presence of the diffusion and another process like friction. The additional energy–momentum tensor is also regarded as due to the so-called curvature fluid or background fluid. Here we assume the presence of interaction between matter and the background fluid in the form of physical processes like diffusion, friction, etc. We also assume that there is ‘interplay’ between diffusion process and friction. In other words, the diffusion process and friction are not independent. As examples, we consider some viable models of [Formula: see text] that satisfy both cosmological and local gravity constraints, i.e. [Formula: see text], and [Formula: see text]. Furthermore, we apply it to explain the diffusion and friction processes in the expanding universe by considering the Friedmann–Lemaitre–Robertson–Walker (FLRW) model.