Cosmologically designed modified gravity theories

Abstract

Versions of parameterized pseudo-Newtonian gravity theories specially designed for cosmology have been introduced in recent cosmology literature. The modifications often consider the zero-pressure fluid in the context of versions of modified Poisson-like equation with two different gravitational potentials or an effective gravitational constant. We consider such modifications available in the context of relativistic gravity theories where the action is a general algebraic function of the scalar curvature, the scalar field, and the kinetic term of the field. We show that in general it is not possible to isolate the fluid component even in Einstein's gravity. Only in the small-scale (far inside the horizon) limit, to the linear order, and assuming the quasistatic approximation, we can realize some special forms of the attempted modifications with limited validity. Theoretically motivated relativistic generalized gravity theories we are considering have much richer cosmological aspects than simply captured by some pseudo-Newtonian modifications. We show that even Einstein's gravity with a minimally coupled scalar field as a dynamical dark energy demands similar modification in Poisson's equation and the baryon density perturbation equation.