On cosmologically designed modified gravity theories

TL;DR

This paper examines the limitations of pseudo-Newtonian modifications in cosmology within relativistic gravity theories, highlighting the potential of future gravitational lensing and velocity observations to test Einstein's gravity.

Contribution

It analyzes the feasibility of pseudo-Newtonian modifications in relativistic gravity theories and discusses how future observations could test Einstein's gravity in cosmology.

Findings

Pseudo-Newtonian modifications are limited to small-scale regimes.

Isolating zero-pressure fluid components is generally not feasible.

Future gravitational lensing and velocity data can test Einstein's gravity.

Abstract

Versions of parameterized pseudo-Newtonian gravity theories specially designed for cosmology have been introduced in recent cosmology literature. The modifications demand a zero-pressure fluid in the context of versions of modified Poisson-like equation with two different gravitational potentials. We consider such modifications 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. In general it is not possible to isolate the zero-pressure fluid component simultaneously demanding a modification in the Poisson-like equation. Only in the small-scale limit we can realize some special forms of the attempted modifications. We address some loopholes in the possibility of showing non-Einstein gravity nature based on pseudo-Newtonian modifications in the cosmological context. We point out that future observations of gravitational weak lensing together with velocity perturbation can potentially test the validity of Einstein's gravity in cosmology context.