Effect of peculiar velocities of inhomogeneities on the shape of gravitational potential in spatially curved universe

TL;DR

This paper analyzes how peculiar velocities of inhomogeneities and the universe's spatial curvature influence the shape of gravitational potential, providing analytical solutions for open and closed universes with dark matter and cosmological constant.

Contribution

It presents analytical solutions for the gravitational potential in curved universes considering peculiar velocities, highlighting their impact on screening length and potential shape.

Findings

Peculiar velocities significantly alter the gravitational interaction screening length.

The shape of the gravitational potential depends on the universe's spatial curvature sign.

Analytical solutions are derived for open and closed universe models.

Abstract

We investigate the effect of peculiar velocities of inhomogeneities and the spatial curvature of the universe on the shape of the gravitational potential. To this end, we consider scalar perturbations of the FLRW metric. The gravitational potential satisfies a Helmholtz-type equation which follows from the system of linearized Einstein equations. We obtain analytical solutions of this equation in the cases of open and closed universes, filled with cold dark matter in presence of the cosmological constant. We demonstrate that, first, peculiar velocities significantly affect the screening length of the gravitational interaction and, second, the form of the gravitational potential depends on the sign of the spatial curvature.