First-order Cosmological Perturbations Engendered by Point-like Masses

TL;DR

This paper derives first-order scalar and vector cosmological perturbations caused by point-like masses within the standard model, valid across all scales, revealing Yukawa potential behavior and discussing implications for cosmic homogeneity.

Contribution

It provides a comprehensive derivation of metric perturbations from point-like sources without extra approximations, valid at all scales, and links the Yukawa interaction range to the homogeneity scale.

Findings

Perturbations are valid at all scales, including super-horizon.

Scalar perturbations include a Yukawa potential with a finite interaction range.

First-order backreaction effects are absent as average metric corrections are zero.

Abstract

In the framework of the concordance cosmological model the first-order scalar and vector perturbations of the homogeneous background are derived in the weak gravitational field limit without any supplementary approximations. The sources of these perturbations (inhomogeneities) are presented in the discrete form of a system of separate point-like gravitating masses. The found expressions for the metric corrections are valid at all (sub-horizon and super-horizon) scales and converge at all points except at locations of the sources. The average values of these metric corrections are zero (thus, first-order backreaction effects are absent). Both the Minkowski background limit and the Newtonian cosmological approximation are reached under certain well-defined conditions. An important feature of the velocity-independent part of the scalar perturbation is revealed: up to an additive constant this part represents a sum of Yukawa potentials produced by inhomogeneities with the same finite time-dependent Yukawa interaction range. The suggested connection between this range and the homogeneity scale is briefly discussed along with other possible physical implications.