McVittie-Plummer Spacetime: Plummer Sphere Immersed in the FLRW Universe

TL;DR

This paper investigates the McVittie-Plummer spacetime, modeling a star system within an expanding universe, and finds a weak, decreasing gravitational coupling between the local system and the cosmological background.

Contribution

It introduces the McVittie-Plummer model and analyzes the weak, scale-factor-dependent coupling between local inhomogeneities and the expanding universe.

Findings

Weak time-dependent coupling between local system and background

Coupling term decreases as universe expands

Misner-Sharp mass-energy function used for analysis

Abstract

The McVittie-Plummer spacetime is a spherically symmetric inhomogeneous cosmological model that represents a spherical star system embedded in a standard FLRW cosmological model. We study the main physical properties of this gravitational field. Regarding the interplay between the physics of the local system and the expanding background, we employ the Misner-Sharp mass-energy function to show that there is a relatively weak time-dependent general relativistic coupling between the astrophysical system and the background FLRW cosmological model. The coupling term is proportional to the inverse of the scale factor and decreases as the universe expands.