Generalized McVittie geometry in Horndeski gravity with matter

TL;DR

This paper explores generalized McVittie solutions within Horndeski gravity, incorporating matter and scalar fields, revealing diverse configurations of inhomogeneities embedded in cosmological backgrounds.

Contribution

It introduces new generalized McVittie solutions in the extended cuscuton model of Horndeski gravity with matter, classifying configurations based on key physical parameters.

Findings

Classified solutions by gravitational coupling and energy flow

Included matter in the analysis of McVittie geometries

Demonstrated scalar field's role in inhomogeneity dynamics

Abstract

We investigate McVittie and generalized McVittie solutions for Horndeski gravity with a spatially homogeneous gravitational scalar field, which is stealth at small scales near the central object but, at large scales, sources the FLRW universe in which the central inhomogeneity is embedded. Unlike previous studies, we include matter and obtain generalized McVittie solutions in the extended cuscuton model. The possible configurations are classified according to the time-dependence of the gravitational coupling, the radial energy flow, the accretion rate onto the central object, and the Hubble rate.