Inhomogeneous model with a space dependent Cosmological Constant

TL;DR

This paper explores an inhomogeneous cosmological model with a space-dependent cosmological constant, analyzing its perturbative solutions, cosmographic parameters, and redshift drift to understand local and global universe dynamics.

Contribution

It introduces a spherically symmetric inhomogeneous model with spatially varying dark energy and dark matter components, deriving perturbative solutions and cosmological observables.

Findings

Derived perturbative solutions around the center and homogeneous universe regimes.

Computed cosmographic parameters and redshift profiles for the model.

Analyzed redshift drift behavior in a Lemaître metric context.

Abstract

We analyse an inhomogeneous cosmological model featuring a spherically symmetric bubble solution induced by a unified single perfect fluid, comprising spatially dependent Dark Energy (with $w=-1$) and Dark Matter (with $w=0$) components. We impose an Hubble profile that matches the Planck value at early times ($H_0=67.4\pm0.5$ Km/s\,Mpc) and the local value (${\cal H}_0=73.52\pm 1.62$ Km/s\,Mpc). We explicitly derive perturbative solutions in two distinct regimes: one expanded around the center (for small $r\,{\cal H}_0\ll1$) and the other expanded around a homogeneous FRW universe. In both cases, we compute the cosmographic parameters, redshift profiles for the Hubbles expansion rates, and effective equations of state. Furthermore, we investigate the redshift drift behaviour extended to a Lema$\hat{\rm i}$tre metric.