Szekeres models: a covariant approach

TL;DR

This paper develops a covariant formalism for Szekeres models using the 1+1+2 approach, defining an average scale length and analyzing horizons, with potential applications in observational cosmology.

Contribution

It introduces a covariant description of Szekeres models with a new average scale length and explores horizon definitions, enhancing the understanding of inhomogeneous cosmologies.

Findings

Defined a covariant average scale length satisfying a 2D equation of motion.

Identified three intrinsic Killing vector fields justifying quasi-symmetry.

Presented gauge-invariant forms for apparent horizons.

Abstract

We exploit the 1+1+2 formalism to covariantly describe the inhomogeneous and anisotropic Szekeres models. It is shown that an \emph{average scale length} can be defined \emph{covariantly} which satisfies a 2d equation of motion driven from the \emph{effective gravitational mass} (EGM) contained in the dust cloud. The contributions to the EGM are encoded to the energy density of the dust fluid and the free gravitational field $E_{ab}$. We show that the quasi-symmetric property of the Szekeres models is justified through the existence of 3 independent \emph{Intrinsic Killing Vector Fields (IKVFs)}. In addition the notions of the Apparent and Absolute Apparent Horizons are briefly discussed and we give an alternative gauge-invariant form to define them in terms of the kinematical variables of the spacelike congruences. We argue that the proposed program can be used in order to express Sachs' optical equations in a covariant form and analyze the confrontation of a spatially inhomogeneous irrotational overdense fluid model with the observational data.