A ready-to-fit inhomogeneous cosmological model: the axially symmetric Szekeres spacetime

TL;DR

This paper introduces an axially symmetric Szekeres spacetime model to better fit small-scale cosmological data, addressing tensions in the standard $ ext{Lambda}$CDM model by parameterizing metric functions with Chebyshev polynomials.

Contribution

The work presents a novel inhomogeneous cosmological model based on the Szekeres solution, with a practical parameter estimation approach using Chebyshev polynomial expansions.

Findings

Model reduces functional inference to parameter estimation.

Eight parameters are sufficient for fitting data between observer and homogeneity transition.

Framework sets the stage for future data fitting and model testing.

Abstract

The purpose of the present work is based on two main observations: the tensions encountered by the standard $\Lambda$CDM model when confronted to precision small scale cosmological data and the finding that the matter distribution and the expansion of the Universe are axially symmetric roughly in the direction of the CMB dipole. Therefore, we propose, as a model for the inhomogeneous local universe, an axially symmetric Szekeres solution. After describing its main properties, we are left with three metric functions to be fitted to data between the observer and the transition to homogeneity which is an intrinsic feature of Szekeres spacetimes. So as to turn a difficult functional inference problem into a classical parameter estimation problem, we propose to use Chebyshev polynomial expansions, which, as a first step, we truncate after the second order terms. We are thus left with eight constant parameters: six for the metric functions, plus the observer's radial location and the cosmological constant. Here are the proper ingredients needed to implement the data fitting to the model in the future.