Towards the geometry of the universe from data

TL;DR

This paper introduces a new algorithm to reconstruct the universe's geometry from observational data, capable of testing inhomogeneous models and constraining the cosmological constant using luminosity and age data up to redshift 1.75.

Contribution

The paper presents a novel algorithm for reconstructing spherically symmetric dust universe metrics from data, enabling direct confrontation of inhomogeneous models with observations.

Findings

Current data are compatible with homogeneous models.

Radially inhomogeneous void models cannot yet be ruled out.

Reconstructed dark matter density and metric components up to z=1.75.

Abstract

We present a new algorithm that can reconstruct the full distributions of metric components within the class of spherically symmetric dust universes that may include a cosmological constant. The algorithm is capable of confronting this class of solutions with arbitrary data and opens a new observational window to determine the value of the cosmological constant. In this work we use luminosity and age data to constrain the geometry of the universe up to a redshift of $z = 1.75$. We show that, although current data are perfectly compatible with homogeneous models of the universe, simple radially inhomogeneous void models that are sometimes used as alternative explanations for the apparent acceleration of the late time universe cannot yet be ruled out. In doing so we reconstruct the density of cold dark matter out to $z = 1.75$ and derive constraints on the metric components when the universe was 10.5 Gyr old within a comoving volume of approximately 1 Gpc$^{3}$.