The Metric of the Cosmos from Luminosity and Age Data

TL;DR

This paper develops an algorithm to fit Lemaitre-Tolman models to cosmological data, addressing data handling challenges and uncertainty estimation, demonstrating the method's potential despite current data limitations.

Contribution

It introduces a new algorithm for fitting LT models to luminosity and age data, with methods to handle data inconsistencies and estimate uncertainties.

Findings

The method can fit LT models to current data with or without a cosmological constant.

Corrections for maximum diameter distance regions improve model consistency.

Current data quality limits confidence in the results.

Abstract

This paper presents the algorithm for determining the Lemaitre-Tolman (LT) model that best fits given datasets for maximum stellar ages, and SNIa luminosities, both as functions of redshift. It then applies it to current cosmological data. Special attention must be given to the handling of the origin, and the region of the maximum diameter distances. As with a previous combination of datasets (galaxy number counts and luminosity distances versus redshift), there are relationships that must hold at the region of the maximum diameter distance, which are unlikely to be obeyed exactly by real data. We show how to make corrections that enable a self-consistent solution to be found. We address the questions of the best way to approximate discrete data with smooth functions, and how to estimate the uncertainties of the output - the 3 free functions that determine a specific LT metric. While current data does not permit any confidence in our results, we show that the method works well, and reasonable LT models do fit with or without a cosmological constant.