When can we compute analytically lookback time, age of the universe, and luminosity distance?

TL;DR

This paper classifies conditions under which key cosmological quantities like lookback time, universe age, and luminosity distance can be computed analytically in FLRW cosmology, using the Chebyshev theorem.

Contribution

It introduces a classification framework based on the Chebyshev theorem to identify when these cosmological integrals are expressible with elementary functions.

Findings

Identifies specific conditions for analytical solutions in cosmology

Provides examples illustrating the classification

Enhances understanding of when closed-form expressions are possible

Abstract

In Friedmann-Lema\^itre-Robertson-Walker cosmology, it is sometimes possible to compute analytically lookback time, age of the universe, and luminosity distance versus redshift, expressing them in terms of a finite number of elementary functions. We classify these situations using the Chebyshev theorem of integration and providing examples.