An analytical solution in the complex plane for the luminosity distance in flat cosmology

TL;DR

This paper derives an analytical complex-plane solution for luminosity distance in flat cosmology, enabling precise parameter estimation and simplified supernova distance calculations.

Contribution

It introduces a novel complex analytical solution for luminosity distance in flat cosmology, facilitating parameter determination and easier supernova data analysis.

Findings

Real part effectively determines H_0 and Ω_m

Negligible imaginary component simplifies calculations

Provides a minimax approximation for supernova distance modulus

Abstract

We present an analytical solution for the luminosity distance in spatially flat cosmology with pressureless matter and the cosmological constant. The complex analytical solution is made of a real part and a negligible imaginary part. The real part of the luminosity distance allows finding the two parameters $H_0$ and $\om$. A simple expression for the distance modulus for SNs of type Ia is reported in the framework of the minimax approximation.