# A new analytical solution for the distance modulus in flat cosmology

## TL;DR

This paper derives a new analytical solution for the luminosity distance in flat $
m extLambda$CDM cosmology using elliptical integrals, enabling precise evaluation of key cosmological parameters.

## Contribution

It introduces a novel analytical expression for luminosity distance in flat cosmology using elliptical integrals, improving computational efficiency and accuracy.

## Key findings

- Hubble constant estimated as 69.77 km/s/Mpc
- Matter density parameter $
m extOmega_m$ is 0.295
- Cosmological constant $
m extLambda$ is approximately 1.194 x 10^{-52} m^{-2}

## Abstract

A new analytical solution for the luminosity distance in flat $\Lambda$CDM cosmology is derived in terms of elliptical integrals of first kind with real argument. The consequent derivation of the distance modulus allows evaluating the Hubble constant, $H_0=69.77\pm 0.33$, $\om= 0.295\pm0.008$ and the cosmological constant, $\Lambda= (1.194 \pm 0.017)10^{-52} \frac{1}{m^2}$.