Exact solutions of Friedmann equation for supernovae data

TL;DR

This paper derives exact analytical solutions to the Friedmann equation for supernovae data within standard and conformal cosmology models, showing both fit the data well with conformal cosmology offering simpler physical interpretation.

Contribution

It presents new exact solutions of the Friedmann equation in both models and demonstrates their fit to supernovae data using analytical functions, notably Weierstrass functions.

Findings

Both models fit the supernovae Hubble diagram equally well.

Conformal cosmology offers a simpler physical interpretation.

Exact analytical solutions are expressed in terms of Weierstrass functions.

Abstract

An intrinsic time of homogeneous models is global. The Friedmann equation by its sense ties time intervals. Exact solutions of the Friedmann equation in Standard cosmology and Conformal cosmology are presented. Theoretical curves interpolated the Hubble diagram on latest supernovae are expressed in analytical form. The class of functions in which the concordance model is described is Weierstrass meromorphic functions. The Standard cosmological model and Conformal one fit the modern Hubble diagram equivalently. However, the physical interpretation of the modern data from concepts of the Conformal cosmology is simpler, so is preferable.