Cycles of Time in Classical Cosmology

TL;DR

This paper derives exact solutions to the Friedmann equation in classical cosmology using special functions, showing that integrating for simple equations of state reduces to solving Abel integrals for algebraic functions.

Contribution

It provides a comprehensive method to solve the Friedmann equation exactly with Weierstrass and Jacobi functions, generalizing previous approaches.

Findings

Exact solutions expressed in Weierstrass and Jacobi functions.

Reduction of Friedmann equation integration to Abel integrals for algebraic functions.

General framework applicable to various matter sources in cosmology.

Abstract

We present exact solutions to the Friedmann equation in standard cosmology in Weierstrass and Jacobi functions. The right hand side of the Friedmann equation describing various contributions of matter sources is considered in generic form. It is proved that the problem of integration of the Friedmann equation for simple EoS of medium is reduced to solving Abel integrals for algebraic functions.