Applications of Elliptic and Theta Functions to Friedmann-Robertson-Lemaitre-Walker Cosmology with Cosmological Constant

TL;DR

This paper explores how elliptic and theta functions are used to find exact solutions in FRLW cosmology with a cosmological constant, revealing mathematical structures in Einstein's equations.

Contribution

It explicitly demonstrates the role of Jacobi and Weierstrass elliptic functions in solving Einstein's equations in cosmology, highlighting a lesser-known application.

Findings

Elliptic functions appear naturally in FRLW solutions.

Connections between elliptic functions and theta functions are established.

Provides explicit examples of elliptic functions in cosmological models.

Abstract

Elliptic functions are known to appear in many problems, applied and theoretical. However, a lesser known application is in the study of exact solutions to Einstein's gravitational field equations in a Friedmann-Robertson-Lemaitre-Walker (FRLW) cosmology. We will show explicitly how Jacobi and Weierstrass elliptic functions arise in this context, and will additionally show connections with theta functions.