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

2009/08/18 by Jennie D’Ambroise, Jennie D'Ambroise, D'Ambroise, Jennie
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph) #Relativity and Gravitational Theory #gr-qc #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.0908.2481

from lectures of MSRI summer graduate workshop: A Window into Zeta and Modular Physics, June 16, 2008 to June 27, 2008

arxiv created 2009/08/18 · openalex publication_date 2009/08/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• A non-linear Schrodinger type formulation of FLRW scalar field cosmology
• The Elliptic Solutions to the Friedmann equation and the Verlinde's Maps

Related

• Parametric Solution Of Certain Nonlinear Differential Equations In Cosmology II
• Cycles of Time in Classical Cosmology
• The Elliptic Solutions to the Friedmann equation and the Verlinde's Maps
• On the astrodynamics applications of Weierstrass elliptic and related functions
• Solutions of Schlesinger system and Ernst equation in terms of theta-functions