Hypergeometric solutions to coupled Klein-Gordon equations in cosmology with small-field excursions
Abstract
The Klein-Gordon equation is a second order differential equation that appears in a variety of applications in mathematics, physics and engineering. This equation is often solved using numerical methods, since a general analytical solution is unattainable. However, one can find very useful analytical solutions for some special cases. In cosmology, the Klein-Gordon equation of a field can explain the physics of inflation and has important consequences on understanding the origin and evolution of the universe. An analytical solution to the Klein-Gordon equation in cosmology has been obtained in the small-field excursion approximation, and it turns out that the solution can be written in terms of the confluent hypergeometric limit function. In this work, we derive this result again while showing the details of the calculations and then generalize to the case of two coupled Klein-Gordon equations. We show that the solution of this coupled system can be written in terms of Kummer's hypergeometric limit function while considering minimal assumptions. We carry out a full numerical calculation of the coupled system and compare it to the results from the analytical expressions.
Related
- Infinitely many nonradial positive solutions for two-coupled nonlinear Schrödinger equations in bbrN without symmetry
- Hypergeometric Solutions for Variants of the q-Hypergeometric Equation
- Canonical differential equations for Feynman integrals from 𝒜-hypergeometric systems in the Schwinger representation
- Group averaging and the geometry of physical quantum states: from normalizable solutions to solvable loop quantum cosmology
- Diffusion stabilises time-periodic solutions in conservation laws coupled to a relaxation oscillator
BibTeX
@misc{aboubrahim2026hypergeometric,
title = {{Hypergeometric solutions to coupled Klein-Gordon equations in cosmology with small-field excursions}},
author = {Amin Aboubrahim and Anastasiia Minenkova and Tomas Yonkers},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18586},
eprint = {2610.18586},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18586},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Hypergeometric solutions to coupled Klein-Gordon equations in cosmology with small-field excursions
AU - Amin Aboubrahim
AU - Anastasiia Minenkova
AU - Tomas Yonkers
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18586
UR - https://arxiv.org/abs/2610.18586
AB - The Klein-Gordon equation is a second order differential equation that appears in a variety of applications in mathematics, physics and engineering. This equation is often solved using numerical methods, since a general analytical solution is unattainable. However, one can find very useful analytical solutions for some special cases. In cosmology, the Klein-Gordon equation of a field can explain the physics of inflation and has important consequences on understanding the origin and evolution of the universe. An analytical solution to the Klein-Gordon equation in cosmology has been obtained in the small-field excursion approximation, and it turns out that the solution can be written in terms of the confluent hypergeometric limit function. In this work, we derive this result again while showing the details of the calculations and then generalize to the case of two coupled Klein-Gordon equations. We show that the solution of this coupled system can be written in terms of Kummer's hypergeometric limit function while considering minimal assumptions. We carry out a full numerical calculation of the coupled system and compare it to the results from the analytical expressions.
ER -