Revisiting solving procedure for Ermakov-Pinney equation (with applications in the field of cosmology)

TL;DR

This paper introduces a novel analytical method for solving the Ermakov-Pinney equation, with specific focus on applications in cosmology such as rotating early Universe models with vortices.

Contribution

It presents a new solving procedure for the Ermakov-Pinney equation, including solutions with symmetry reduction relevant to cosmological scenarios.

Findings

New analytical solutions for Ermakov-Pinney equation in cosmology

Solutions applicable to rotating early Universe models with vortices

Enhanced understanding of nonlinear equations in cosmological physics

Abstract

It is known that Ermakov-Pinney equation is a nonlinear equation with wide applications in dynamics, physics, cosmology (e.g., Ermakov equation can be connected to Bose-Einstein Condensate cosmology which unifies the dark energy and the dark matter). In this analytical study, we have presented a new type of solving procedure to obtain analytical solution of Ermakov-Pinney equation, specifically for the case of rotating early Universe with vortex. The particular case of solution of the aforementioned equation is presented also (such the solution of special kind is important for cosmological applications) which corresponds to the class of solutions with symmetry reduction.