Superfluid Rayleigh-Plesset extension of FLRW cosmology

TL;DR

This paper extends the FLRW cosmological model by incorporating superfluid Rayleigh-Plesset dynamics, deriving parametric solutions with elliptic functions for specific equations of state, and providing numerical solutions for others.

Contribution

It introduces a novel superfluid-inspired extension to FLRW cosmology and derives explicit parametric solutions using elliptic functions for certain parameters.

Findings

Explicit solutions for the scale factor using Weierstrass elliptic functions.

Numerical solutions for different equations of state.

Extension of cosmological models inspired by superfluid dynamics.

Abstract

Guided by the analogy with the Rayleigh-Plesset dynamics of multielectron bubbles in superfluid He-4, we consider the cosmological FLRW evolution equation with additional cubic and sixth powers of the inverse of the scale factor of the universe. For the barotropic parameter w=2/3 (coasting universe), along with zero cosmological constant in the absence of viscous terms, by using the Sundman time as evolution parameter, we present parametric solutions for the scale factor of the universe in terms of rational expressions of Weierstrass elliptic functions and their particular cases thereof. For other values of the equation of state parameter w, such as w=-1, but also the same coasting case, we present a more standard discussion in the conformal time variable using solutions obtained by numerical integration.