Barotropic FRW cosmologies with Chiellini damping

TL;DR

This paper explores a novel class of barotropic Friedmann-Robertson-Walker cosmologies derived from nonlinear Ermakov-Pinney equations with Chiellini damping, revealing new relationships between the scale factor and adiabatic index.

Contribution

It introduces a new approach linking nonlinear dissipative equations with cosmological models, expanding the understanding of barotropic universe dynamics.

Findings

Cosmologies resemble standard models but with rescaled adiabatic indices.

Scale factor amplitudes are inversely proportional to the adiabatic index.

New solutions are obtained via the linear limit of Chiellini-damped Ermakov-Pinney equations.

Abstract

It is known that barotropic FRW equations written in the conformal time variable can be reduced to simple linear equations for an exponential function involving the conformal Hubble rate. Here, we show that an interesting class of barotropic universes can be obtained in the linear limit of a special type of nonlinear dissipative Ermakov-Pinney equations with the nonlinear dissipation built from Chiellini's integrability condition. These cosmologies, which evolutionary are similar to the standard ones, correspond to barotropic fluids with adiabatic indices rescaled by a particular factor and have amplitudes of the scale factors inverse proportional to the adiabatic index