The linearization method and new classes of exact solutions in cosmology

TL;DR

This paper introduces a linearization method for deriving exact cosmological solutions to Einstein's equations, enabling the construction of complex models with multiple parameters that can describe inflationary behaviors and match observational data.

Contribution

The authors present a novel linearization technique that generates a broad class of exact cosmological solutions with many free parameters, including solutions capable of modeling inflation and its exit without fine-tuning.

Findings

Three-parameter solutions exhibit inflationary regimes.

Solutions can describe exit from inflation without fine-tuning.

Multiple inflationary regimes can be modeled consecutively.

Abstract

We develop a method for constructing exact cosmological solutions of the Einstein equations based on representing them as a second-order linear differential equation. In particular, the method allows using an arbitrary known solution to construct a more general solution parameterized by a set of 3\textit{N} constants, where \textit{N} is an arbitrary natural number. The large number of free parameters may prove useful for constructing a theoretical model that agrees satisfactorily with the results of astronomical observations. Cosmological solutions on the Randall-Sundrum brane have similar properties. We show that three-parameter solutions in the general case already exhibit inflationary regimes. In contrast to previously studied two-parameter solutions, these three-parameter solutions can describe an exit from inflation without a fine tuning of the parameters and also several consecutive inflationary regimes.