Inflation on a single brane - exact solutions

TL;DR

This paper develops algorithms to generate exact cosmological solutions in braneworld models with a scalar field, revealing specific potentials and solutions relevant for inflationary scenarios in higher-dimensional theories.

Contribution

It introduces a method to find exact solutions for braneworld cosmologies with scalar fields, including the identification of potentials that produce perfect fluid behavior.

Findings

Derived a first-order system of equations for braneworld cosmologies.

Found multiple exact solutions to the equations of motion.

Identified scalar field potentials corresponding to perfect fluid models.

Abstract

Algorithms are developed for generating a class of exact braneworld cosmologies, where a self-interacting scalar field is confined to a positive-tension brane embedded in a bulk containing a negative cosmological constant. It is assumed that the five-dimensional Planck scale exceeds the brane tension but is smaller than the four-dimensional Planck mass. It is shown that the field equations can be expressed as a first-order system. A number of solutions to the equations of motion are found. The potential resulting in the perfect fluid model is identified.