New exact solutions for power-law inflation Friedmann models

TL;DR

This paper derives new exact solutions for power-law inflation in Friedmann models across various gravity theories, including higher-dimensional and scalar field models, expanding the understanding of inflationary cosmologies.

Contribution

It introduces novel exact solutions for power-law inflation in Friedmann models within different gravitational frameworks, including higher-dimensional and scalar field theories.

Findings

Exact solutions for power-law inflation with L = R^m

Solutions for scalar field models with exponential potential

Special solutions for closed and open Friedmann models

Abstract

We consider the spatially flat Friedmann model. For a(t) = t^p, especially, if p is larger or equal to 1, this is called power-law inflation. For the Lagrangian L = R^m with p = - (m - 1)(2m - 1)/(m - 2), power-law inflation is an exact solution, as it is for Einstein gravity with a minimally coupled scalar field Phi in an exponential potential V(Phi) = exp(mu Phi) and also for the higher-dimensional Einstein equation with a special Kaluza-Klein ansatz. The synchronized coordinates are not adapted to allow a closed-form solution, so we use another gauge. Finally, special solutions for the closed and open Friedmann model are found.