Exact inflationary solutions

TL;DR

This paper introduces a new class of exact inflationary solutions in a curved universe with a scalar field, perfect fluid, and cosmological constant, highlighting solutions with graceful exit behavior.

Contribution

It provides novel exact solutions for inflationary cosmology involving specific scalar field potentials and spatial curvature, expanding the set of known analytical models.

Findings

Scale factor exhibits graceful exit with negative cosmological constant.

Exact solutions derived for scalar field potentials V_+(φ) and V_-(φ).

Physical implications of solutions briefly discussed.

Abstract

We present a new class of exact inflationary solutions for the evolution of a universe with spatial curvature, filled with a perfect fluid, a scalar field with potential $V_{\pm}(\phi)=\lambda(\phi^2\pm\delta^2)^2$ and a cosmological constant $\Lambda$. With the $V_+(\phi)$ potential and a negative cosmological constant, the scale factor experiments a graceful exit. We give a brief discussion about the physical meaning of the solutions.