General solution of scalar field cosmology with a (piecewise) exponential potential

TL;DR

This paper derives the general solution for scalar field cosmology with exponential and piecewise exponential potentials, correcting previous inaccuracies and extending the solution to more complex potential forms with discontinuities.

Contribution

It provides a corrected and generalized solution framework for scalar field cosmology with piecewise exponential potentials, including cases with cusps.

Findings

Corrected previous inaccuracies in scalar field solutions.

Extended solutions to piecewise exponential potentials with discontinuities.

Established a comprehensive framework for analyzing such cosmological models.

Abstract

We study in detail the general solution for a scalar field cosmology with an exponential potential, correcting some imprecisions, encountered previously in the literature. In addition, we generalize this solution for a piecewise exponential potential, which is continuous, but not smooth (with cusps).