General Analytic Solutions of Scalar Field Cosmology with Arbitrary Potential

TL;DR

This paper derives general analytic solutions for scalar field cosmology with any potential in FLRW spacetime, using a nonlocal integral of motion, applicable to flat and curved universes, and extends to dark energy models.

Contribution

It introduces a method to find analytic solutions for scalar fields with arbitrary potentials in cosmology, including non-flat cases and matter components.

Findings

Derived solution space for scalar field cosmology with arbitrary potential.

Extended solutions to include non-interacting perfect fluids.

Applied solutions to parametric dark energy models.

Abstract

We present the solution space for the case of a minimally coupled scalar field with arbitrary potential in a FLRW metric. This is made possible due to the existence of a nonlocal integral of motion corresponding to the conformal Killing field of the two-dimensional minisuperspace metric. The case for both spatially flat and non flat are studied first in the presence of only the scalar field and subsequently with the addition of non interacting perfect fluids. It is verified that this addition does not change the general form of the solution, but only the particular expressions of the scalar field and the potential. The results are applied in the case of parametric dark energy models where we derive the scalar field equivalence solution for some proposed models in the literature.