Dynamical analysis in scalar field cosmology

TL;DR

This paper introduces a method to find exact solutions in scalar field cosmology using invariant transformations of the Wheeler De Witt equation, analyzing the universe's dynamics and dark energy evolution.

Contribution

It extends previous work by providing explicit solutions for scalar field cosmologies with perfect fluids and analyzing their stability and evolution.

Findings

Exact solutions for Hubble parameter and dark energy equation of state.

Existence of a unique stable de-Sitter phase in integrable models.

Effects of spatial curvature on cosmological solutions.

Abstract

We give a general method to find exact cosmological solutions for scalar-field dark energy in the presence of perfect fluids. We use the existence of invariant transformations for the Wheeler De Witt (WdW) equation. We show that the existence of a point transformation under which the WdW equation is invariant is equivalent to the existence of conservation laws for the field equations, which indicates the existence of analytical solutions. We extend previous work by providing exact solutions for the Hubble parameter and the effective dark-energy equation of state parameter for cosmologies containing a combination of perfect fluid and a scalar field whose self-interaction potential is a power of hyperbolic functions. We find solutions explicitly when the perfect fluid is radiation or cold dark matter and determine the effects of non-zero spatial curvature. Using the Planck 2015 data, we determine the evolution of the effective equation of state of the dark energy. Finally, we study the global dynamics using dimensionless variables. We find that if the current cosmological model is Liouville integrable (admits conservation laws) then there is a unique stable point which describes the de-Sitter phase of the universe.