The effective two-dimensional phase space of cosmological scalar fields

TL;DR

This paper demonstrates that a two-dimensional effective phase space description, using scalar field and its velocity, applies broadly to Horndeski theories of gravity, simplifying initial condition setting in cosmology.

Contribution

It extends the known two-dimensional phase space framework from canonical scalar fields to the full Horndeski class of scalar-tensor theories.

Findings

Effective 2D phase space exists for general Horndeski models.

Special coordinates facilitate initial condition analysis in complex scalar-tensor theories.

The approach applies to cosmologically relevant subsets of Horndeski actions.

Abstract

It has been shown by Remmen and Carroll that, for a model universe which contains only a kinetically canonical scalar field minimally coupled to gravity it is possible to choose 'special coordinates' to describe a two-dimensional effective phase space. The special, non-canonical, coordinates are $\phi$,$\dot{\phi}$ and the ability to describe an effective phase space with these coordinates empowers the common usage of $\phi-\dot{\phi}$ as the space to define inflationary initial conditions. This paper extends the result to the full Horndeski action. The existence of a two-dimensional effective phase space is shown for the general case. Subsets of the Horndeski action, relevant to cosmology are considered as particular examples to highlight important aspects of the procedure.