Tracking our Universe to de Sitter by a Horndeski scalar

TL;DR

This paper investigates conditions under which a Horndeski scalar field can drive the universe towards a de Sitter phase, showing that such a state is a universal attractor in these theories and exploring specific models like the Galileon-Slotheon system.

Contribution

It identifies the conditions for de Sitter critical points in shift-symmetric Horndeski theories and demonstrates their role as universal attractors, including analysis of the Galileon-Slotheon model.

Findings

De Sitter critical points exist under specific conditions in Horndeski theories.

These points act as universal attractors for the universe's evolution.

The tracker trajectory in the Galileon-Slotheon system differs from previous assumptions.

Abstract

Assuming both that our Universe is evolving into a de Sitter space and a vanishing cosmological constant, leaves only the option that the observed acceleration is provided by a "kinetic" energy of a scalar field. From an effective field theory point of view, the absence of Ostrogradsky instabilities restricts the choice to shift-symmetric Horndeski theories. Within these theories, we find the conditions for the existence of a de Sitter critical point in a universe filled by matter, radiation and a Horndeski scalar. Moreover, we show that this point is a universal attractor and we provide the tracking trajectory. Therefore, if a de Sitter fixed point exists within these models, our Universe will eventually evolve into a de Sitter space. As an example, we have discussed the case of the combined Galileon-Slotheon system, in which the Galileon is kinetically non-minimal coupled to the Einstein tensor. Interestingly, we have also found that the tracker trajectory of this system does not follow previous literature assumptions.