Extending Horndeski theories into Lovelock gravity

TL;DR

This paper extends Horndeski theories into Lovelock gravity, introducing a Lovelock scalar field with second-order equations of motion, and explores its cosmological solutions in seven-dimensional spacetime.

Contribution

It introduces the Lovelock scalar field as a subclass of Horndeski theories with second-order equations, and studies its cosmological implications in higher-dimensional spacetime.

Findings

Lovelock scalar field has second-order equations of motion.

Cosmological solutions in 7D spacetime are derived.

The scalar field exhibits rich physics deserving further investigation.

Abstract

The Horndeski theories are extended into the Lovelock gravity theory. When the canonical scalar field is uniquely kinetically coupled to the Lovelock tensors, it is named after Lovelock scalar field. The Lovelock scalar field model is a subclass of the new Horndeski theories. A most attractive feature of the Lovelock scalar field is its equation of motion is second order. So it is free of ghosts. We study the cosmology of Lovelock scalar field in the background of $7$ dimensional spacetime and present a class of cosmic solutions. These solutions reveal the physics of the scalar field is rather rich and merit further study.