Plane waves in the generalized Galileon theory

TL;DR

This paper derives an exact plane wave solution in the most general shift-symmetric Horndeski (generalized Galileon) theory, revealing how scalar and gravitational waves coexist and generalize known solutions in flat spacetime.

Contribution

It provides the first exact plane wave solution in the full shift-symmetric Horndeski theory, including scalar and tensor modes with arbitrary scalar profiles.

Findings

Scalar field induces additional polarization modes.

Reduces to known solutions in special cases like Minkowski space.

Generalizes plane wave solutions beyond General Relativity.

Abstract

We present an exact plane wave solution of the most general shift-symmetric Horndeski (generalized Galileon) theory. The solution consists of the scalar part, and the gravitational part with two polarization modes. The former is due to the presence of the non-trivial Galileon scalar field, and it is parametrized by an arbitrary function of the light-cone coordinate. For a trivial scalar field configuration the solution is equivalent to the plane gravitational wave in General Relativity. When the metric is Minkowski, we reproduce known results for the plane waves of k-essence and a soliton-like solutions of a non-covariant Galileon model in a flat space-time.