Extended Cuscuton: Formulation

TL;DR

This paper introduces the extended cuscuton, a new class of scalar-tensor theories with only two propagating degrees of freedom, and analyzes their cosmological perturbations with matter.

Contribution

It formulates the extended cuscuton as a generalization within beyond Horndeski theories, maintaining the unique degree-of-freedom property.

Findings

Extended cuscuton theories have only two propagating degrees of freedom.

Cosmological perturbations in these theories are studied with matter presence.

Theories are consistent with the special properties of the original cuscuton.

Abstract

Among single-field scalar-tensor theories, there is a special class called "cuscuton," which is represented as some limiting case of k-essence in general relativity. This theory has a remarkable feature that the number of propagating degrees of freedom is only two in the unitary gauge in contrast to ordinary scalar-tensor theories with three degrees of freedom. We specify a general class of theories with the same property as the cuscuton in the context of the beyond Horndeski theory, which we dub as the extended cuscuton. We also study cosmological perturbations in the presence of matter in these extended cuscuton theories.