Consistency of higher-derivative couplings to matter fields in scalar-tensor gravity
Tact Ikeda, Kazufumi Takahashi, Tsutomu Kobayashi
Abstract
Recently, a generalization of invertible disformal transformations containing higher-order derivatives of a scalar field has been proposed in the context of scalar-tensor theories of gravity. By applying this generalized disformal transformation to the Horndeski theory, one can obtain the so-called generalized disformal Horndeski (GDH) theories which are more general healthy scalar-tensor theories than ever. However, it is unclear whether or not the GDH theories can be coupled consistently to matter fields because introducing matter fields could break the degeneracy conditions of higher-order scalar-tensor theories and hence yield the unwanted Ostrogradsky ghost. We investigate this issue and explore the conditions under which a minimal coupling to a matter field is consistent in the GDH theories without relying on any particular gauge such as the unitary gauge. We find that all the higher-derivative terms in the generalized disformal transformation are prohibited to avoid the appearance of an extra degree of freedom in a generic gauge. Our analysis shows that, if one considers matter-coupled GDH theories, an extra degree of freedom shows up, though it might be a harmless nonpropagating mode when the scalar field has a timelike gradient.