Degeneracy, matter coupling, and disformal transformations in scalar-tensor theories

Understand

Degenerate scalar-tensor theories of gravity extend general relativity by a single degree of freedom, despite their equations of motion being higher than second order.

• In some cases, this is a mere consequence of a disformal field redefinition carried out in a non-degenerate theory.
• More generally, this is made possible by the existence of an additional constraint that removes the would-be ghost.
• It has been noted that this constraint can be thwarted when the coupling to matter involves time derivatives of the metric, which results in a modification of the canonical momenta of the gravitational sector.