Abstract
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. In this note we expand on this issue by analyzing the precise ways in which the extra degree of freedom may reappear upon minimal coupling to matter. Specifically, we study examples of matter sectors that lead either to a direct loss of the special constraint or to a failure to generate a pair of secondary constraints. We also discuss the recurrence of the extra degree of freedom using the language of disformal transformations in particular for what concerns "veiled" gravity. On the positive side, we show that the minimal coupling of spinor fields is healthy and does not spoil the additional constraint. We argue that this virtue of spinor fields to preserve the number of degrees of freedom in the presence of higher derivatives is actually very general and can be seen from the level decomposition of Grassmann-valued classical variables.
Highlights
Scalar-tensor theories of gravity are appealing for a number of reasons [1,2]
For a generic degenerate higher-order scalartensor theories (DHOST), an increase of the degrees of freedom (DOF) might stem from minimal matter coupling when the latter contains derivatives of the metric, e.g., connections contained in covariant derivatives, as we explore below
Our essential criterion that determined whether a given matter field can be described consistently within DHOST was that the interaction between the matter and scalartensor sectors that derives from the minimal coupling prescription should not introduce extra degrees of freedom
Summary
Scalar-tensor theories of gravity are appealing for a number of reasons [1,2]. The resounding experimental success of general relativity (GR) suggests that if gravity is to be modified in the infrared, we had better do so in a conservative way, and the most minimal tweak to be done is to add a single scalar degree of freedom besides the graviton described by GR. In the context of the Hamilton-Dirac analysis, these degeneracies manifest themselves as additional pairs of second class constraints, making very transparent that some of the DOF that one would naively infer from the action are nondynamical [8,9,10,11,12,13,14,15] This leads to the generalization of Horndeski theories to “beyond Horndeski” [8,10,16,17,18] and eventually to the larger class of degenerate higher-order scalartensor theories (DHOST) [19,20,21] (see [22,23,24] for reviews).
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
