Generalizing the matter coupling in massive gravity: A search for new interactions

Abstract

Massive gravity theory introduced by de Rham, Gabadadze, Tolley (dRGT) is restricted by several uniqueness theorems that protect the form of the potential and kinetic terms, as well as the matter coupling. These restrictions arise from the requirement that the degrees of freedom match the expectation from Poincaré representations of a spin-2 field. Any modification beyond the dRGT form is known to invalidate a constraint that the theory enjoys and revive a dangerous sixth mode. One loophole is to exploit the effective nature of the theory by pushing the sixth mode beyond the strong coupling scale without completely removing it. In this paper, we search for modifications to dRGT action by coupling the matter sector to an arbitrary metric constructed out of the already existing degrees of freedom in the dRGT action. We formulate the conditions that such an extension should satisfy in order to prevent the sixth mode from contaminating the effective theory. Our approach provides a new perspective for the "composite coupling" which emerges as the unique extension up to four-point interactions. * Electronic address: emir.gumrukcuoglu@port.ac.uk † Electronic address: kazuya.koyama@port.ac.uk 1 In our formulation, we assume a universal matter coupling. In the case where weak equivalence principle is broken, different matter sectors can flow on different geometries. Justification for a restricted version of this scenario is presented in Section VI. 2 In Bekenstein's nomenclature, g is the gravitational metric whileg is the physical metric [1]. Since matter follows the geodesics ofg, the physical metric is uniquely defined. However, the interpretation of the gravitational metric is more ambiguous in modern modified gravity theories, where it is not always possible to define a field variable to reduce the vacuum action to general relativity and minimally coupled extra fields. 3 Although representations related by a change of variable are classically equivalent (see e.g. [2-4]), subtle differences arise in their interpretations [5], while quantum anomalies may invalidate the physical equivalence [6].

Cosmic acceleration and growth of structure in massive gravity

“…[16], including nonminimal couplings. Finally, relaxing the dRGT constraint to be valid only within the range of the effective field theory, we expect that disformal couplings to matter can be allowed [30]. A natural next step is to exploit the full freedom of this theory class, determining new ways to achieve self-acceleration and finding other applications in cosmology.…”

Massive gravity with nonminimal coupling

“…The trace of any square-root tensor can be written in terms of one without square-roots (see Ref. [35] for details). This allows us to rewrite (15) in terms of ½Z n , and the theory (15) with (22) is manifestly included in (38).…”

“…In the previous section, we have proposed two distinct types of the extended theories (35) and (38). It is now interesting to ask whether all the polarization modes are healthy or not on physically relevant backgrounds.…”

“…It is now interesting to ask whether all the polarization modes are healthy or not on physically relevant backgrounds. To this end, we study FLRW cosmologies in the obtained theories (35) and (38) and derive the conditions for avoiding the ghost and gradient instabilities. Following [9], we choose the Stückelberg fields as 4…”

“…In this subsection, we focus on the nonminimally coupled generalized massive gravity (35), with the general reference metric,…”