Abstract
In the context of massive gravity, bi-gravity and multi-gravity non-minimal matter couplings via a specific composite effective metric were investigated recently. Even if these couplings generically reintroduce the Boulware-Deser ghost, this composite metric is unique in the sense that the ghost reemerges only beyond the decoupling limit and the matter quantum loop corrections do not detune the potential interactions. We consider non-minimal derivative couplings of the composite metric to matter fields for a specific subclass of Horndeski scalar-tensor interactions. We first explore these couplings in the mini-superspace and investigate in which scenario the ghost remains absent. We further study these non-minimal derivative couplings in the decoupling-limit of the theory and show that the equation of motion for the helicity-0 mode remains second order in derivatives. Finally, we discuss preliminary implications for cosmology.
Highlights
The accelerated expansion of the late Universe is confirmed by many cosmological observations like supernovae, CMB, baryon acoustic oscillations and lensing
In this work we have studied the theoretical implication of non-minimal derivative couplings of the effective composite metric, proposed in [35], to matter fields
The motivation for this comes from the fact, that these interactions are naturally generated by the covariantisation procedure of the decoupling limit of massive gravity
Summary
The accelerated expansion of the late Universe is confirmed by many cosmological observations like supernovae, CMB, baryon acoustic oscillations and lensing. These new degrees of freedom could play the role of a condensate, whose energy density either sources self-acceleration or compensates the cosmological constant Such scenarios could for instance arise in massive gravity or in higher-dimensional frameworks. In this work we would like to further study the theoretical implications of this effective composite metric in the context of non-minimally coupled scalar-tensor theories motivated by the proxy theory For this purpose, we consider the specific scalartensor interactions of the covariantized decoupling limit, that live on the effective composite metric. It is important to investigate whether non-minimal couplings to this effective metric maintain the ghost absent in the decoupling limit, and whether this might yield richer cosmological phenomenology than the standard Horndeski type of theories living in the standard metric
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