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Register a new userWhen is Multimetric Gravity Ghost-free?
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We study ghosts in multimetric gravity by combining the mini-superspace and the Hamiltonian constraint analysis. We first revisit bimetric gravity and explain why it is ghost-free. Then, we apply our method to trimetric gravity and clarify when the model contains a ghost. More precisely, we prove trimetric gravity generically contains a ghost. However, if we cut the interaction of a pair of metrics, trimetric gravity becomes ghost-free. We further extend the Hamiltonian analysis to general multimetric gravity and calculate the number of ghosts in various models. Thus, we find multimetric gravity with loop type interactions never becomes ghost-free.
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It is possible to couple Dirac-Born-Infeld (DBI) scalars possessing generalized Galilean internal shift symmetries (Galileons) to nonlinear massive gravity in four dimensions, in such a manner that the interactions maintain the Galilean symmetry. Such a construction is of interest because it is not possible to couple such fields to massless General Relativity in the same way. We show that this theory has the primary constraint necessary to eliminate the Boulware-Deser ghost, thus preserving the attractive properties of both the Galileons and ghost-free massive gravity.
We analyze conformal gravity in translationally invariant approximation, where the metric is taken to depend on time but not on spatial coordinates. We find that the field mode which in perturbation theory has a ghostlike kinetic term, turns into a tachyon when nonlinear interaction is accounted for. The kinetic term and potential for this mode have opposite signs. Solutions of nonlinear classical equations of motion develop a singularity in finite time determined by the initial conditions.
The Becchi-Rouet-Stora-Tyutin (BRST) transformations and equations of motion of a gravity-two-form-dilaton system are derived from the product of two Yang-Mills theories in a BRST covariant form, to linear approximation. The inclusion of ghost fields facilitates the separation of the graviton and dilaton. The gravitational gauge fixing term is uniquely determined by those of the Yang-Mills factors which can be freely chosen. Moreover, the resulting gravity-two-form-dilaton Lagrangian is anti-BRST invariant and the BRST and anti-BRST charges anti commute as a direct consequence of the formalism.
In this paper we present an iterative method to generate an infinite class of new nonlocal field theories whose propagators are ghost-free. We first examine the scalar field case and show that the pole structure of such generalized propagators possesses the standard two derivative pole and in addition can contain complex conjugate poles which, however, do not spoil at least tree level unitarity as the optical theorem is still satisfied. Subsequently, we define analogous propagators for the fermionic sector which is also devoid of unhealthy degrees of freedom. As a third case, we apply the same construction to gravity and define a new set of theories whose graviton propagators around the Minkowski background are ghost-free. Such a wider class also includes nonlocal theories previously studied, and Einsteins general relativity as a peculiar limit. Moreover, we compute the linearized gravitational potential generated by a static point-like source for several gravitational theories belonging to this new class and show that the nonlocal nature of gravity regularizes the singularity at the origin.
We present a classical analysis on the issue of vector superluminality in the decoupling limit ghost-free massive gravity with a Minkowski reference metric. We show explicitly in the Lorenz gauge that the theory is free of superluminal vector excitations around a nontrivial solution at the cubic order in the fields. In the same gauge, we demonstrate that superluminal vector modes arise at the quartic order and compute some superluminal propagating solutions. We then generalize our findings to all orders in a gauge-independent way. We check the physical consistency of the vector superluminalities, arguing that they are not physically detectable in the perturbation theory but could be trusted classically in the strong coupling region. Nevertheless, these superluminalities involve only low frequency group and phase velocities and are unable to determine the acausality of the theory.
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