Abstract
Many theories of modified gravity with higher order derivatives are usually ignored because of serious problems that appear due to an additional ghost degree of freedom. Most dangerously, it causes an immediate decay of the vacuum. However, breaking Lorentz invariance can cure such abominable behavior. By analyzing a model that describes a massive graviton together with a remaining Boulware-Deser ghost mode we show that even ghostly theories of modified gravity can yield models that are viable at both classical and quantum levels and, therefore, they should not generally be ruled out. Furthermore, we identify the most dangerous quantum scattering process that has the main impact on the decay time and find differences to simple theories that only describe an ordinary scalar field and a ghost. Additionally, constraints on the parameters of the theory including some upper bounds on the Lorentz-breaking cutoff scale are presented. In particular, for a simple theory of massive gravity we find that a breaking of Lorentz invariance is allowed to happen even at scales above the Planck mass. Finally, we discuss the relevance to other theories of modified gravity.
Highlights
Background cosmology on, let us fix the reference metric to a flat Minkowski background, i.e., fμν = ημν
We have discussed the influence of a ghost on the viability of an EFT by considering the violation of Lorentz invariance above certain energy scales in a particular theory of modified gravity describing a massive graviton with an additional Boulware-Deser ghost, which we called haunted massive gravity (HMG)
Even though we do not believe that our HMG model is able to play a major role in the class of theories of modified gravity attempting to explain, e.g., the late-time acceleration of our Universe, we do expect that its quantum properties can be mapped onto a huge class of other theories of gravity that introduce an Ostrogradski ghost
Summary
Since we are interested in a theory of a massive graviton with an additional BD ghost, we could study any non-linear theory that does not coincide with the dRGT theory. Like all other combinations that satisfy α3 + α4 > 0, does not lead to a Higuchi ghost, at least around an FLRW background for large H2 [27] This is important because we will use this theory as a ghost-free limit which should ensure the absence of the BD ghost and the presence of five healthy graviton degrees of freedom. Introduce a metric-dependent (and, lapse-dependent) prefactor like α g−1f , with α ∈ R, and study the action This theory would certainly allow for dynamical FLRW backgrounds, we found only unviable solutions for which the scale factor would become imaginary or the lapse would cross zero, indicating an instability. The additional dynamical factors will enable us to have dynamical FLRW solutions by modifying the Bianchi constraint, and, we expect the vacuum to decay more slowly at late times since g−1f ∝ a−2 for FLRW backgrounds.
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