On the extra mode and inconsistency of Hořava gravity

By D. Blas, O. Pujolàs, S. Sibiryakov, S. Sibiryakov. 2009

389 citations recorded by the source corpus.

We address the consistency of Hořava's proposal for a theory of quantum gravity from the low-energy perspective. We uncover the additional scalar degree of freedom arising from the explicit breaking of the general covariance and study its properties. The analysis is performed both in the original formulation of the theory and in the Stuckelberg picture. A peculiarity of the new mode is that it satisfies an equation of motion that is of first order in time derivatives. At linear level the mode is manifest only around spatially inhomogeneous and time-dependent backgrounds. We find two serious problems associated with this mode. First, the mode develops very fast exponential instabilities at short distances. Second, it becomes strongly coupled at an extremely low cutoff scale. We also discuss the ``projectable'' version of Hořava's proposal and argue that this version can be understood as a certain limit of the ghost condensate model. The theory is still problematic since the additional field generically forms caustics and, again, has a very low strong coupling scale. We clarify some subtleties that arise in the application of the Stuckelberg formalism to Hořava's model due to its non-relativistic nature.

Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b4b0f1bfac5c8611ea78be1373021b5554a09ec1

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Citations in the corpus

Dark matter as integration constant in Horava-Lifshitz gravity (2009, neutral): “(iii) The strong coupling away from λ = 1 found in [52] indicates sickness of their description, i.”
Dust of dark energy (2010, background): “[18] on caustics in the ghost condensate [19] and the discussion in Refs [20, 21] on caustics in Hořava gravity [22].”
Spherical collapse in quintessence models with zero speed of sound (2009, methodology): “This corresponds to the formation of cusps in the quintessence field, similarly to what discussed in the ghost condensate case [36] and more recently in the context of Hořava-Lifshift gravity [46, 47].”
Modified Gravity and Cosmology (2011, methodology): “But how small does |cs| need to be? The timescale of this instability is ts ∼ 1/|cs|k > 1/|cs|kUV , and as this would need to exceed the age of the universe, we infer |cs| < H0/kUV , where H0 is the current Hubble scale [167].”
A dynamical inconsistency of Horava gravity (2009, methodology): “1 The model The model [9] is obtained by setting all couplings equal to zero, except λ and ξ.”
Hořava gravity at a Lifshitz point: A progress report (2017, methodology): “To restore the full general covariance, one way is to make the foliation dynamical by using the Stückelberg trick [194], in which the space-like hypersurfaces of t = constant in the (3+1) ADM decompositions are replaced by a scalar field φ = constant, which is always time-like [88, 195],”
hi_class: Horndeski in the Cosmic Linear Anisotropy Solving System (2016, background): “The models can be extended even further to those which contain higher derivatives in space but not in time [44–47].”
General covariance in quantum gravity at a Lifshitz point (2010, background): “As was pointed out already in [1, 2] and further elaborated in [8, 9], in this effective field theory approach to the nonprojectable theory, all terms compatible with the gauge symmetry should be allowed in the Lagrangian.”
A unifying description of dark energy (2014, background): “In particular, the so-called healthy non-projectable extension has been shown to be free of instabitilities [32, 33].”
Zoology of condensed matter: framids, ordinary stuff, extra-ordinary stuff (2015, background): “A field enjoying such an internal symmetry arises for instance in the infrared limit of Hořava-Lifshitz gravity [17, 18] and has been dubbed khronon in the gravity/cosmology literature [19].”