We propose a natural extension of Hořava's model for quantum gravity, which is free from the notorious pathologies of the original proposal. The new model endows the scalar graviton mode with a regular quadratic action and remains power-counting renormalizable. At low energies, it reduces to a Lorentzviolating scalar-tensor gravity theory. The deviations with respect to general relativity can be made weak by an appropriate choice of parameters. Introduction.-Recently, Hořava has proposed a new approach to quantum gravity [1]. The key idea is to abandon local Lorentz invariance as fundamental and to assume instead that it appears at low energies as an approximate symmetry. The breaking of Lorentz invariance is achieved by equipping the space-time with a preferred foliation by three-dimensional spacelike surfaces, which defines the splitting of coordinates into space and time. This allows us to complete the action of general relativity (GR) with higher spatial derivatives of the metric, improving the UV behavior of the graviton propagator and making the theory power-counting renormalizable. Besides, the action remains second order in time derivatives, avoiding the ghosts of covariant theories of higher-derivative gravity [2].The concrete realization of this idea as developed in [1] unfolds as follows. One considers the 3 þ 1 decomposition of the space-time metric in the preferred foliation,

We analyse the self-consistency of inflation in the Standard Model, where the Higgs field has a large non-minimal coupling to gravity. We determine the domain of energies in which this model represents a valid effective field theory as a function of the background Higgs field. This domain is bounded above by the cutoff scale which is found to be higher than the relevant dynamical scales throughout the whole history of the Universe, including the inflationary epoch and reheating. We present a systematic scheme to take into account quantum loop corrections to the inflationary calculations within the framework of effective field theory. We discuss the additional assumptions that must be satisfied by the ultra-violet completion of the theory to allow connection between the parameters of the inflationary effective theory and those describing the low-energy physics relevant for the collider experiments. A class of generalisations of inflationary theories with similar properties is constructed.Comment: 25 pages, 1 figur

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 Stückelberg 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 Stückelberg formalism to Hořava's model due to its non-relativistic nature. 1Recently, Hořava has proposed a new approach to the theory of quantum gravity [1]. The key idea of the proposal is to equip space-time with a new structure: a foliation by spacelike surfaces. This foliation defines the splitting of the coordinates into "space" and "time" and breaks the general covariance of general relativity (GR). Then one can improve the UV behavior of the graviton propagator and ultimately make the theory power-counting renormalizable by adding to the GR action terms with higher spatial derivatives. At the same time the action in the ADM formalism contains only first order time derivatives, which allows to circumvent the problems with the ghosts appearing in covariant higher order gravity theories [2]. The higher derivative terms naively become irrelevant in the infrared and it was argued in [1] that the theory reduces to GR at large distances.However, the consistency of the above proposal is far from being clear. The main concern comes from the fact that the introduction of a preferred foliation explicitly breaks the gauge group of GR down to the group of space-time diffeomorphisms preserving this foliation. As already pointed out in [1] this breaking is expected to introduce extra degrees of freedom compared to GR. The new degrees of freedom can persist down to the infrared and lead to various pathologies (instabilities, strong coupling) that may invalidate the theory. An illustration of this phenomenon is provided by theories of massive gravity where special care is needed to make the additional degrees of freedom well-behaved [3,4,5].