A dynamical inconsistency of Hořava gravity

We consider Galileon models on curved spacetime, as well as the counterterms introduced to maintain the second-order nature of the field equations of these models when both the metric and the scalar are made dynamical. Working in a gauge invariant framework, we first show how all the third-order time derivatives appearing in the field equations -both metric and scalar -of a Galileon model or one defined by a given counterterm can be eliminated to leave field equations which contain at most second-order time derivatives of the metric and of the scalar. The same is shown to hold for arbitrary linear combinations of such models, as well as their k-essencelike/Horndeski generalizations. This supports the claim that the number of degrees of freedom in these models is only 3, counting 2 for the graviton and 1 for the scalar. We comment on the arguments given previously in support of this claim. We then prove that this number of degrees of freedom is strictly less that 4 in one particular such model by carrying out a full-fledged Hamiltonian analysis. In contrast to previous results, our analyses do not assume any particular gauge choice of restricted applicability.

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“…This dependence of (38) and (39) on the same contraction C ofg ij allows us to cancel it in the linear combination…”

Section: (N+1p) and Their Linear Combinationsmentioning

confidence: 99%

“…The fact that the same contraction C ofg ij enters both (38) and (39) will be crucial below. Whilst this looks miraculous, it is actually simply a consequence of the diffeomorphism invariance of the theory, together with the fact that T αβ involves at most second derivatives of the metric as proved in Eq.…”

Section: (N+1p) and Their Linear Combinationsmentioning

confidence: 99%

Counting the degrees of freedom of generalized Galileons

2015

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“…Indeed, whenever Þ 0 the lapse N is no longer a Lagrange multiplier, and the Hamiltonian constraint (obtained as the variation of the action with respect to N, H S N ¼ 0) together with the equation N ¼ 0 form a pair of second-class constraints (they have a nonvanishing Poisson bracket), which can be used to eliminate N and N . Hence, the pathologies [6,15] present in Hořava's original proposal do not appear.…”

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confidence: 99%

Consistent Extension of Hořava Gravity

2010

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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,

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“…Therefore, as a modification to General Relativity at high energies, this theory was explored significantly within the context of cosmology: cosmological solutions with matter and the possibility of a nonsingular bounce were studied in [273][274][275][276]. HL gravity was shown to have inconsistencies in [277] and more recently, to be UV-incomplete [278]. We therefore do not dwell on these models further.…”

Section: Hořava-lifshitzmentioning

confidence: 99%

A critical review of classical bouncing cosmologies

2015

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Given the proliferation of bouncing models in recent years, we gather and critically assess these proposals in a comprehensive review. The PLANCK data shows an unmistakably red, quasi scaleinvariant, purely adiabatic primordial power spectrum and no primary non-Gaussianities. While these observations are consistent with inflationary predictions, bouncing cosmologies aspire to provide an alternative framework to explain them. Such models face many problems, both of the purely theoretical kind, such as the necessity of violating the NEC and instabilities, and at the cosmological application level, as exemplified by the possible presence of shear. We provide a pedagogical introduction to these problems and also assess the fitness of different proposals with respect to the data. For example, many models predict a slightly blue spectrum and must be fine-tuned to generate a red spectral index; as a side effect, large non-Gaussianities often result.We highlight several promising attempts to violate the NEC without introducing dangerous instabilities at the classical and/or quantum level. If primordial gravitational waves are observed, certain bouncing cosmologies, such as the cyclic scenario, are in trouble, while others remain valid. We conclude that, while most bouncing cosmologies are far from providing an alternative to the inflationary paradigm, a handful of interesting proposals have surfaced, which warrant further research. The constraints and lessons learned as laid out in this review might guide future research.

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A dynamical inconsistency of Hořava gravity

Cited by 145 publications

References 54 publications

Counting the degrees of freedom of generalized Galileons

Counting the degrees of freedom of generalized Galileons

Consistent Extension of Hořava Gravity

A critical review of classical bouncing cosmologies

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