Preferred Time Foliation Research Articles

Erratum: Neutron star sensitivities in Hořava gravity after GW170817 [Phys. Rev. D 100 , 084053 (2019)

Hořava gravity breaks boost invariance in the gravitational sector by introducing a preferred time foliation. The dynamics of this preferred slicing is governed, in the low-energy limit suitable for most astrophysical applications, by three dimensionless parameters α, β and λ. The first two of these parameters are tightly bound by Solar System and gravitational-wave propagation experiments, but λ remains relatively unconstrained (0≤λ≲0.01–0.1). We restrict here to the parameter-space region defined by α=β=0 (with λ kept generic), which in a previous paper we showed to be the only one where black hole solutions are nonpathological at the universal horizon, and we focus on possible violations of the strong equivalence principle in systems involving neutron stars. We compute neutron star “sensitivities,” which parametrize violations of the strong equivalence principle at the leading post-Newtonian order, and find that they vanish identically, like in the black hole case, for α=β=0 and generic λ≠0. This implies that no violations of the strong equivalence principle (neither in the conservative sector nor in gravitational-wave fluxes) can occur at the leading post-Newtonian order in binaries of compact objects, and that data from binary pulsars and gravitational interferometers are unlikely to further constrain λ.

Neutron star sensitivities in Hořava gravity after GW170817

Ho\v{r}ava gravity breaks boost invariance in the gravitational sector by introducing a preferred time foliation. The dynamics of this preferred slicing is governed, in the low-energy limit suitable for most astrophysical applications, by three dimensionless parameters $\alpha$, $\beta$ and $\lambda$. The first two of these parameters are tightly bound by solar system and gravitational wave propagation experiments, but $\lambda$ remains relatively unconstrained ($0\leq\lambda\lesssim 0.01-0.1$). We restrict here to the parameter space region defined by $\alpha=\beta=0$ (with $\lambda$ kept generic), which in a previous paper we showed to be the only one where black hole solutions are non-pathological at the universal horizon, and we focus on possible violations of the strong equivalence principle in systems involving neutron stars. We compute neutron star 'sensitivities', which parametrize violations of the strong equivalence principle at the leading post-Newtonian order, and find that they vanish identically, like in the black hole case, for $\alpha=\beta=0$ and generic $\lambda\neq0$. This implies that no violations of the strong equivalence principle (neither in the conservative sector nor in gravitational wave fluxes) can occur at the leading post-Newtonian order in binaries of compact objects, and that data from binary pulsars and gravitational interferometers are unlikely to further constrain $\lambda$.

Dispersion relations in non-relativistic two-dimensional materials from quasinormal modes in H\u01d2rava Gravity

We compute dispersion relations of non-hydrodynamic and hydrodynamic modes in a non-relativistic strongly coupled two-dimensional quantum field theory. This is achieved by numerically computing quasinormal modes (QNMs) of a particular analytically known black brane solution to 3+1-dimensional Hǒrava Gravity. Hǒrava Gravity is distinguished from Einstein Gravity by the presence of a scalar field, termed the khronon, defining a preferred time-foliation. Surprisingly, for this black brane solution, the khronon fluctuation numerically decouples from all others, having its own set of purely imaginary eigenfrequencies, for which we provide an analytic expression. All other Hǒrava Gravity QNMs are expressed analytically in terms of QNMs of Einstein Gravity, in units involving the khronon coupling constants and various horizons. Our numerical computation reproduces the analytically known momentum diffusion mode, and extends the analytic expression for the sound modes to a wide range of khronon coupling values. In the eikonal limit (large momentum limit), the analytically known dispersion of QNM frequencies with the momentum is reproduced by our numerics. We provide a parametrization of all QNM frequencies to fourth order in the momentum. We demonstrate perturbative stability in a wide range of coupling constants and momenta.

New asymptotically Lifshitz black holes in Hořava gravity

We study asymptotically Lifshitz solutions with critical exponent $z \neq 1$ in Horava gravity in three and four spacetime dimensions. For $z=2$ and $z=3/2$, we find a novel class of numerical solutions with regular universal horizon, but are characterized by non-analytic behavior near infinity. In the interior, inside the universal horizon, the unit timelike vector field associated with the preferred time foliation exhibits oscillatory behavior, qualitatively similar to that found earlier in asymptotically flat solutions. For $z>2$ no solutions of this type appear to exist. We comment on potential applications to holographic Lifshitz dualities.

Wavepacket of the Universe and its Spreading

Wavepackets in quantum mechanics spread and the Universe in cosmology expands. We discuss a formalism where the two effects can be unified. The basic assumption is that the Universe is determined by a unitarily evolving wavepacket defined on space-time. Space-time is static but the Universe is dynamic. Spreading analogous to expansion known from observational cosmology is obtained if one regards time evolution as a discrete process with probabilities of jumps determined by a variational principle employing Kolmogorov-Nagumo-R\'enyi averages. The choice of the R\'enyi calculus implies that the form of the Universe involves an implicit fractal structure. The formalism automatically leads to two types of "time" parameters: $\tau$, with dimension of $x^0$, and dimensionless $\varepsilon=\ln \epsilon_\tau$, related to the form of diffeomorphism that defines the dynamics. There is no preferred time foliation, but effectively the dynamics leads to asymptotic concentration of the Universe on spacelike surfaces that propagate in space-time. The analysis is performed explicitly in $1+1$ dimensions, but the unitary evolution operator is brought to a form that makes generalizations to other dimensions and other fields quite natural.

Completing Lorentz violating massive gravity at high energies

Theories with massive gravitons are interesting for a variety of physical applications, ranging from cosmological phenomena to holographic modeling of condensed matter systems. To date, they have been formulated as effective field theories with a cutoff proportional to a positive power of the graviton mass m_g and much smaller than that of the massless theory (M_P ~ 10^19 GeV in the case of general relativity). In this paper we present an ultraviolet completion for massive gravity valid up to a high energy scale independent of the graviton mass. The construction is based on the existence of a preferred time foliation combined with spontaneous condensation of vector fields. The perturbations of these fields are massive and below their mass the theory reduces to a model of Lorentz violating massive gravity. The latter theory possesses instantaneous modes whose consistent quantization we discuss in detail. We briefly study some modifications to gravitational phenomenology at low-energies. The homogeneous cosmological solutions are the same as in the standard cosmology. The gravitational potential of point sources agrees with the Newtonian one at distances small with respect to m_g^(-1). Interestingly, it becomes repulsive at larger distances.

Horava-Lifshitz black hole hydrodynamics

We consider the holographic hydrodynamics of black holes in generally covariant gravity theories with a preferred time foliation. Gravitational perturbations in these theories have spin two and spin zero helicity modes with generically different speeds. The black hole solutions possess a spacelike causal boundary called the universal horizon. We relate the flux of the spin zero perturbation across the universal horizon to the new dissipative transport in Lifshitz field theory hydrodynamics found in arXiv:1304.7481. We construct in detail the hydrodynamics of one such black hole solution, and calculate the ratio of the shear viscosity to the entropy density.

Modified gravity approach based on a preferred time foliation

We propose, in a heuristic way, a relativistic modified gravity model as an alternative to particle dark matter at galactic scales. The model is based on a postulated preferred time foliation described by a dynamical scalar field called the "Khronon". In coordinates adapted to the foliation it appears as a modification of general relativity violating local Lorentz invariance in a regime of weak gravitational fields. The model is a particular case of non-canonical Einstein-aether theory, but in which the aether vector field is hypersurface orthogonal. We show that this model recovers the phenomenology of the modified Newtonian dynamics (MOND) in the non-relativistic limit, and predicts the same gravitational lensing as general relativity but with a modified Poisson-type potential.

Models of non-relativistic quantum gravity: the good, the bad and the healthy

Hořava’s proposal for non-relativistic quantum gravity introduces a preferred time foliation of space-time which violates the local Lorentz invariance. The foliation is encoded in a dynamical scalar field which we call ‘khronon’. The dynamics of the khronon field is sensitive to the symmetries and other details of the particular implementations of the proposal. In this paper we examine several consistency issues present in three non-relativistic gravity theories: Hořava’s projectable theory, the healthy non-projectable extension, and a new extension related to ghost condensation. We find that the only model which is free from instabilities and strong coupling is the non-projectable one. We elaborate on the phenomenology of the latter model including a discussion of the couplings of the khronon to matter. In particular, we obtain the parameters of the post-Newtonian expansion in this model and show that they are compatible with current observations.