Inflationary perturbations with Lifshitz scaling

Instead of Lorentz invariance, gravitational degrees of freedom may obey Lifshitz scaling at high energies, as it happens in Horava's proposal for quantum gravity. We study consequences of this proposal for the spectra of primordial perturbations generated at inflation. Breaking of 4D diffeomorphism (Diff) invariance down to the foliation-preserving Diff in Horava-Lifshitz (HL) gravity leads to appearance of a scalar degree of freedom in the gravity sector, khronon, which describes dynamics of the time foliation. One can naively expect that mixing between inflaton and khronon will jeopardize conservation of adiabatic perturbations at super Hubble scales. This indeed happens in the projectable version of the theory. By contrast, we find that in the non-projectable version of HL gravity, khronon acquires an effective mass which is much larger than the Hubble scale well before the Hubble crossing time and decouples from the adiabatic curvature perturbation zeta sourced by the inflaton fluctuations. As a result, at super Hubble scales the adiabatic perturbation zeta behaves as in an effectively single field system and its spectrum is conserved in time. Lifshitz scaling is imprinted in the power spectrum of zeta through the modi fied dispersion relation of the inflaton. We point out violation of the consistency relation between the tensor-to-scalar ratio and the spectral tilt of primordial gravitational waves and suggest that it can provide a signal of Lorentz violation in inflationary era.

Consistent Extension of Horava Gravity

Diego Blas Temino, Sergey Sibiryakov

We propose a natural extension of Horava'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 Lorentz-violating scalar-tensor gravity theory. The deviations with respect to general relativity can be made weak by an appropriate choice of parameters.

2010

Cosmological constraints on deviations from Lorentz invariance in gravity and dark matter

Benjamin Audren, Diego Blas Temino, Mikhail Ivanov, Julien Lesgourgues, Sergey Sibiryakov

We consider a scenario where local Lorentz invariance is violated by the existence of a preferred time direction at every space-time point. This scenario can arise in the context of quantum gravity and its description at low energies contains a unit time-like vector field which parameterizes the preferred direction. The particle physics tests of Lorentz invariance preclude a direct coupling of this vector to the fields of the Standard Model, but do not bear implications for dark matter. We discuss how the presence of this vector and its possible coupling to dark matter affect the evolution of the Universe. At the level of homogeneous cosmology the only effect of Lorentz invariance violation is a rescaling of the expansion rate. The physics is richer at the level of perturbations. We identify three effects crucial for observations: the rescaling of the matter contribution to the Poisson equation, the appearance of an extra contribution to the anisotropic stress and the scale-dependent enhancement of dark matter clustering. These effects result in distinctive features in the power spectra of the CMB and density fluctuations. Making use of the data from Planck and WiggleZ we obtain the most stringent cosmological constraints to date on departures from Lorentz symmetry. Our analysis provides the first direct bounds on deviations from Lorentz invariance in the dark matter sector.

Iop Publishing Ltd2015

Scale-Invariant Models of Gravity and Particle Physics and their Cosmological Implications

Daniel Zenhäusern

Currently, the best theoretical description of fundamental matter and its gravitational interaction is given by the Standard Model (SM) of particle physics and Einstein's theory of General Relativity (GR). These theories contain a number of seemingly unrelated scales. While Newton's gravitational constant and the mass of the Higgs boson are parameters in the classical action, the masses of other elementary particles are due to the electroweak symmetry breaking. Yet other scales, like ΛQCD associated to the strong interaction, only appear after the quantization of the theory. We reevaluate the idea that the fundamental theory of nature may contain no fixed scales and that all observed scales could have a common origin in the spontaneous break-down of exact scale invariance. To this end, we consider a few minimal scale-invariant extensions of GR and the SM, focusing especially on their cosmological phenomenology. In the simplest considered model, scale invariance is achieved through the introduction of a dilaton field. We find that for a large class of potentials, scale invariance is spontaneously broken, leading to induced scales at the classical level. The dilaton is exactly massless and practically decouples from all SM fields. The dynamical break-down of scale invariance automatically provides a mechanism for inflation. Despite exact scale invariance, the theory generally contains a cosmological constant, or, put in other words, flat spacetime need not be a solution. We next replace standard gravity by Unimodular Gravity (UG). This results in the appearance of an arbitrary integration constant in the equations of motion, inducing a run-away potential for the dilaton. As a consequence, the dilaton can play the role of a dynamical dark-energy component. The cosmological phenomenology of the model combining scale invariance and unimodular gravity is studied in detail. We find that the equation of state of the dilaton condensate has to be very close to the one of a cosmological constant. If the spacetime symmetry group of the gravitational action is reduced from the group of all diffeomorphisms (Diff) to the subgroup of transverse diffeomorphisms (TDiff), the metric in general contains a propagating scalar degree of freedom. We show that the replacement of Diff by TDiff makes it possible to construct a scale-invariant theory of gravity and particle physics in which the dilaton appears as a part of the metric. We find the conditions under which such a theory is a viable description of particle physics and in particular reproduces the SM phenomenology. The minimal theory with scale invariance and UG is found to be a particular case of a theory with scale and TDiff invariance. Moreover, cosmological solutions in models based on scale and TDiff invariance turn out to generically be similar to the solutions of the model with UG. In usual quantum field theories, scale invariance is anomalous. This might suggest that results based on classical scale invariance are necessarily spoiled by quantum corrections. We show that this conclusion is not true. Namely, we propose a new renormalization scheme which allows to construct a class of quantum field theories that are scale-invariant to all orders of perturbation theory and where the scale symmetry is spontaneously broken. In this type of theory, all scales, including those related to dimensional transmutation, like ΛQCD, appear as a consequence of the spontaneous break-down of the scale symmetry. The proposed theories are not renormalizable. Nonetheless, they are valid effective theories below a field-dependent cut-off scale. If the scale-invariant renormalization scheme is applied to the presented minimal scale-invariant extensions of GR and the SM, the goal of having a common origin of all scales, spontaneous breaking of scale invariance, is achieved.

EPFL2011

Scale-Invariant Models of Gravity and Particle Physics and their Cosmological Implications

Daniel Zenhäusern

EPFL2011