General relativity limit of Horava-Lifshitz gravity with a scalar field in gradient expansion

We present a fully nonlinear study of long wavelength cosmological perturbations within the framework of the projectable Horava-Lifshitz gravity, coupled to a single scalar field. Adopting the gradient expansion technique, we explicitly integrate the dynamical equations up to any order of the expansion, then restrict the integration constants by imposing the momentum constraint. While the gradient expansion relies on the long wavelength approximation, amplitudes of perturbations do not have to be small. When the $\lambda\to 1$ limit is taken, the obtained nonlinear solutions exhibit a continuous behavior at any order of the gradient expansion, recovering general relativity in the presence of a scalar field and the "dark matter as an integration constant". This is in sharp contrast to the results in the literature based on the "standard" (and naive) perturbative approach where in the same limit, the perturbative expansion of the action breaks down and the scalar graviton mode appears to be strongly coupled. We carry out a detailed analysis on the source of these apparent pathologies and determine that they originate from an improper application of the perturbative approximation in the momentum constraint. We also show that there is a new branch of solutions, valid in the regime where $|\lambda-1|$ is smaller than the order of perturbations. In the limit $\lambda\to1$, this new branch allows the theory to be continuously connected to general relativity (plus "dark matter").Comment: 21 pages; v2. minor update to match the published versio

Charged Rotating Black Holes on a 3-Brane

We study exact stationary and axisymmetric solutions describing charged rotating black holes localized on a 3-brane in the Randall-Sundrum braneworld. The charges of the black holes are considered to be of two types, the first being an induced tidal charge that appears as an imprint of nonlocal gravitational effects from the bulk space and the second is a usual electric charge arising due to a Maxwell field trapped on the brane. We assume a special ansatz for the metric on the brane taking it to be of the Kerr-Schild form and show that the Kerr-Newman solution of ordinary general relativity in which the electric charge is superceded by a tidal charge satisfies a closed system of the effective gravitational field equations on the brane. It turns out that the negative tidal charge may provide a mechanism for spinning up the black hole so that its rotation parameter exceeds its mass. This is not allowed in the framework of general relativity. We also find a new solution that represents a rotating black hole on the brane carrying both charges. We show that for a rapid enough rotation the combined influence of the rotational dynamics and the local bulk effects of the "squared" energy momentum tensor on the brane distort the horizon structure of the black hole in such a way that it can be thought of as composed of non-uniformly rotating null circles with growing radii from the equatorial plane to the poles. We finally study the geodesic motion of test particles in the equatorial plane of a rotating black hole with tidal charge. We show that the effects of negative tidal charge tend to increase the horizon radius, as well as the radii of the limiting photon orbit, the innermost bound and the innermost stable circular orbits for both direct and retrograde motions of the particles.Comment: RevTeX 4, 33 pages, 4 figures, new references adde

Gravity Waves Signatures from Anisotropic pre-Inflation

We show that expanding or contracting Kasner universes are unstable due to the amplification of gravitational waves (GW). As an application of this general relativity effect, we consider a pre-inflationary anisotropic geometry characterized by a Kasner-like expansion, which is driven dynamically towards inflation by a scalar field. We investigate the evolution of linear metric fluctuations around this background, and calculate the amplification of the long-wavelength GW of a certain polarization during the anisotropic expansion (this effect is absent for another GW polarization, and for scalar fluctuations). These GW are superimposed to the usual tensor modes of quantum origin from inflation, and are potentially observable if the total number of inflationary e-folds exceeds the minimum required to homogenize the observable universe only by a small margin. Their contribution to the temperature anisotropy angular power spectrum decreases with the multipole l as l^(-p), where p depends on the slope of the initial GW power-spectrum. Constraints on the long-wavelength GW can be translated into limits on the total duration of inflation and the initial GW amplitude. The instability of classical GW (and zero-vacuum fluctuations of gravitons) during Kasner-like expansion (or contraction) may have other interesting applications. In particular, if GW become non-linear, they can significantly alter the geometry before the onset of inflation

Inflationary perturbations in anisotropic backgrounds and their imprint on the CMB

We extend the standard theory of cosmological perturbations to homogeneous but anisotropic universes. We present an exhaustive computation for the case of a Bianchi I model, with a residual isotropy between two spatial dimensions, which is undergoing complete isotropization at the onset of inflation; we also show how the computation can be further extended to more general backgrounds. In presence of a single inflaton field, there are three physical perturbations (precisely as in the isotropic case), which are obtained (i) by removing gauge and nondynamical degrees of freedom, and (ii) by finding the combinations of the remaining modes in terms of which the quadratic action of the perturbations is canonical. The three perturbations, which later in the isotropic regime become a scalar mode and two tensor polarizations (gravitational wave), are coupled to each other already at the linearized level during the anisotropic phase. This generates nonvanishing correlations between different modes of the CMB anisotropies, which can be particularly relevant at large scales (and, potentially, be related to the large scale anomalies in the WMAP data). As an example, we compute the spectrum of the perturbations in this Bianchi I geometry, assuming that the inflaton is in a slow roll regime also in the anisotropic phase. For this simple set-up, fixing the initial conditions for the perturbations appears more difficult than in the standard case, and additional assumptions seem to be needed to provide predictions for the CMB anisotropies.Comment: 31 pages, 3 figure