Testing the Isotropy of the Universe with Type Ia Supernovae

We analyze the magnitude-redshift data of type Ia supernovae included in the Union and Union2 compilations in the framework of an anisotropic Bianchi type I cosmological model and in the presence of a dark energy fluid with anisotropic equation of state. We find that the amount of deviation from isotropy of the equation of state of dark energy, the skewness \delta, and the present level of anisotropy of the large-scale geometry of the Universe, the actual shear \Sigma_0, are constrained in the ranges -0.16 < \delta < 0.12 and -0.012 < \Sigma_0 < 0.012 (1\sigma C.L.) by Union2 data. Supernova data are then compatible with a standard isotropic universe (\delta = \Sigma_0 = 0), but a large level of anisotropy, both in the geometry of the Universe and in the equation of state of dark energy, is allowed.Comment: 12 pages, 7 figures, 2 tables. Union2 analysis added. New references added. To appear in Phys. Rev.

The importance of precession in modelling the direction of the final spin from a black-hole merger

The prediction of the spin of the black hole resulting from the merger of a generic black-hole binary system is of great importance to study the cosmological evolution of supermassive black holes. Several attempts have been recently made to model the spin via simple expressions exploiting the results of numerical-relativity simulations. Here, I first review the derivation of a formula, proposed in Barausse & Rezzolla, Apj 704 L40, which accurately predicts the final spin magnitude and direction when applied to binaries with separations of hundred or thousands of gravitational radii. This makes my formula particularly suitable for cosmological merger-trees and N-body simulations, which provide the spins and angular momentum of the two black holes when their separation is of thousands of gravitational radii. More importantly, I investigate the physical reason behind the good agreement between my formula and numerical relativity simulations, and nail it down to the fact that my formula takes into account the post-Newtonian precession of the spins and angular momentum in a consistent manner.Comment: 6 pages, 2 figures. Panel added to fig 2, discussion extended to comply with referee's comments. Version accepted for publication as proceeding of the 8th Amaldi International Conference on Gravitational Waves, NYC, 21-26 June 200

Constraints on the anisotropy of dark energy

If the equation of state of dark energy is anisotropic there will be additional quadrupole anisotropy in the cosmic microwave background induced by the time dependent anisotropic stress quantified in terms of $\Delta w$. Assuming that the entire amplitude of the observed quadrupole is due to this anisotropy, we conservatively impose a limit of $|\Delta w| < 2.1\times 10^{-4}$ for any value of $w\ge -1$ assuming that $\Omega_{\rm m}<0.5$. This is considerably tighter than that which comes from SNe. Stronger limits, upto a factor of 10, are possible for specific values of $\Omega_{\rm m}$ and $w$. Since we assume this component is uncorrelated with the stochastic component from inflation, we find that both the expectation value and the sample variance are increased. There no improvement in the likelihood of an anomalously low quadrupole as suggested by previous work on an elliptical universe

The Lazarus project: A pragmatic approach to binary black hole evolutions

We present a detailed description of techniques developed to combine 3D numerical simulations and, subsequently, a single black hole close-limit approximation. This method has made it possible to compute the first complete waveforms covering the post-orbital dynamics of a binary black hole system with the numerical simulation covering the essential non-linear interaction before the close limit becomes applicable for the late time dynamics. To determine when close-limit perturbation theory is applicable we apply a combination of invariant a priori estimates and a posteriori consistency checks of the robustness of our results against exchange of linear and non-linear treatments near the interface. Once the numerically modeled binary system reaches a regime that can be treated as perturbations of the Kerr spacetime, we must approximately relate the numerical coordinates to the perturbative background coordinates. We also perform a rotation of a numerically defined tetrad to asymptotically reproduce the tetrad required in the perturbative treatment. We can then produce numerical Cauchy data for the close-limit evolution in the form of the Weyl scalar $\psi_4$ and its time derivative $\partial_t\psi_4$ with both objects being first order coordinate and tetrad invariant. The Teukolsky equation in Boyer-Lindquist coordinates is adopted to further continue the evolution. To illustrate the application of these techniques we evolve a single Kerr hole and compute the spurious radiation as a measure of the error of the whole procedure. We also briefly discuss the extension of the project to make use of improved full numerical evolutions and outline the approach to a full understanding of astrophysical black hole binary systems which we can now pursue.Comment: New typos found in the version appeared in PRD. (Mostly found and collected by Bernard Kelly

A perturbative solution for gravitational waves in quadratic gravity

We find a gravitational wave solution to the linearized version of quadratic gravity by adding successive perturbations to the Einstein's linearized field equations. We show that only the Ricci squared quadratic invariant contributes to give a different solution of those found in Einstein's general relativity. The perturbative solution is written as a power series in the $\beta$ parameter, the coefficient of the Ricci squared term in the quadratic gravitational action. We also show that, for monochromatic waves of a given angular frequency $\omega$, the perturbative solution can be summed out to give an exact solution to linearized version of quadratic gravity, for $0<\omega<c/\mid\beta\mid^{1/2}$. This result may lead to implications to the predictions for gravitational wave backgrounds of cosmological origin.Comment: 9 pages, to appear in CQ

The close limit from a null point of view: the advanced solution

We present a characteristic algorithm for computing the perturbation of a Schwarzschild spacetime by means of solving the Teukolsky equation. We implement the algorithm as a characteristic evolution code and apply it to compute the advanced solution to a black hole collision in the close approximation. The code successfully tracks the initial burst and quasinormal decay of a black hole perturbation through 10 orders of magnitude and tracks the final power law decay through an additional 6 orders of magnitude. Determination of the advanced solution, in which ingoing radiation is absorbed by the black hole but no outgoing radiation is emitted, is the first stage of a two stage approach to determining the retarded solution, which provides the close approximation waveform with the physically appropriate boundary condition of no ingoing radiation.Comment: Revised version, published in Phys. Rev. D, 34 pages, 13 figures, RevTe

Cosmic Parallax in Ellipsoidal Universe

The detection of a time variation of the angle between two distant sources would reveal an anisotropic expansion of the Universe. We study this effect of "cosmic parallax" within the "ellipsoidal universe" model, namely a particular homogeneous anisotropic cosmological model of Bianchi type I, whose attractive feature is the potentiality to account for the observed lack of power of the large-scale cosmic microwave background anisotropy. The preferred direction in the sky, singled out by the axis of symmetry inherent to planar symmetry of ellipsoidal universe, could in principle be constrained by future cosmic parallax data. However, that will be a real possibility if and when the experimental accuracy will be enhanced at least by two orders of magnitude.Comment: 9 pages, 2 figures, 1 table. Revised version to match published version. References adde

Cosmology of a Scalar Field Coupled to Matter and an Isotropy-Violating Maxwell Field

Motivated by the couplings of the dilaton in four-dimensional effective actions, we investigate the cosmological consequences of a scalar field coupled both to matter and a Maxwell-type vector field. The vector field has a background isotropy-violating component. New anisotropic scaling solutions which can be responsible for the matter and dark energy dominated epochs are identified and explored. For a large parameter region the universe expands almost isotropically. Using that the CMB quadrupole is extremely sensitive to shear, we constrain the ratio of the matter coupling to the vector coupling to be less than 10^(-5). Moreover, we identify a large parameter region, corresponding to a strong vector coupling regime, yielding exciting and viable cosmologies close to the LCDM limit.Comment: Refs. added, some clarifications. Published in JHEP10(2012)06

Anisotropic dark energy and ellipsoidal universe

A cosmological model with anisotropic dark energy is analyzed. The amount of deviation from isotropy of the equation of state of dark energy, the skewness \delta, generates an anisotropization of the large-scale geometry of the Universe, quantifiable by means of the actual shear \Sigma_0. Requiring that the level of cosmic anisotropization at the time of decoupling is such to solve the "quadrupole problem" of cosmic microwave background radiation, we find that |\delta| \sim 10^{-4} and |\Sigma_0| \sim 10^{-5}, compatible with existing limits derived from the magnitude-redshift data on type Ia supernovae.Comment: 10 pages, 3 figures. Revised version to match published version. References adde

Reconstruction of Black Hole Metric Perturbations from Weyl Curvature

Perturbation theory of rotating black holes is usually described in terms of Weyl scalars $\psi_4$ and $\psi_0$, which each satisfy Teukolsky's complex master wave equation and respectively represent outgoing and ingoing radiation. On the other hand metric perturbations of a Kerr hole can be described in terms of (Hertz-like) potentials $\Psi$ in outgoing or ingoing {\it radiation gauges}. In this paper we relate these potentials to what one actually computes in perturbation theory, i.e $\psi_4$ and $\psi_0$. We explicitly construct these relations in the nonrotating limit, preparatory to devising a corresponding approach for building up the perturbed spacetime of a rotating black hole. We discuss the application of our procedure to second order perturbation theory and to the study of radiation reaction effects for a particle orbiting a massive black hole.Comment: 6 Pages, Revtex