The Evolution of Bias - Generalized

Fry (1996) showed that galaxy bias has the tendency to evolve towards unity, i.e. in the long run, the galaxy distribution tends to trace that of matter. Generalizing slightly Fry's reasoning, we show that his conclusion remains valid in theories of modified gravity (or equivalently, complex clustered dark energy). This is not surprising: as long as both galaxies and matter are subject to the same force, dynamics would drive them towards tracing each other. This holds, for instance, in theories where both galaxies and matter move on geodesics. This relaxation of bias towards unity is tempered by cosmic acceleration, however: the bias tends towards unity but does not quite make it, unless the formation bias were close to unity. Our argument is extended in a straightforward manner to the case of a stochastic or nonlinear bias. An important corollary is that dynamical evolution could imprint a scale dependence on the large scale galaxy bias. This is especially pronounced if non-standard gravity introduces new scales to the problem: the bias at different scales relaxes at different rates, the larger scales generally more slowly and retaining a longer memory of the initial bias. A consistency test of the current (general relativity + uniform dark energy) paradigm is therefore to look for departure from a scale independent bias on large scales. A simple way is to measure the relative bias of different populations of galaxies which are at different stages of bias relaxation. Lastly, we comment on the possibility of directly testing the Poisson equation on cosmological scales, as opposed to indirectly through the growth factor.Comment: 8 pages, 2 figures. References added. Accepted for publication in Physical Review

Testing Alternative Theories of Gravity using LISA

We investigate the possible bounds which could be placed on alternative theories of gravity using gravitational wave detection from inspiralling compact binaries with the proposed LISA space interferometer. Specifically, we estimate lower bounds on the coupling parameter \omega of scalar-tensor theories of the Brans-Dicke type and on the Compton wavelength of the graviton \lambda_g in hypothetical massive graviton theories. In these theories, modifications of the gravitational radiation damping formulae or of the propagation of the waves translate into a change in the phase evolution of the observed gravitational waveform. We obtain the bounds through the technique of matched filtering, employing the LISA Sensitivity Curve Generator (SCG), available online. For a neutron star inspiralling into a 10^3 M_sun black hole in the Virgo Cluster, in a two-year integration, we find a lower bound \omega > 3 * 10^5. For lower-mass black holes, the bound could be as large as 2 * 10^6. The bound is independent of LISA arm length, but is inversely proportional to the LISA position noise error. Lower bounds on the graviton Compton wavelength ranging from 10^15 km to 5 * 10^16 km can be obtained from one-year observations of massive binary black hole inspirals at cosmological distances (3 Gpc), for masses ranging from 10^4 to 10^7 M_sun. For the highest-mass systems (10^7 M_sun), the bound is proportional to (LISA arm length)^{1/2} and to (LISA acceleration noise)^{-1/2}. For the others, the bound is independent of these parameters because of the dominance of white-dwarf confusion noise in the relevant part of the frequency spectrum. These bounds improve and extend earlier work which used analytic formulae for the noise curves.Comment: 16 pages, 9 figures, submitted to Classical & Quantum Gravit

Test of constancy of speed of light with rotating cryogenic optical resonators

A test of Lorentz invariance for electromagnetic waves was performed by comparing the resonance frequencies of two optical resonators as a function of orientation in space. In terms of the Robertson-Mansouri-Sexl theory, we obtain $\beta-\delta-1/2=(+0.5\pm 3\pm 0.7) E-10$, a ten-fold improvement compared to the previous best results. We also set a first upper limit for a so far unknown parameter of the Standard Model Extension test theory, $|(\tilde{\kappa}_{e-})^{ZZ}| < 2\cdot E-14$.Comment: 4 pages, 2 figures, accepted for publication Phys. Rev. A (2005

Cosmological test of gravity with polarizations of stochastic gravitational waves around 0.1-1 Hz

In general relativity, a gravitational wave has two polarization modes (tensor mode), but it could have additional polarizations (scalar and vector modes) in the early stage of the universe, where the general relativity may not strictly hold and/or the effect of higher-dimensional gravity may become significant. In this paper, we discuss how to detect extra-polarization modes of stochastic gravitational wave background (GWB), and study the separability of each polarization using future space-based detectors such as BBO and DECIGO. We specifically consider two plausible setups of the spacecraft constellations consisting of two and four clusters, and estimate the sensitivity to each polarization mode of GWBs. We find that a separate detection of each polarization mode is rather sensitive to the geometric configuration and distance between clusters and that the clusters should be, in general, separated by an appropriate distance. This seriously degrades the signal sensitivity, however, for suitable conditions, space-based detector can separately detect scalar, vector and tensor modes of GWBs with energy density as low as ~10^-15.Comment: 16 pages, 11 figure

The low dimensional dynamical system approach in General Relativity: an example

In this paper we explore one of the most important features of the Galerkin method, which is to achieve high accuracy with a relatively modest computational effort, in the dynamics of Robinson-Trautman spacetimes.Comment: 7 pages, 5 figure

Einstein and Jordan frames reconciled: a frame-invariant approach to scalar-tensor cosmology

Scalar-Tensor theories of gravity can be formulated in different frames, most notably, the Einstein and the Jordan one. While some debate still persists in the literature on the physical status of the different frames, a frame transformation in Scalar-Tensor theories amounts to a local redefinition of the metric, and then should not affect physical results. We analyze the issue in a cosmological context. In particular, we define all the relevant observables (redshift, distances, cross-sections, ...) in terms of frame-independent quantities. Then, we give a frame-independent formulation of the Boltzmann equation, and outline its use in relevant examples such as particle freeze-out and the evolution of the CMB photon distribution function. Finally, we derive the gravitational equations for the frame-independent quantities at first order in perturbation theory. From a practical point of view, the present approach allows the simultaneous implementation of the good aspects of the two frames in a clear and straightforward way.Comment: 15 pages, matches version to be published on Phys. Rev.

On gravitational-wave spectroscopy of massive black holes with the space interferometer LISA

Newly formed black holes are expected to emit characteristic radiation in the form of quasi-normal modes, called ringdown waves, with discrete frequencies. LISA should be able to detect the ringdown waves emitted by oscillating supermassive black holes throughout the observable Universe. We develop a multi-mode formalism, applicable to any interferometric detectors, for detecting ringdown signals, for estimating black hole parameters from those signals, and for testing the no-hair theorem of general relativity. Focusing on LISA, we use current models of its sensitivity to compute the expected signal-to-noise ratio for ringdown events, the relative parameter estimation accuracy, and the resolvability of different modes. We also discuss the extent to which uncertainties on physical parameters, such as the black hole spin and the energy emitted in each mode, will affect our ability to do black hole spectroscopy.Comment: 44 pages, 21 figures, 10 tables. Minor changes to match version in press in Phys. Rev.

Improved tests of Local Position Invariance using 87Rb and 133Cs fountains

We report tests of local position invariance based on measurements of the ratio of the ground state hyperfine frequencies of 133Cs and 87Rb in laser-cooled atomic fountain clocks. Measurements extending over 14 years set a stringent limit to a possible variation with time of this ratio: d ln(nu_Rb/nu_Cs)/dt=(-1.39 +/- 0.91)x 10-16 yr-1. This improves by a factor of 7.7 over our previous report (H. Marion et al., Phys. Rev. Lett. 90, 150801 (2003)). Our measurements also set the first limit to a fractional variation of the Rb/Cs ratio with gravitational potential at the level of c^2 d ln(nu_Rb/nu_Cs)/dU=(0.11 +/- 1.04)x 10^-6, providing a new stringent differential redshift test. The above limits equivalently apply to the fractional variation of the quantity alpha^{-0.49}x(g_Rb/g_Cs), which involves the fine structure constant alpha and the ratio of the nuclear g-factors of the two alkalis. The link with variations of the light quark mass is also presented together with a global analysis combining with other available highly accurate clock comparisons.Comment: 5 pages, 3 figures, 3 tables, 34 reference

Post-Newtonian gravitational radiation and equations of motion via direct integration of the relaxed Einstein equations. III. Radiation reaction for binary systems with spinning bodies

Using post-Newtonian equations of motion for fluid bodies that include radiation-reaction terms at 2.5 and 3.5 post-Newtonian (PN) order (O[(v/c)^5] and O[(v/c)^7] beyond Newtonian order), we derive the equations of motion for binary systems with spinning bodies. In particular we determine the effects of radiation-reaction coupled to spin-orbit effects on the two-body equations of motion, and on the evolution of the spins. For a suitable definition of spin, we reproduce the standard equations of motion and spin-precession at the first post-Newtonian order. At 3.5PN order, we determine the spin-orbit induced reaction effects on the orbital motion, but we find that radiation damping has no effect on either the magnitude or the direction of the spins. Using the equations of motion, we find that the loss of total energy and total angular momentum induced by spin-orbit effects precisely balances the radiative flux of those quantities calculated by Kidder et al. The equations of motion may be useful for evolving inspiraling orbits of compact spinning binaries.Comment: 19 pages, small corrections, equivalent to published versio