Orbital Tests of Relativistic Gravity using Artificial Satellites

We reexamine non-Einsteinian effects observable in the orbital motion of low-orbit artificial Earth satellites. The motivations for doing so are twofold: (i) recent theoretical studies suggest that the correct theory of gravity might contain a scalar contribution which has been reduced to a small value by the effect of the cosmological expansion; (ii) presently developed space technologies should soon give access to a new generation of satellites endowed with drag-free systems and tracked in three dimensions at the centimeter level. Our analysis suggests that such data could measure two independent combinations of the Eddington parameters (beta - 1) and (gamma - 1) at the 10^-4 level and probe the time variability of Newton's "constant" at the d(ln G)/dt ~ 10^-13 yr^-1 level. These tests would provide well-needed complements to the results of the Lunar Laser Ranging experiment, and of the presently planned experiments aiming at measuring (gamma -1). In view of the strong demands they make on the level of non- gravitational perturbations, these tests might require a dedicated mission consisting of an optimized passive drag-free satellite.Comment: 17 pages, IHES/P/94/22 and CPT-94/P.E.302

A characteristic observable signature of preferred frame effects in relativistic binary pulsars

In this paper we develop a consistent, phenomenological methodology to measure preferred-frame effects (PFEs) in binary pulsars that exhibit a high rate of periastron advance. We show that in these systems the existence of a preferred frame for gravity leads to an observable characteristic `signature' in the timing data, which uniquely identifies this effect. We expand the standard Damour-Deruelle timing formula to incorporate this `signature' and show how this new PFE timing model can be used to either measure or constrain the parameters related to a violation of the local Lorentz invariance of gravity in the strong internal fields of neutron stars. In particular, we demonstrate that in the presence of PFEs we expect a set of the new timing parameters to have a unique relationship that can be measured and tested incontrovertibly. This new methodology is applied to the Double Pulsar, which turns out to be the ideal test system for this kind of experiments.The currently available dataset allows us only to study the impact of PFEs on the orbital precession rate, d omega/dt, providing limits that are, at the moment, clearly less stringent than existing limits on PFE strong-field parameters. However, simulations show that the constraints improve fast in the coming years, allowing us to study all new PFE timing parameters and to check for the unique relationship between them. Finally, we show how a combination of several suitable systems in a "PFE antenna array", expected to be availabe for instance with the Square-Kilometre-Array (SKA), provides full sensitivity to possible violations of local Lorentz invariance in strong gravitational fields in all directions of the sky. This PFE antenna array may eventually allow us to determine the direction of a preferred frame should it exist.Comment: Accepted for publication in MNRAS, 12 pages, 5 figures, figures 3 and 5 in reduced quality due to size limitation

Gravitational Self Force in a Schwarzschild Background and the Effective One Body Formalism

We discuss various ways in which the computation of conservative Gravitational Self Force (GSF) effects on a point mass moving in a Schwarzschild background can inform us about the basic building blocks of the Effective One-Body (EOB) Hamiltonian. We display the information which can be extracted from the recently published GSF calculation of the first-GSF-order shift of the orbital frequency of the last stable circular orbit, and we combine this information with the one recently obtained by comparing the EOB formalism to high-accuracy numerical relativity (NR) data on coalescing binary black holes. The information coming from GSF data helps to break the degeneracy (among some EOB parameters) which was left after using comparable-mass NR data to constrain the EOB formalism. We suggest various ways of obtaining more information from GSF computations: either by studying eccentric orbits, or by focussing on a special zero-binding zoom-whirl orbit. We show that logarithmic terms start entering the post-Newtonian expansions of various (EOB and GSF) functions at the fourth post-Newtonian (4PN) level, and we analytically compute the first logarithm entering a certain, gauge-invariant "redshift" GSF function (defined along the sequence of circular orbits).Comment: 44 page

About the Statistical Properties of Cosmological Billiards

We summarize some recent progress in the understanding of the statistical properties of cosmological billiards.Comment: 10 pages, 5 figures, 2 tables, Proceedings of The second Galileo-XuGuangqi Meeting, 11-16/07/2010, Ventimiglia, Ital

Post-Newtonian accurate parametric solution to the dynamics of spinning compact binaries in eccentric orbits: The leading order spin-orbit interaction

We derive Keplerian-type parametrization for the solution of post-Newtonian (PN) accurate conservative dynamics of spinning compact binaries moving in eccentric orbits. The PN accurate dynamics that we consider consists of the third post-Newtonian accurate conservative orbital dynamics influenced by the leading order spin effects, namely the leading order spin-orbit interactions. The orbital elements of the representation are explicitly given in terms of the conserved orbital energy, angular momentum and a quantity that characterizes the leading order spin-orbit interactions in Arnowitt, Deser, and Misner-type coordinates. Our parametric solution is applicable in the following two distinct cases: (i) the binary consists of equal mass compact objects, having two arbitrary spins, and (ii) the binary consists of compact objects of arbitrary mass, where only one of them is spinning with an arbitrary spin. As an application of our parametrization, we present gravitational wave polarizations, whose amplitudes are restricted to the leading quadrupolar order, suitable to describe gravitational radiation from spinning compact binaries moving in eccentric orbits. The present parametrization will be required to construct `ready to use' reference templates for gravitational waves from spinning compact binaries in inspiralling eccentric orbits. Our parametric solution for the post-Newtonian accurate conservative dynamics of spinning compact binaries clearly indicates, for the cases considered, the absence of chaos in these systems. Finally, we note that our parametrization provides the first step in deriving a fully second post-Newtonian accurate `timing formula', that may be useful for the radio observations of relativistic binary pulsars like J0737-3039.Comment: 18 pages, accepted by Phys. Rev.

Measurability of the tidal polarizability of neutron stars in late-inspiral gravitational-wave signals

The gravitational wave signal from a binary neutron star inspiral contains information on the nuclear equation of state. This information is contained in a combination of the tidal polarizability parameters of the two neutron stars and is clearest in the late inspiral, just before merger. We use the recently defined tidal extension of the effective one-body formalism to construct a controlled analytical description of the frequency-domain phasing of neutron star inspirals up to merger. Exploiting this analytical description we find that the tidal polarizability parameters of neutron stars can be measured by the advanced LIGO-Virgo detector network from gravitational wave signals having a reasonable signal-to-noise ratio of $\rho=16$. This measurability result seems to hold for all the nuclear equations of state leading to a maximum mass larger than $1.97M_\odot$. We also propose a promising new way of extracting information on the nuclear equation of state from a coherent analysis of an ensemble of gravitational wave observations of separate binary merger events.Comment: 28 pages, 6 figures. Submitted to Phys. Rev.

Theoretical Aspects of the Equivalence Principle

We review several theoretical aspects of the Equivalence Principle (EP). We emphasize the unsatisfactory fact that the EP maintains the absolute character of the coupling constants of physics while General Relativity, and its generalizations (Kaluza-Klein,..., String Theory), suggest that all absolute structures should be replaced by dynamical entities. We discuss the EP-violation phenomenology of dilaton-like models, which is likely to be dominated by the linear superposition of two effects: a signal proportional to the nuclear Coulomb energy, related to the variation of the fine-structure constant, and a signal proportional to the surface nuclear binding energy, related to the variation of the light quark masses. We recall the various theoretical arguments (including a recently proposed anthropic argument) suggesting that the EP be violated at a small, but not unmeasurably small level. This motivates the need for improved tests of the EP. These tests are probing new territories in physics that are related to deep, and mysterious, issues in fundamental physics.Comment: 21 pages, no figures; submitted to a "focus issue" of Classical and Quantum Gravity on Tests of the Weak Equivalence Principle, organized by Clive Speake and Clifford Wil

Testing gravity to second post-Newtonian order: a field-theory approach

A new, field-theory-based framework for discussing and interpreting tests of gravity, notably at the second post-Newtonian (2PN) level, is introduced. Contrary to previous frameworks which attempted at parametrizing any conceivable deviation from general relativity, we focus on the best motivated class of models, in which gravity is mediated by a tensor field together with one or several scalar fields. The 2PN approximation of these "tensor-multi-scalar" theories is obtained thanks to a diagrammatic expansion which allows us to compute the Lagrangian describing the motion of N bodies. In contrast with previous studies which had to introduce many phenomenological parameters, we find that the 2PN deviations from general relativity can be fully described by only two new 2PN parameters, epsilon and zeta, beyond the usual (Eddington) 1PN parameters beta and gamma. It follows from the basic tenets of field theory, notably the absence of negative-energy excitations, that (beta-1), epsilon and zeta (as well as any new parameter entering higher post-Newtonian orders) must tend to zero with (gamma-1). It is also found that epsilon and zeta do not enter the 2PN equations of motion of light. Therefore, light-deflection or time-delay experiments cannot probe any theoretically motivated 2PN deviation from general relativity, but they can give a clean access to (gamma-1), which is of greatest significance as it measures the basic coupling strength of matter to the scalar fields. Because of the importance of self-gravity effects in neutron stars, binary-pulsar experiments are found to constitute a unique testing ground for the 2PN structure of gravity. A simplified analysis of four binary pulsars already leads to significant constraints: |epsilon| < 7x10^-2, |zeta| < 6x10^-3.Comment: 63 pages, 11 figures.ps.tar.gz.uu, REVTeX 3.

Effective field theory calculation of second post-Newtonian binary dynamics

We use the effective field theory for gravitational bound states, proposed by Goldberger and Rothstein, to compute the interaction Lagrangian of a binary system at the second Post-Newtonian order. Throughout the calculation, we use a metric parametrization based on a temporal Kaluza-Klein decomposition and test the claim by Kol and Smolkin that this parametrization provides important calculational advantages. We demonstrate how to use the effective field theory method efficiently in precision calculations, and we reproduce known results for the second Post-Newtonian order equations of motion in harmonic gauge in a straightforward manner.Comment: Replaced with published versio