arXiv subjects

Laura Bernard

Publications and source records attributed to Laura Bernard.

35 records · Page 2Linked to original sources

arXiv2019

Black holes, gravitational waves and fundamental physics: a roadmap

The grand challenges of contemporary fundamental physics---dark matter, dark energy, vacuum energy, inflation and early universe cosmology, singularities and the hierarchy problem---all involve gravity as a key component. And of all gravitational phenomena, black holes stand out in their elegant simplicity, while harbouring some of the most remarkable predictions of General Relativity: event horizons, singularities and ergoregions. The hitherto invisible landscape of the gravitational Universe is being unveiled before our eyes: the historical direct detection of gravitational waves by the LIGO-Virgo collaboration marks the dawn of a new era of scientific exploration. Gravitational-wave astronomy will allow us to test models of black hole formation, growth and evolution, as well as models of gravitational-wave generation and propagation. It will provide evidence for event horizons and ergoregions, test the theory of General Relativity itself, and may reveal the existence of new fundamental fields. The synthesis of these results has the potential to radically reshape our understanding of the cosmos and of the laws of Nature. The purpose of this work is to present a concise, yet comprehensive overview of the state of the art in the relevant fields of research, summarize important open problems, and lay out a roadmap for future progress.

gr-qc↗

arXiv2018

Dynamics of compact binary systems in scalar-tensor theories: II. Center-of-mass and conserved quantities to 3PN order

The equations of motion of nonspinning compact binary systems at the third post-Newtonian (PN) order in massless scalar-tensor theories have recently been obtained. In the present paper, we complete this work by computing at 3PN order the ten integrals of motion together with the equations of motion in the center-of-mass frame. We then perform the reduction of the center-of-mass equations to quasi-circular orbits and determine the conserved energy and angular momentum for circular orbits.

gr-qc↗

arXiv2018

Scattering of scalar, electromagnetic and gravitational waves from binary systems

The direct detection of gravitational waves crowns decades of efforts in the modelling of sources and of increasing detectors' sensitivity. With future third-generation Earth-based detectors or space-based observatories, gravitational-wave astronomy will be at its full bloom. Previously brushed-aside questions on environmental or other systematic effects in the generation and propagation of gravitational waves are now begging for a systematic treatment. Here, we study how electromagnetic and gravitational radiation is scattered by a binary system. Scattering cross-sections, resonances and the effect of an impinging wave on a gravitational-bound binary are worked out for the first time. The ratio between the scattered-wave amplitude and the incident wave can be of order $10^{-5}$ for known pulsars, bringing this into the realm of future gravitational-wave observatories. For currently realistic distribution of compact-object binaries, the interaction cross-section is too small to be of relevance.

gr-qc↗

arXiv2018

Partially Massless Graviton on Beyond Einstein Spacetimes

We show that a partially massless graviton can propagate on a large set of spacetimes which are not Einstein spacetimes. Starting from a recently constructed theory for a massive graviton that propagates the correct number of degrees of freedom on an arbitrary spacetime, we first give the full explicit form of the scalar constraint responsible for the absence of a sixth degree of freedom. We then spell out generic conditions for the constraint to be identically satisfied, so that there is a scalar gauge symmetry which makes the graviton partially massless. These simplify if one assumes that spacetime is Ricci symmetric. Under this assumption, we find explicit non-Einstein spacetimes allowing for the propagation of a partially massless graviton.

hep-th↗

arXiv2018

Center-of-Mass Equations of Motion and Conserved Integrals of Compact Binary Systems at the Fourth Post-Newtonian Order

The dynamics of compact binary systems at the fourth post-Newtonian (4PN) approximation of general relativity has been recently completed in a self-consistent way. In this paper, we compute the ten Poincaré constants of the motion and present the equations of motion in the frame of the center of mass (CM), together with the corresponding CM Lagrangian, conserved energy and conserved angular momentum. Next, we investigate the reduction of the CM dynamics to the case of quasi-circular orbits. The non local (in time) tail effect at the 4PN order is consistently included, as well as the relevant radiation-reaction dissipative contributions to the energy and angular momentum.

gr-qc↗

arXiv2018

Ambiguity-Free Completion of the Equations of Motion of Compact Binary Systems at the Fourth Post-Newtonian Order

We present the first complete (i.e., ambiguity-free) derivation of the equations of motion of two non-spinning compact objects up to the 4PN order, based on the Fokker action of point particles in harmonic coordinates. The last ambiguity parameter is determined from first principle, by resorting to a matching between the near zone and far zone fields, and a consistent computation of the 4PN tail effect in d dimensions. Dimensional regularization is used throughout for treating IR divergences appearing at 4PN order, as well as UV divergences due to the model of point particles describing compact objects.

gr-qc↗

arXiv2018

Dimensional regularization of the IR divergences in the Fokker action of point-particle binaries at the fourth post-Newtonian order

The Fokker action of point-particle binaries at the fourth post-Newtonian (4PN) approximation of general relativity has been determined previously. However two ambiguity parameters associated with infra-red (IR) divergencies of spatial integrals had to be introduced. These two parameters were fixed by comparison with gravitational self-force (GSF) calculations of the conserved energy and periastron advance for circular orbits in the test-mass limit. In the present paper together with a companion paper, we determine both these ambiguities from first principle, by means of dimensional regularization. Our computation is thus entirely defined within the dimensional regularization scheme, for treating at once the IR and ultra-violet (UV) divergencies. In particular, we obtain crucial contributions coming from the Einstein-Hilbert part of the action and from the non-local tail term in arbitrary dimensions, which resolve the ambiguities.

gr-qc↗

arXiv2017

Conservative Dynamics of Binary Systems of Compact Objects at the Fourth Post-Newtonian Order

We review our recent derivation of a Fokker action describing the conservative dynamics of a compact binary system at the fourth post-Newtonian (4PN) approximation of general relativity. The two bodies are modeled by point particles, which induces ultraviolet (UV) divergences that are cured by means of dimensional regularization combined with a renormalization of the particle's wordlines. Associated with the propagation of wave tails at infinity is the appearance of a non-local-in-time conservative tail effect at the 4PN order in the Lagrangian. In turn this implies the appearance of infrared (IR) divergent integrals which are also regularized by means of dimensional regularization. We compute the Noetherian conserved energy and periastron advance for circular orbits at 4PN order, paying special attention to the treatment of the non-local terms. One ambiguity parameter remaining in the current formalism is determined by comparing those quantities, expressed as functions of the orbital frequency, with self-force results valid in the small mass ratio limit.

gr-qc↗

arXiv2017

Energy and periastron advance of compact binaries on circular orbits at the fourth post-Newtonian order

In this paper, we revisit and complete our preceding work on the Fokker Lagrangian describing the dynamics of compact binary systems at the fourth post-Newtonian (4PN) order in harmonic coordinates. We clarify the impact of the non-local character of the Fokker Lagrangian or the associated Hamiltonian on both the conserved energy and the relativistic periastron precession for circular orbits. We show that the non-locality of the action, due to the presence of the tail effect at the 4PN order, gives rise to an extra contribution to the conserved integral of energy with respect to the Hamiltonian computed on shell, which was not taken into account in our previous work. We also provide a direct derivation of the periastron advance by taking carefully into account this non-locality. We then argue that the infra-red (IR) divergences in the calculation of the gravitational part of the action are problematic, which motivates us to introduce a second ambiguity parameter, in addition to the one already assumed previously. After fixing these two ambiguity parameters by requiring that the conserved energy and the relativistic periastron precession for circular orbits are in agreement with numerical and analytical gravitational self-force calculations, valid in the limiting case of small mass ratio, we find that our resulting Lagrangian is physically equivalent to the one obtained in the ADM Hamiltonian approach.

gr-qc↗

arXiv2016

Linear spin-2 fields in most general backgrounds

We derive the full perturbative equations of motion for the most general background solutions in ghost-free bimetric theory in its metric formulation. Clever field redefinitions at the level of fluctuations enable us to circumvent the problem of varying a square-root matrix appearing in the theory. This greatly simplifies the expressions for the linear variation of the bimetric interaction terms. We show that these field redefinitions exist and are uniquely invertible if and only if the variation of the square-root matrix itself has a unique solution, which is a requirement for the linearised theory to be well-defined. As an application of our results we examine the constraint structure of ghost-free bimetric theory at the level of linear equations of motion for the first time. We identify a scalar combination of equations which is responsible for the absence of the Boulware-Deser ghost mode in the theory. The bimetric scalar constraint is in general not manifestly covariant in its nature. However, in the massive gravity limit the constraint assumes a covariant form when one of the interaction parameters is set to zero. For that case our analysis provides an alternative and almost trivial proof of the absence of the Boulware-Deser ghost. Our findings generalise previous results in the metric formulation of massive gravity and also agree with studies of its vielbein version.

hep-th↗

arXiv2016

Fokker action of non-spinning compact binaries at the fourth post-Newtonian approximation

The Fokker action governing the motion of compact binary systems without spins is derived in harmonic coordinates at the fourth post-Newtonian approximation (4PN) of general relativity. Dimensional regularization is used for treating the local ultraviolet (UV) divergences associated with point particles, followed by a renormalization of the poles into a redefinition of the trajectories of the point masses. Effects at the 4PN order associated with wave tails propagating at infinity are included consistently at the level of the action. A finite part procedure based on analytic continuation deals with the infrared (IR) divergencies at spatial infinity, which are shown to be fully consistent with the presence of near-zone tails. Our end result at 4PN order is Lorentz invariant and has the correct self-force limit for the energy of circular orbits. However, we find that it differs from the recently published result derived within the ADM Hamiltonian formulation of general relativity [T. Damour, P. Jaranowski, and G. Schäfer, Phys. Rev. D 89, 064058 (2014)]. More work is needed to understand this discrepancy.

gr-qc↗

arXiv2015

Bimetric gravity and dark matter

We review some recent proposals for relativistic models of dark matter in the context of bimetric gravity. The aim is to solve the problems of cold dark matter (CDM) at galactic scales, and to reproduce the phenomenology of the modified Newtonian dynamics (MOND), while still being in agreement with the standard cosmological model $Λ$-CDM at large scales. In this context a promising alternative is dipolar dark matter (DDM) in which two different species of dark matter particles are separately coupled to the two metrics of bigravity and are linked together by an internal vector field. The phenomenology of MOND then results from a mechanism of gravitational polarization. Probably the best formulation of the model is within the framework of recently developed massive bigravity theories. Then the gravitational sector of the model is safe by construction, but a ghostly degree of freedom in the decoupling limit is still present in the dark matter sector. Future work should analyse the cosmological solutions of the model and check the post-Newtonian parameters in the solar system.

gr-qc↗

arXiv2015

Phenomenology of Dark Matter via a Bimetric Extension of General Relativity

We propose a relativistic model of dark matter reproducing at once the concordance cosmological model $Λ$-Cold-Dark-Matter ($Λ$-CDM) at cosmological scales, and the phenomenology of the modified Newtonian dynamics (MOND) at galactic scales. To achieve this we postulate a non-standard form of dark matter, consisting of two different species of particles coupled to gravity via a bimetric extension of general relativity, and linked together through an internal vector field (a "graviphoton") generated by the mass of these particles. We prove that this dark matter behaves like ordinary cold dark matter at the level of first order cosmological perturbation, while a pure cosmological constant plays the role of dark energy. The MOND equation emerges in the non-relativistic limit through a mechanism of gravitational polarization of the dark matter medium in the gravitational field of ordinary matter. Finally we show that the model is viable in the solar system as it predicts the same parametrized post-Newtonian parameters as general relativity.

astro-ph.CO↗

arXiv2015

Consistent massive graviton on arbitrary backgrounds

We obtain the fully covariant linearized field equations for the metric perturbation in the de Rham-Gabadadze-Tolley (dRGT) ghost free massive gravities. For a subset of these theories, we show that the non dynamical metric that appears in the dRGT setup can be completely eliminated leading to the theory of a massive graviton moving in a single metric. This has a mass term which contains non trivial contributions of the space-time curvature. We show further how 5 covariant constraints can be obtained including one which leads to the tracelessness of the graviton on flat space-time and removes the Boulware-Deser ghost. The 5 constraints are obtained for a background metric which is arbitrary, i.e. which does not have to obey the background field equations.

hep-th↗

arXiv2015

Massive graviton on arbitrary background: derivation, syzygies, applications

We give the detailed derivation of the fully covariant form of the quadratic action and the derived linear equations of motion for a massive graviton in an arbitrary background metric (which were presented in arXiv:1410.8302 [hep-th]). Our starting point is the de Rham-Gabadadze-Tolley (dRGT) family of ghost free massive gravities and using a simple model of this family, we are able to express this action and these equations of motion in terms of a single metric in which the graviton propagates, hence removing in particular the need for a "reference metric" which is present in the non perturbative formulation. We show further how 5 covariant constraints can be obtained including one which leads to the tracelessness of the graviton on flat space-time and removes the Boulware-Deser ghost. This last constraint involves powers and combinations of the curvature of the background metric. The 5 constraints are obtained for a background metric which is unconstrained, i.e. which does not have to obey the background field equations. We then apply these results to the case of Einstein space-times, where we show that the 5 constraints become trivial, and Friedmann-Lema\^ıtre-Robertson-Walker space-times, for which we correct in particular some results that appeared elsewhere. To reach our results, we derive several non trivial identities, syzygies, involving the graviton fields, its derivatives and the background metric curvature. These identities have their own interest. We also discover that there exist backgrounds for which the dRGT equations cannot be unambiguously linearized.

hep-th↗

arXiv2014

Phenomenology of MOND and gravitational polarization

The phenomenology of MOND (flat rotation curves of galaxies, baryonic Tully-Fisher relation, etc.) is a basic set of phenomena relevant to galaxy dynamics and dark matter distribution at galaxy scales. Still unexplained today, it enjoys a remarkable property, known as the dielectric analogy, which could have far-reaching implications. In the present paper we discuss this analogy in the framework of simple non-relativistic models. We show how a specific form of dark matter, made of two different species of particles coupled to different Newtonian gravitational potentials, could permit to interpret in the most natural way the dielectric analogy of MOND by a mechanism of gravitational polarization.

astro-ph.CO↗

arXiv2012

String Derived Exophobic SU(6)xSU(2) GUTs

With the apparent discovery of the Higgs boson, the Standard Model has been confirmed as the theory accounting for all sub-atomic phenomena. This observation lends further credence to the perturbative unification in Grand Unified Theories (GUTs) and string theories. The free fermionic formalism yielded fertile ground for the construction of quasi--realistic heterotic--string models, which correspond to toroidal Z2xZ2 orbifold compactifications. In this paper we study a new class of heterotic-string models in which the GUT group is SU(6)xSU(2) at the string level. We use our recently developed fishing algorithm to extract an example of a three generation SU(6)xSU(2) GUT model. We explore the phenomenology of the model and show that it contains the required symmetry breaking Higgs representations. We show that the model admits flat directions that produce a Yukawa coupling for a single family. The novel feature of the SU(6)xSU(2) string GUT models is that they produce an additional family universal anomaly free U(1)symmetry that may remain unbroken below the string scale. The massless spectrum of the model is free of exotic states.

hep-th↗