We study in detail static spherically symmetric solutions of non linear Pauli-Fierz theory. We obtain a numerical solution with a constant density source. This solution shows a recovery of the corresponding solution of General Relativity via the Vainshtein mechanism. This result has already been presented by us in a recent letter, and we give here more detailed information on it as well as on the procedure used to obtain it. We give new analytic insights upon this problem, in particular for what concerns the question of the number of solutions at infinity. We also present a weak field limit which allows to capture all the salient features of the numerical solution, including the Vainshtein crossover and the Yukawa decay.
Ghost-free theories beyond the Horndeski class exhibit a partial breaking of the Vainshtein mechanism inside non-relativistic sources of finite extent. We exploit this breaking to identify new and novel astrophysical probes of these theories. Non-relativistic objects feel a gravitational force that is weaker than that predicted by general relativity. The new equation of hydrostatic equilibrium equation is derived and solved to predict the modified behaviour of stars. It is found that main-sequence stars are dimmer and cooler than their general relativity counterparts but the red giant phase is…
We study static spherically symmetric solutions of massive bi-gravity theory, free from the Boulware-Deser ghost. We show the recovery of General Relativity via the Vainshtein mechanism, in the weak limit of the physical metric. We find a single polynomial equation determining the behavior of the solution for distances smaller than the inverse graviton mass. This equation is generically of the seventh order, while for a specific choice of the parameters of the theory it can be reduced to lower orders. The solution is analytic in different regimes: for distances below the Vainshtein radius (whe…
We compute the scalar gravitational radiation from a binary pulsar system in the simplest model that exhibits the Vainshtein mechanism. The mechanism is successful in screening the effect from scalar fields conformally coupled to matter, although gravitational radiation is less suppressed relative to its general relativity predictions than static fifth forces effects within the pulsar system. This is due to a combination of two effects: firstly the existence of monopole and dipole radiation; secondly the Vainshtein suppression comes from the hierarchy of scales between the inverse frequency sc…
We investigate the observational consequences of scalar instabilities in bimetric theory, under the assumption that the Vainshtein mechanism restores general relativity within a certain distance from gravitational sources. We argue that early time instabilities have a negligible impact on observed structures. Assuming that the instabilities affect sub-horizon density fluctuations, we constrain the redshift, z_i, below which instabilities are ruled out. For the "minimal" beta_1-model, observational constraints are close to the theoretical expectations of z_i = 0.5, potentially allowing the mode…
We investigate static spherically symmetric solutions of nonlinear massive gravities. We first identify, in an ansatz appropriate to the study of those solutions, the analog of the decoupling limit (DL) that has been used in the Goldstone picture description. We show that the system of equations left over in the DL has regular solutions featuring a Vainshtein-like recovery of solutions of General Relativity (GR). Hence, the singularities found to arise integrating the full nonlinear system of equations are not present in the DL, despite the fact those singularities are usually thought to be du…
We reinvestigate the fate of the Vainhstein mechanism in the minimal model of dRGT massive gravity. As the latter is characterised by the complete absence of interactions in the decoupling limit, we study their structure at higher energies. We show that in static spherically symmetric configurations, the lowest energy scale of interactions is pushed up to the Planck mass. This fact points towards an absence of Vainshtein mechanism in this framework, but does not prove it. By resorting to the exact vacuum equations of motion, we show that there is indeed an obstruction that precludes any recove…
We develop a full four-dimensional numerical code to study scalar gravitational radiation emitted from binary systems and probe the Vainshtein mechanism in situations that break the static and spherical symmetry, relevant for binary pulsars as well as black holes and neutron stars binaries. The present study focuses on the cubic Galileon which arises as the decoupling limit of massive theories of gravity. Limitations associated with the numerical methods prevent us from reaching a physically realistic hierarchy of scales; nevertheless, within this context we observe the same power law scaling …
We study relativistic stars in Hordenski theories that evade the gravitational wave constraints and exhibit the Vainshtein mechanism, focusing on a model based on the cubic Galileon Lagrangian. We derive the scalar field profile for static spherically symmetric objects in asymptotically de Sitter space-time with a linear time dependence. The exterior solution matches to the black hole solution found in the literature. Due to the Vainshtein mechanism, the stellar structure is indistinguishable from that of General Relativity with the same central density as long as the radius of the star is sho…
We find static charged black hole solutions in nonlinear massive gravity. In the parameter space of two gravitational potential parameters $(α, β)$ we show that below the Compton wavelength the black hole solutions reduce to that of Reissner-Nordström via the Vainshtein mechanism in the weak field limit. In the simplest case with $α=β=0$ the solution exhibits the vDVZ discontinuity but ordinary General Relativity is recovered deep inside the horizon due to the existence of electric charge. For $α\neq0$ and $β=0$, the post-Newtonian parameter of the charged black hole evolves to that of General…
Theories which modify general relativity to explain the accelerated expansion of the Universe often use screening mechanisms to satisfy constraints on Solar System scales. We investigate the effects of the cosmic web and the local environmental density of dark matter halos on the screening properties of the Vainshtein and chameleon screening mechanisms. We compare the cosmic web morphology of dark matter particles, mass functions of dark matter halos, mass and radial dependence of screening, velocity dispersions and peculiar velocities, and environmental dependence of screening mechanisms in $…
We obtain static, spherically symmetric, and asymptotically flat numerical solutions of massive gravity with a source. Those solutions show, for the first time explicitly, a recovery of the Schwarzschild solution of General Relativity via the so-called Vainshtein mechanism.
We consider the massless limit of Higgs gravity, where the graviton becomes massive when the scalar fields acquire expectation values. We determine the Vainshtein scale and prove that massive gravity smoothly goes to General Relativity below this scale. We find that the Vainshtein scale depends on the particular action of scalar fields used to give mass to the graviton.
We study the third order solutions of the cosmological density perturbations in the Horndeski's most general scalar-tensor theory under the condition that the Vainshtein mechanism is at work. In this work, we thoroughly investigate the independence property of the functions describing the nonlinear mode-couplings, which is also useful for models within the general relativity. Then, we find that the solutions of the density contrast and the velocity divergence up to the third order ones are characterized by 6 parameters. Furthermore, the 1-loop order power spectra obtained with the third order …
We show that the strong self-interaction of the scalar polarization of a massive graviton can be understood in terms of the propagation of an extra ghost-like degree of freedom, thus relating strong coupling to the sixth degree of freedom discussed by Boulware and Deser in their Hamiltonian analysis of massive gravity. This enables one to understand the Vainshtein recovery of solutions of massless gravity as being due to the effect of the exchange of this ghost which gets frozen at distances larger than the Vainshtein radius. Inside this region, we can trust the two-field Lagrangian perturbati…
There has been a lot of research interest in modified gravity theories which utilise the Vainshtein mechanism to recover standard general relativity in regions with high matter density, such as the Dvali-Gabadadze-Porrati and Galileon models. The strong nonlinearity in the field equations of these theories implies that accurate theoretical predictions could only be made using high-resolution cosmological simulations. Previously, such simulations were usually done on regular meshes, which limits both their performance and the accuracy. In this paper, we report the development of a new algorithm…
In this paper we study long range modifications of gravity in the consistent framework of bigravity, which introduces a second massive spin-2 field and allows to continuously interpolate between the regime of General Relativity (mediated by a massless spin-2 field) and massive gravity (mediated by a massive spin-2 field). In particular we derive for the first time the equations for light deflection in this framework and study the effect on the lensing potential of galaxy clusters. By comparison of kinematic and lensing mass reconstructions, stringent bounds can be set on the parameter space of…
We study cosmic structures in the quadratic Degenerate Higher Order Scalar Tensor (qDHOST) model, which has been proposed as the most general scalar-tensor theory (up to quadratic dependence on the covariant derivatives of the scalar field), which is not plagued by the presence of ghost instabilities. We then study a static, spherically symmetric object embedded in de Sitter space-time for the qDHOST model. This model exhibits breaking of the Vainshtein mechanism inside the cosmic structure and Schwarzschild-de Sitter space-time outside, where General Relativity (GR) can be recovered within th…
In the context of a cubic Galileon model in which the Vainshtein mechanism suppresses the scalar field interactions with matter, we study low-density stars with slow rotation and static relativistic stars. We develop an expansion scheme to find approximated solutions inside the Vainshtein radius, and show that deviations from General Relativity (GR), while considering rotation, are also suppressed by the Vainshtein mechanism. In a quadratic coupling model, in which the scalarisation effect can significantly enhance deviations from GR in normal scalar tensor gravity, the Galileon term successfu…
Assuming static and spherically symmetric spacetimes in the ghost-free bigravity theory, we find a relativistic star solution, which is very close to that in general relativity. The coupling constants are classified into two classes: Class [I] and Class [II]. Although the Vainshtein screening mechanism is found in the weak gravitational field for both classes, we find that there is no regular solution beyond the critical value of the compactness in Class [I]. This implies that the maximum mass of a neutron star in Class [I] becomes much smaller than that in GR. On the other hand, for the solut…
We study spherically symmetric solutions in a covariant massive gravity model, which is a candidate for a ghost-free non-linear completion of the Fierz-Pauli theory. There is a branch of solutions that exhibits the Vainshtein mechanism, recovering General Relativity below a Vainshtein radius given by $(r_g m^2)^{1/3}$, where $m$ is the graviton mass and $r_g$ is the Schwarzschild radius of a matter source. Another branch of exact solutions exists, corresponding to Schwarzschild-de Sitter spacetimes where the curvature scale of de Sitter space is proportional to the mass squared of the graviton…
We investigate strong coupling effects in a covariant massive gravity model, which is a candidate for a ghost free non-linear completion of Fierz-Pauli. We analyse the conditions to recover general relativity via Vainshtein mechanism in the weak field limit, and find three main cases depending on the choice of parameters. In the first case, the potential is such that all non-linearities disappear and the vDVZ discontinuity cannot be avoided. In the second case, the Vainshtein mechanism allows to recover general relativity within a macroscopic radius from a source. In the last case, the strong …
I derive general conditions in order to explain the origin of the Vainshtein radius inside dRGT. The set of equations, which I have called "Vainshtein" conditions are extremal conditions of the dynamical metric ($g_{μν}$) containing all the degrees of freedom of the theory. The Vainshtein conditions are able to explain the coincidence between the Vainshtein radius in dRGT and the scale $r_0=\left(\frac{3}{2}r_s r_Λ^2\right)^{1/3}$, obtained naturally from the Schwarzschild de-Sitter (S-dS) space inside General Relativity (GR). In GR, this scale was interpreted as the maximum distance in order …
Massive gravity is a good theoretical laboratory to study modifications of General Relativity. The theory offers a concrete set-up to study models of dark energy, since it admits cosmological self-accelerating solutions in the vacuum, in which the size of the acceleration depends on the graviton mass. Moreover, non-linear gravitational self-interactions, in the proximity of a matter source, manage to mimic the predictions of linearised General Relativity, hence agreeing with solar-system precision measurements. In this article, we review our work in the subject, classifying, on one hand, stati…
We discuss static spherically symmetric solutions in a recently proposed non-local infrared modification of Einstein equations induced by a term $m^2g_{μν}\Box^{-1} R$, where $m$ is a mass scale. We find that, contrary to what happens in usual theories of massive gravity, in this non-local theory there is no vDVZ discontinuity and classical non-linearities do not become large below a Vainshtein radius parametrically larger than the Schwarzschild radius $r_S$. Rather on the contrary, in the regime $r\ll m^{-1}$ the corrections to the metric generated by a static body in GR are of the form $1+{\…
The recent observational data in cosmology seem to indicate that the universe is currently expanding in an accelerated way. An intriguing interpretation of these data is that they may just be signalling that Einstein's General Relativity is not the correct description of gravity when we consider distances of the order of the present horizon of the universe. In this thesis we consider two models which modify General Relativity at very large distances, the Cascading DGP and the dRGT massive gravity, and investigate their phenomenological viability. We start with a general introduction to standar…
The Brans-Dicke theory of gravity is one of the oldest ideas to extend general relativity by introducing a non-minimal coupling between the scalar field and gravity. The Solar System tests put tight constraints on the theory. In order to evade these constraints, various screening mechanisms have been proposed. These screening mechanisms allow the scalar field to couple to matter as strongly as gravity in low density environments while suppressing it in the Solar System. The Vainshtein mechanism, which is found in various modified gravity models such as massive gravity, braneworld models and sc…
We compare analytic predictions for real and Fourier space two-point statistics for biased tracers from a variety of Lagrangian Perturbation Theory approaches against those from state of the art N-body simulations in $f(R)$ Hu-Sawicki and the nDGP braneworld modified gravity theories. We show that the novel physics of gravitational collapse in scalar tensor theories with the chameleon or the Vainshtein screening mechanism can be effectively factored in with bias parameters analytically predicted using the Peak-Background Split formalism when updated to include the environmental sensitivity of …
We show that the ghost-free models of massive gravity and their multi-graviton extensions follow from considering higher dimensional General Relativity in Einstein-Cartan form on a discrete extra dimension, according to the Dimensional Deconstruction paradigm. We show that Dimensional Deconstruction is equivalent to a truncation of the Kaluza-Klein tower at the nonlinear level. Higher dimensional gravity is not recovered from a lower dimensional multi-graviton theory in the limit of a continuous extra dimension (infinite Kaluza-Klein tower) due to the appearance of a low strong coupling scale …
Gravitational waves provide a new probe into the strong-field regime of gravity. It is thus essential to identify the predictions of General Relativity on the nature of the two-body problem, and to contrast them to alternative theories. This thesis aims at comparing the predictions of General Relativity and scalar-tensor theories on gravitational observables using Effective Field Theory techniques. In a first part, we show how simple scalar-tensor theories can be embedded in the Non-Relativistic General Relativity approach to the two-body problem and highlight their essential features. Further…
This article extends bimetric formulations of massive gravity to make the mass of the graviton to depend on its environment. This minimal extension offers a novel way to reconcile massive gravity with local tests of general relativity without invoking the Vainshtein mechanism. On cosmological scales, it is argued that the model is stable and that it circumvents the Higuchi bound, hence relaxing the constraints on the parameter space. Moreover, with this extension the strong coupling scale is also environmentally dependent in such a way that it is kept sufficiently higher than the expansion rat…
We present a survey of the known cosmological and black hole solutions in ghost-free bigravity and massive gravity theories. These can be divided into three classes. First, there are solutions with proportional metrics, which are the same as in General Relativity with a cosmological term, which can be positive, negative or zero. Secondly, for spherically symmetric systems, there are solutions with non-bidiagonal metrics. The g-metric fulfills Einstein equations with a positive cosmological term and a matter source, while the f-metric is anti-de Sitter. The third class contains solutions with b…
Must a theory of quantum gravity have some truth to it if it can recover general relativity in some limit of the theory? This paper answers this question in the negative by indicating that general relativity is multiply realizable in quantum gravity. The argument is inspired by spacetime functionalism - multiple realizability being a central tenet of functionalism - and proceeds via three case studies: induced gravity, thermodynamic gravity, and entanglement gravity. In these, general relativity in the form of the Einstein field equations can be recovered from elements that are either manifest…
In Einstein's general relativity, gravity is mediated by a massless metric field. The extension of general relativity to consistently include a mass for the graviton has profound implications for gravitation and cosmology. Salient features of various massive gravity theories can be captured by Galileon models, the simplest of which is the cubic Galileon. The presence of the Galileon field leads to additional gravitational radiation in binary pulsars where the Vainshtein mechanism is less suppressed than its fifth-force counterpart, which deserves a detailed confrontation with observations. We …
We solve the Einstein equations in the Randall-Sundrum framework with a static, spherically symmetric matter distribution on the {\it physical brane} and obtain an approximate expression for the gravitational field outside the source to second order in the gravitational coupling. This expression when confined on the {\it physical brane} coincides with the standard form of the Schwarzschild metric. Therefore, the Randall-Sundrum scenario is consistent with the Mercury precession test of General Relativity.
We constrain effective field theories by going beyond the familiar positivity bounds that follow from unitarity, analyticity, and crossing symmetry of the scattering amplitudes. As interesting examples, we discuss the implications of the bounds for the Galileon and ghost-free massive gravity. The combination of our theoretical bounds with the experimental constraints on the graviton mass implies that the latter is either ruled out or unable to describe gravitational phenomena, let alone to consistently implement the Vainshtein mechanism, down to the relevant scales of fifth-force experiments, …
The conventional spacetime formulation of general relativity may be recast as a dynamics of spatial 3-geometries (geometrodynamics). Furthermore, geometrodynamics can be derived from first principles. I investigate two distinct sets of these: (i) Hojman, Kuchař and Teitelboim's, which presuppose that the spatial 3-geometries are embedded in spacetime. (ii) The 3-space approach of Barbour, Foster, Ó Murchadha and Anderson in which the spatial 3-geometries are presupposed but spacetime is not. I consider how the constituent postulates of the conventional approach to relativity emerge or are to b…
Barbour, Foster and Ó Murchadha have recently developed a new framework, called here {\it{the 3-space approach}}, for the formulation of classical bosonic dynamics. Neither time nor a locally Minkowskian structure of spacetime are presupposed. Both arise as emergent features of the world from geodesic-type dynamics on a space of 3-dimensional metric--matter configurations. In fact gravity, the universal light cone and Abelian gauge theory minimally coupled to gravity all arise naturally through a single common mechanism. It yields relativity -- and more -- without presupposing relativity. This…
The LARES (LAser RElativity Satellite) satellite was successfully launched in February 2012. The LARES space experiment is based on the orbital determinations of the laser ranged satellites LARES, LAGEOS (LAser GEOdynamics Satellite) and LAGEOS 2 together with the determination of the Earth's gravity field by the GRACE (Gravity Recovery And Climate Experiment) mission. It will test some fundamental physics predictions and provide accurate measurements of the framedragging effect predicted by Einstein's theory of General Relativity. By one hundred Monte Carlo simulations of the LARES experiment…
Einstein's vierbein formulation of general relativity based on the notion of distant parallelism (teleparallelism) naturally introduces a covariant surface term in addition to the Einstein-Hilbert action. We investigate the action principle in teleparallelism with the existence of spacetime boundaries and find that the covariant surface term exactly eliminates all the unwanted surface terms reside in the metric formulation of general relativity, as the role of a Gibbons-Hawking-York (GHY) term. The identity of such a covariant GHY term is further confirmed by the recovery of the correct black …
We use the open source, community-driven, numerical relativity software, the Einstein Toolkit to study the physics of eccentric, spinning, nonprecessing binary black hole mergers with mass-ratios $q=\{2, 4, 6\}$, individual dimensionless spin parameters $χ_{1z}=\pm0.6$, $χ_{2z}=\pm0.3$, that include higher order gravitational wave modes $\ell\leq4$, except for memory modes. Assuming stellar mass binary black hole mergers that may be detectable by the advanced LIGO detectors, we find that including modes up to $\ell=4$ increases the signal-to-noise of compact binaries between $3.5\%$ to $35\%$,…
Time is absolute in standard quantum theory and dynamical in general relativity. The combination of both theories into a theory of quantum gravity leads therefore to a "problem of time". In my essay I shall investigate those consequences for the concept of time that may be drawn without a detailed knowledge of quantum gravity. The only assumptions are the experimentally supported universality of the linear structure of quantum theory and the recovery of general relativity in the classical limit. Among the consequences are the fundamental timelessness of quantum gravity, the approximate nature …
Consistent Canonical Quantization of Gravity: Recovery of Classical GR from BRST-invariant Coherent States
Max-Planck-Institut für Physik（马克斯·普朗克物理研究所）；Arnold Sommerfeld Center, Ludwig-Maximilians-Universität（慕尼黑大学阿诺德·索末菲中心）；Sydney Consortium for Particle Physics and Cosmology, School of Physics, The University of Sydney（悉尼大学物理学院粒子物理与宇宙学联盟）
The recent observation of GW190412, the first high-mass ratio binary black-hole (BBH) merger, by the LIGO-Virgo Collaboration (LVC) provides a unique opportunity to probe the impact of subdominant harmonics and precession effects encoded in a gravitational wave signal. We present refined estimates of source parameters for GW190412 using \texttt{NRSur7dq4}, a recently developed numerical relativity waveform surrogate model that includes all $\ell \leq 4$ spin-weighted spherical harmonic modes as well as the full physical effects of precession. We compare our results with two different variants …
We investigate whether a spontaneously-broken gauge theory of the group $SU(2,2)$ may be a genuine competitor to General Relativity. The basic ingredients of the theory are an $SU(2,2)$ gauge field $A_μ$ and a Higgs field $W$ in the adjoint representation of the group with the Higgs field producing the symmetry breaking $SU(2,2)\rightarrow SO(1,3)\times SO(1,1)$. The action for gravity is polynomial in $\{A_μ,W\}$ and the field equations are first-order in derivatives of these fields. The new $SO(1,1)$ symmetry in the gravitational sector is interpreted in terms of an emergent scale symmetry a…
Coalescing binaries of neutron stars (NS) and black holes (BH) are one of the most important sources of gravitational waves for the upcoming network of ground based detectors. Detection and extraction of astrophysical information from gravitational-wave signals requires accurate waveform models. The Effective-One-Body and other phenomenological models interpolate between analytic results and $10-30$ orbit numerical relativity (NR) merger simulations. In this paper we study the accuracy of these models using new NR simulations that span $36-88$ orbits, with mass-ratios and black hole spins $(q,…
The covariance of loop quantum gravity studies of spherically symmetric space-times has recently been questioned. This is a reasonable worry, given that they are formulated in terms of slicing-dependent variables. We show explicitly that the resulting space-times, obtained from Dirac observables of the quantum theory, are covariant in the usual sense of the way -- they preserve the quantum line element -- for any gauge that is stationary (in the exterior, if there is a horizon). The construction depends crucially on the details of the Abelianized quantization considered, the satisfaction of th…
