In this work we study the gravitational radiation produced by a keplerian binary system within the context of Very Special Linear Gravity (VSLG), a novel theory of linearized gravity in the framework of Very Special Relativity (VSR) allowing for a gauge-invariant mass $m_g$ of the graviton. For this task, we exploit Effective Field Theory's techniques, which require, among others, the calculation of the squared amplitude of the emission process and therefore the polarization sum for VSLG gravitons. Working in the radiation zone and using the standard energy momentum tensor's expression for keplerian binaries, we derive and study the properties of the VSLG energy loss and period decrease rates, also verifying they reduce to the correct General Relativity limit when sending $m_g\to0$. Finally, using astronomical data from the Hulse-Taylor binary and the Double Pulsar J0737-3039, we obtain an upperbound on the VSLG graviton mass of $m_g\sim 10^{-21}eV$ that, while being comparable to bounds obtained in this same way for other massive gravity models, is still weaker than the kinematical bound $\sim 10^{-22}eV$ obtained from the combined observation of the astronomical events GW170817 and GRB170817A, which should still hold in VSLG.
By comparing the observed orbital decay of the binary pulsars PSRB1913+16 and PSRB1534+12 to that predicted by general relativity due to gravitational-wave emission, we are able to bound the mass of the graviton to be less than $7.6\times10^{-20} \text{eV}/c^2$ at 90% confidence. This is the first such bound to be derived from dynamic gravitational fields. It is approximately two orders of magnitude weaker than the static-field bound from solar system observations, and will improve with further observations.
Using a formulation of the post-Newtonian expansion in terms of Feynman graphs, we discuss how various tests of General Relativity (GR) can be translated into measurement of the three- and four-graviton vertices. In problems involving only the conservative dynamics of a system, a deviation of the three-graviton vertex from the GR prediction is equivalent, to lowest order, to the introduction of the parameter beta_{PPN} in the parametrized post-Newtonian formalism, and its strongest bound comes from lunar laser ranging, which measures it at the 0.02% level. Deviation of the three-graviton verte…
In this paper we provide a possible realization of Penrose's idea of nonlinear gravitons using a new description of nonmetric general relativity. In the addressal of issues surrounding the normalizability of the Kodama state and its reliability as a ground state for gravity, we expand the theory in fluctuations about the Kodama state. This produces a theory of complex gravity with a well-defined Hilbert space structure, whose quantization we carry out both at the linearized level and in the full nonlinear theory. The results of this paper demonstrate the preservation of the physical degrees of…
Massive gravitons are features of some alternatives to general relativity. This has motivated experiments and observations that, so far, have been consistent with the zero mass graviton of general relativity, but further tests will be valuable. A basis for new tests may be the high sensitivity gravitational wave experiments that are now being performed, and the higher sensitivity experiments that are being planned. In these experiments it should be feasible to detect low levels of dispersion due to nonzero graviton mass. One of the most promising techniques for such a detection may be the puls…
In Einstein's general relativity (GR), gravity is described by a massless spin-2 metric field, and the extension of GR to include a mass term for the graviton has profound implication for gravitation and cosmology. Besides the gravity experiments carried out in the Solar System and those recently with gravitational waves (GWs), pulsar timing observations provide a complementary means to test the masslessness of graviton. In this contribution, I overview three methods in probing the mass of graviton from precision timing of binary pulsars via the modified gravitational radiation (hence, the obs…
Traditional derivations of general relativity from the graviton degrees of freedom assume space-time Lorentz covariance as an axiom. In this essay, we survey recent evidence that general relativity is the unique spatially-covariant effective field theory of the transverse, traceless graviton degrees of freedom. The Lorentz covariance of general relativity, having not been assumed in our analysis, is thus plausibly interpreted as an accidental or emergent symmetry of the gravitational sector. From this point of view, Lorentz covariance is a necessary feature of low-energy graviton dynamics, not…
The close agreement between the predictions of dynamical general relativity for the radiated power of a compact binary system and the observed orbital decay of the binary pulsars PSR B1913+16 and PSR B1534+12 allows us to bound the graviton mass to be less than 7.6 x 10^{-20} eV with 90% confidence. This bound is the first to be obtained from dynamic, as opposed to static-field, relativity. The resulting limit on the graviton mass is within two orders of magnitude of that from solar system measurements, and can be expected to improve with further observations.
The effect of a narrow-band isotropic stochastic GW background on pulsar timing and astrometric measurements is studied. Such a background appears in some theories of gravity. We show that the existing millisecond pulsar timing accuracy ($\sim 0.2 \rm{μs}$) strongly constrains possible observational consequences of theory of massive gravity with spontaneous Lorentz braking \cite{dtt:2005}, essentially ruling out significant contribution of massive gravitons to the local dark halo density. The present-day accuracy of astrometrical measurements ($\sim 100 \rm{μas}$) sets less stringent constrain…
In Einstein's general relativity, gravity is mediated by a massless spin-2 metric field, and its extension to include a mass for the graviton has profound implication for gravitation and cosmology. In 2002, Finn and Sutton used the gravitational-wave (GW) back-reaction in binary pulsars, and provided the first bound on the mass of graviton. Here we provide an improved analysis using 9 well-timed binary pulsars with a phenomenological treatment. First, individual mass bounds from each pulsar are obtained in the frequentist approach with the help of an ordering principle. The best upper limit on…
Pulsars, especially millisecond pulsars, are intrinsically very stable celestial clocks, and their great pulse period stability open up a wide range of potential applications to astronomical phenomena, such as a natural detector for very low frequency ($10^{-7}-10^{-9}$ Hz) gravitational waves (GWs) background from supermassive black hole binaries. Double neutron star (DNS) binary systems, containing one or two radio pulsars, lose orbital energy by gravitational radiation, which leads to the orbital shrink. As a result, two neutron stars get closer and closer, during which it contributes to th…
We introduce the concept of stationary graviton non-Gaussianity (nG), an observable that can be probed in terms of 3-point correlation functions of a stochastic gravitational wave (GW) background. When evaluated in momentum space, stationary nG corresponds to folded bispectra of graviton nG. We determine 3-point overlap functions for testing stationary nG with pulsar timing array GW experiments, and we obtain the corresponding optimal signal-to-noise ratio. For the first time, we consider 3-point overlap functions including scalar graviton polarizations (which can be motivated in theories of m…
It is a review paper. General relativity (GR) is presented in the field theoretical form, where gravitational field (metric perturbations) together with other physical fields are propagated in an auxiliary arbitrary curved background spacetime. Conserved currents are constructed and expressed through divergences of antisymmetrical tensor densities (superpotentials). This permits to connect local properties of perturbations with the quasi-local nature of the conserved quantities in GR. The problem of the non-localization of energy in GR is presented in exact mathematical expressions. A modifica…
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 …
In this review we aim to describe the most stringent tests of the strong equivalence principle, the fundamental principle of General Relativity, using pulsar timing. For this purpose, we first construct the parametrized post-Newtonian and post-Keplerian formalism together with their parameters. Then we constrain the post-Newtonian parameters associated to the violation of the strong equivalence principle with the most stringent tests using pulsar timing techniques. We will in particular see that these bounds are the most constraining limits on a violation of the principle. Finally we will disc…
The dynamic status of scalar fields is studied in the Hamiltonian approach to the General Relativity. We show that the conformal coupling of the scalar field violates the standard geometrical structure of the Einstein equations in GR and their solutions including the Schwarzschild one and the Newton static interaction. In order to restore the standard geometrical structure of GR, the scalar field is mixed with the scale metric component by the Bekenstein type transformation. This "scalar-scale" mixing converts the conformal coupling scalar field with conformal weight (n= -1) into the minimal c…
We investigate the production of gravitational waves during the inspiral of compact binaries close to their merger in the context of a conformal gravity model. The model incorporates five massive polarization degrees of freedom, besides the two massless gravitational wave polarizations of general relativity. For small graviton mass, we find that the amplitude of the gravitational waves is strongly suppressed as compared to general relativity and decreases as coalescence is approached, which contradicts the observational fact. We conclude that this model with small graviton mass, including a re…
In this paper we consider photon-photon scattering due to self-induced gravitational perturbations on a Minkowski background. We focus on four-wave interaction between plane waves with weakly space and time dependent amplitudes, since interaction involving a fewer number of waves is excluded by energy-momentum conservation. The Einstein-Maxwell system is solved perturbatively to third order in the field amplitudes and the coupling coefficients are found for arbitrary polarizations in the center of mass system. Comparisons with calculations based on quantum field theoretical methods are made, a…
Testing gravitational theories by binary pulsars nowadays becomes a key issue. For the general screened modified gravity (SMG), the post-Keplerian parameters in the neutron star (NS) - white dwarf (WD) binaries differ from those of general relativity (GR), and the differences are quantified by the scalar charge $ε_{\scriptscriptstyle\rm WD}$ of WD. After deriving the constraints on $ε_{\scriptscriptstyle\rm WD}$ from four different NS-WD binaries, we find that $ε_{\scriptscriptstyle\rm WD}$ is different from zero at the 2$σ$ level in all the cases studied, and there exists an inverse correlati…
Using the instanton representation method, we re-construct graviton solutions about DeSitter spacetime. We have used this example as a testing arena to expose the internal structure of the method and to establish that it works for known solutions. This paper is a precursor for its application to the construction of new General Relativity solutions in future work.
Recent nonlinear completions of Fierz-Pauli theory for a massive spin-2 field include nonlinear massive gravity and bimetric theories. The spectrum of black-hole solutions in these theories is rich, and comprises the same vacuum solutions of Einstein's gravity enlarged to include a cosmological constant. It was recently shown that Schwarzschild (de Sitter) black holes in these theories are generically unstable against spherical perturbations. Here we show that a notable exception is partially massless gravity, where the mass of the graviton is fixed in terms of the cosmological constant by μ^2…
We study all translationally and rotationally invariant local theories involving massless spin 2 and spin 1 particles that mediate long range forces, allowing for general energy relations and violation of boost invariance. Although gauge invariance is not a priori required to describe non Lorentz invariant theories, we first establish that locality requires `soft gauge invariance'. Then by taking the soft graviton limit in scattering amplitudes, we prove that in addition to the usual requirement of universal graviton couplings, the special relativistic energy-momentum relation is also required…
General Relativity extended through a dynamical scalar quartet is proposed as a theory of the scalar-vector-tensor gravity, generically describing the unified gravitational dark matter (DM) and dark energy (DE). The implementation in the weak-field limit of the Higgs mechanism for the gravity, with a redefinition of metric field, is exposed in a generally covariant form. Under a natural restriction on parameters, the redefined theory possesses in the linearized approximation by a residual transverse-diffeomorphism invariance, and consistently comprises the massless tensor graviton and a massiv…
In this paper a solution for a static spherically symmetric body is thoroughly considered in the framework of the Relativistic Theory of Gravitation. By the comparison of this solution with the Schwarzschild solution in General Relativity their substantial difference is established in the region close to the Schwarzschild sphere. Just this difference excludes the possibility of collapse to form ``black holes''.
In this paper, we study the thick brane system in the so-called $f(Q)$ gravity, where the gravitational interaction was encoded by the nonmetricity $Q$ like scalar curvature $R$ in general relativity. With a special choice of $f(Q)=Q-b Q^n$, we find that the thick brane system can be solved analytically with the first-order formalism, where the complicated second-order differential equation is transformed to several first-order differential equations. Moreover, the stability of the thick brane system under tensor perturbation is also investigated. It is shown that the tachyonic states are abse…
We revisit the decay of the orbital period in binary systems that occurs due to the emission of gravitational waves in the context of modified gravity models where the coupling $G_{gw}$ between matter and on-shell gravitons is allowed to differ from the Newton constant $G_N$. Using the most precise orbital parameters of binary pulsars, those of the Double Pulsar, we constrain the ratio $G_{gw}/G_N$ to the level of $10^{-4}$, improving by two orders of magnitude the present bound on this quantity.
In the report, the theory of unimodular bimode gravity built on principles of unimodular gauge invariance/relativity and general covariance is exposed. Besides the massless tensor graviton of General Relativity, the theory includes an (almost) massless scalar graviton treated as the gravitational dark matter. A spherically symmetric vacuum solution, describing the coherent scalar-graviton field for the soft-core dark halos with the asymptotically flat rotation curves, is demonstrated.
Spherical gravitational wave is strictly forbidden in vacuum space in frame of general relativity by the Birkhoff theorem. We prove that spherical gravitational waves do exist in non-linear massive gravity, and find the exact solution. Further more, we find exact gravitational wave solution with a singular string by meticulous studies of familiar equation, in which the horizon becomes non-compact. We analyze the properties of the congruence of graviton rays of these wave solution. We clarify subtle points of dispersion relation, velocity and mass of graviton in massive gravity with linear pert…
It is commonly accepted that general relativity is the only solution to the consistency problem that appears when trying to build a theory of interacting gravitons (massless spin-2 particles). Padmanabhan's 2008 thought-provoking analysis raised some concerns that are having resonance in the community. In this work we present the self-coupling problem in detail and explicitly solve the infinite-iterations scheme associated with it for the simplest theory of a graviton field, which corresponds to an irreducible spin-2 representation of the Poincaré group. We make explicit the non-uniqueness pro…
We continue our investigation of massive gravity in the massless limit of vanishing graviton mass. From gauge invariance we derive the most general coupling between scalar matter and gravity. We get further couplings beside the standard coupling to the energy-momentum tensor. On the classical level this leads to a further modification of general relativity.
After the recent historical discovery of gravitational wave, it is curious to speculate upon the detection prospect of the quantum graviton in the terrestrial accelerator-based experiment. We carefully investigate the "golden" channels, $J/ψ(Υ)\toγ+\text{graviton}$, which can be pursued at \textsf{BESIII} and \textsf{Belle 2} experiments, by searching for single-photon plus missing energy events. Within the effective field theory (EFT) framework of General Relativity (GR) together with Nonrelativistic QCD (NRQCD), we are capable of making solid predictions for the corresponding decay rates. It…
The main contribution to the pulsar power can be calculated by assuming a rotating magnetically-dominated magnetosphere described by the force-free approximation. Although this simple model has been used thoroughly to study pulsar magnetospheres in the flat spacetime regime, only few works have considered the relativistic corrections introduced by the curvature and frame-dragging effects induced by a rotating neutron star. Here we revisit the problem and describe pulsar magnetospheres within full General Relativity, quantifying the corrections as a function of the angular velocity, the compact…
We present a general model of interacting metric fields with the sum of massless non-interacting spin 2 fields as the linear limit. In the non-interacting limit the model is reduced to a sum of general relativity actions, with the usual Einstein-Hilbert kinetic term for each metric field. Until now the accepted view was that such theories are inconsistent since it has been proven that ghost terms and/or discontinuity in the number of degrees of freedom at the zero interaction limit, are unavoidable. We do not refute these results, but instead prove by construction that they do not necessarily …
In this paper, we focus on testing gravity theories in the radiative regime using pulsar timing array observations. After reviewing current techniques to measure the dispersion and alternative polarization of gravitational waves, we extend the framework to the most general situations, where the combinations of a massive graviton and alternative polarization modes are considered. The atlas of the Hellings-Downs functions is completed by the new calculations for these dispersive alternative polarization modes. We find that each mode and corresponding graviton mass introduce characteristic featur…
The status of experimental tests of general relativity and of theoretical frameworks for analysing them are reviewed. Einstein's equivalence principle (EEP) is well supported by experiments such as the Eötvös experiment, tests of special relativity, and the gravitational redshift experiment. Future tests of EEP will search for new interactions arising from unification or quantum gravity. Tests of general relativity have reached high precision, including the light deflection, the Shapiro time delay, the perihelion advance of Mercury, and the Nordtvedt effect in lunar motion. Gravitational wave …
The recent discovery of a double-pulsar PSR J0737-3039A/B provides an opportunity of unequivocally observing, for the first time, spin effects in general relativity. Existing efforts involve detection of the precession of the spinning body itself. However, for a close binary system, spin effects on the orbit may also be discernable. Not only do they add to the advance of the periastron (by an amount which is small compared to the conventional contribution) but they also give rise to a precession of the orbit about the spin direction. The measurement of such an effect would also give informatio…
This talk is based on my work in collaboration with Thibault Damour. We compare the probing power of different classes of gravity experiments: solar-system tests (weak-field regime), binary-pulsar tests (strong-field regime), and future gravitational-wave observations of inspiralling binaries (strong-field effects detected in our weak-gravitational-field conditions). This is done within the most natural class of alternative theories to general relativity, namely tensor-scalar theories, in which the gravitational interaction is mediated by one tensor field (g_munu) together with one or several …
The status of experimental tests of general relativity and of theoretical frameworks for analysing them are reviewed. Einstein's equivalence principle (EEP) is well supported by experiments such as the Eötvös experiment, tests of special relativity, and the gravitational redshift experiment. Future tests of EEP and of the inverse square law will search for new interactions arising from unification or quantum gravity. Tests of general relativity at the post-Newtonian level have reached high precision, including the light deflection, the Shapiro time delay, the perihelion advance of Mercury, and…
We investigate the problem of whether one can anticipate any features of the graviton without a detailed knowledge of a full quantum gravity. Assuming that in linearized gravity the graviton is in a sense similar to the photon, we derive a curious large number coincidence between the number of gravitons emitted by a solar planet during its orbital period and the number of its nucleons. In Einstein's GR the analogy between the graviton and the photon is ill founded. A generic relationship between quanta of a quantum field and plane waves of the corresponding classical field is broken in the cas…
We study a theory of minimally modified gravity called cuscuton/VCDM that propagates only two gravitational degrees of freedom. Despite being apparently different from general relativity (GR), it is in principle possible that this theory might be obtained via a field redefinition starting from the GR action. This would make the vacuum theory equivalent to GR and the theory would differ from GR only in the presence of matter. In this paper, studying the dispersion relation of gravitational waves and the dynamics of the Bianchi-I universe, we prove that such a field redefinition does not exist a…
The quantum field theoretic description of general relativity is a modern approach to gravity where gravitational force is carried by spin-2 gravitons. In the classical limit of this theory, general relativity as described by the Einstein field equations is obtained. This limit, where classical general relativity is derived from quantum field theory is the topic of this thesis. The Schwarzschild-Tangherlini metric, which describes the gravitational field of an inertial point particle in arbitrary space-time dimensions, $D$, is analyzed. The metric is related to the three-point vertex function …
The simplest approach to bootstrap in general relativity is considered. The approach claimed to recover the infinite perturbative series of graviton interaction terms with a recursive coupling metric perturbations to their energy-momentum tensor. We show that the approach provides an incorrect expression for three-graviton interaction term. Other difficulties related with the bootstrap approach are discussed.
We reformulate Euclidean general relativity without cosmological constant as an action governing the complex structure of twistor space. Extending Penrose's non-linear graviton construction, we find a correspondence between twistor spaces with partially integrable almost complex structures and four-dimensional space-times with off-shell metrics. Using this, we prove that our twistor action reduces to Plebanski's action for general relativity via the Penrose transform. This should lead to new insights into the geometry of graviton scattering as well as to the derivation of computational tools l…
Adopting our new method for matching general relativistic, ideal magnetohydrodynamics to its force-free limit, we perform the first systematic simulations of force-free pulsar magnetospheres in general relativity. We endow the neutron star with a general relativistic dipole magnetic field, model the interior with ideal magnetohydrodynamics, and adopt force-free electrodynamics in the exterior. Comparing the spin-down luminosity to its corresponding Minkowski value, we find that general relativistic effects give rise to a modest enhancement: the maximum enhancement for $n=1$ polytropes is $\sim…
In the canonical model of a pulsar, rotational energy is transmitted through the surrounding plasma via two electrical circuits, each connecting to the star over a small region known as a "polar cap." For a dipole-magnetized star, the polar caps coincide with the magnetic poles (hence the name), but in general, they can occur at any place and take any shape. In light of their crucial importance to most models of pulsar emission (from radio to X-ray to wind), we develop a general technique for determining polar cap properties. We consider a perfectly conducting star surrounded by a force-free m…
The status of experimental tests of general relativity and of theoretical frameworks for analysing them is reviewed. Einstein's equivalence principle (EEP) is well supported by experiments such as the Eotvos experiment, tests of special relativity, and the gravitational redshift experiment. Future tests of EEP and of the inverse square law are searching for new interactions arising from unification or quantum gravity. Tests of general relativity at the post-Newtonian level have reached high precision, including the light deflection, the Shapiro time delay, the perihelion advance of Mercury, an…
Pulsar timing arrays (PTA) have the promise to detect gravitational waves (GWs) from sources which are in a unique frequency range of 10^-9 - 10^-6 Hz. This in turn also provides an opportunity to test the theory of general relativity in the low frequency regime. The central concept of the detection of GWs with PTA lies in measuring the time of arrival difference of the pulsar signal due to the passing of GWs i.e. the pulses get red-shifted. In this paper we provide a complete derivation of the redshift computation for all six possible polarizations of GW which arise due to the modifcations to…
The renaissance of General Relativity witnessed considerable progress regarding both understanding and justifying Einstein's equations. Both general relativists and historians of the subject tend to share a view, General Relativity exceptionalism. But does some of the renaissance progress in understanding and justifying Einstein's equations owe something to particle physics egalitarianism? If so, how should the historiography of gravitation and Einstein's equations reflect that fact? The idea of a graviton mass has a 19th century Newtonian pre-history in Neumann's and Seeliger's long-distance …
Any modification on gravity would affect not only gravitational wave (GW) generation but also GW propagation. Therefore, tests of general relativity (GR) with only GW generation or GW propagation will lead to an overestimate for deviations. Here we try to use one set of parameters to parameterize the modifications on both GW generation and GW propagation and then test GR with GW150914. In our simplest case, we find that graviton mass $μ<6.3\times10^{-23}{\rm eV/c^2}$ at $90\%$ C.L. and there are no deviations from GR at $90\%$ C.L..
Binary pulsars allow us to carry out precision tests of gravity and have placed stringent bounds on a broad class of theories beyond general relativity. Current and future radio telescopes, such as FAST, SKA, and MeerKAT, may find a new astrophysical system, a pulsar orbiting around a black hole, which will provide us a new source for probing gravity. In this paper, we systematically study the prospects of testing general relativity with such black hole-pulsar binaries. We begin by finding a mapping between generic non-Einsteinian parameters in the orbital decay rate and theoretical constants …
The quantum effective theory of general relativity, independent of the eventual full theory at high energy, expresses graviton-graviton scattering at one loop order O(E^4) with only one parameter, Newton's constant. Dunbar and Norridge have calculated the one loop amplitude using string based techniques. We complete the calculation by showing that the 1/(d-4) divergence which remains in their result comes from the infrared sector and that the cross section is finite and model independent when the usual bremsstrahlung diagrams are included.
The timing of radio pulsars in binary systems provides a superb testing ground of general relativity. Here we propose a Bayesian approach to carry out these tests, and a relevant efficient numerical implementation, that has several conceptual and practical advantages with respect to traditional methods based on least-square-fits that have been used so far: (i) it accounts for the actual structure of the likelihood function - and it is not predicated on the Laplace approximation which is implicitly built in least-square fits that can potentially bias the inference - (ii) it provides the ratio o…
We investigate propagations of graviton and additional scalar on four-dimensional anti de Sitter (AdS$_4$) space using $f(R)$ gravity models with external sources. It is shown that there is the van Dam-Veltman-Zakharov (vDVZ) discontinuity in $f(R)$ gravity models because $f(R)$ gravity implies GR with additional scalar. This indicates a difference between general relativity and $f(R)$ gravity clearly.
