The gravitational strong equivalence principle (SEP) is a cornerstone of the general theory of relativity (GR). The extreme difference in binding energy between neutron stars and white dwarfs allows for precision tests of the SEP via the technique of pulsar timing.
To date, the best limit on the validity of SEP under strong-field conditions was obtained with a unique pulsar in a triple stellar system, PSR J0337+1715. We report here on an improvement of this test using an independent data set acquired over 6 years with the Nan\c cay radio telescope (NRT). The improvements arise from a uniformly sampled data set, a theoretical analysis, and a treatment that fixes some short-comings in the previously published results, leading to better precision and reliability of the test.
In contrast to the previously published test, we use a different long-term timing data set, developed a new timing model and an independent numerical integration of the motion of the system, and determined the masses and orbital parameters with a different methodology that treats the parameter $Δ$, describing a possible strong-field SEP violation, identically to all other parameters.
We obtain a violation parameter $Δ= (+0.5 \pm 1.8) \times 10^{-6}$ at 95\% confidence level, which is compatible with and improves upon the previous study by 30\%. This result is statistics-limited and avoids limitation by systematics as previously encountered. We find evidence for red noise in the pulsar spin frequency, which is responsible for up to 10\% of the reported uncertainty. We use the improved limit on SEP violation to place constraints on a class of well-studied scalar-tensor theories, in particular we find $ω_{\rm BD} > 140\,000$ for the Brans-Dicke parameter. The conservative limits presented here fully take into account current uncertainties in the equation for state of neutron-star matter.
Pulsar timing observations precisely test general relativity. Recently, the hierarchical triple system PSR J0337+1715 has placed new constraints on the existence of a fifth force from violation in the strong equivalence principle. Many alternative gravity theories exist with massive (pseudo-)scalar fields to explain a variety of phenomena from the accelerating expansion of the universe at large scales to the QCD strong CP problem at small scales. We here develop a generic formalism for the fifth force effect in theories involving massive scalar fields arising from e.g. string theory. With PSR …
A large number of binary black holes (BBHs) with longer orbital periods are supposed to exist as progenitors of BBH mergers recently discovered with gravitational wave (GW) detectors. In our previous papers, we proposed to search for such BBHs in triple systems through the radial-velocity modulation of the tertiary orbiting star. If the tertiary is a pulsar, high precision and cadence observations of its arrival time enable an unambiguous characterization of the pulsar -- BBH triples located at several kpc, which are inaccessible with the radial velocity of stars. The present paper shows that …
Einstein's weak equivalence principle (EEP) can be tested through the arrival time delay between photons with different frequencies. Assuming that the arrival time delay is solely caused by the gravitational potential of the Milky Way, we show that a "nano-shot" giant pulse with a time delay between energies corrected for all known effects, e.g. $Δt<0.4~\rm{ns}$, from the Crab pulsar poses a new upper limit on the deviation from EEP, i.e. $Δγ< (0.6-1.8)\times 10^{-15}$. This result provides the hitherto most stringent constraint on the EEP, improving by at least 2 to 3 orders of magnitude from…
We design a direct test of the local position invariance (LPI) in the post-Newtonian gravity, using the timing observation of the triple pulsar, PSR J0337+1715. The test takes advantage of the large gravitational acceleration exerted by the outer white dwarf to the inner neutron star -- white dwarf binary. Using machine-precision three-body simulations and dedicated Markov-chain Monte Carlo (MCMC) techniques with various sampling strategies and noise realizations, we estimate that the Whitehead's parameter could have already been limited to $|ξ| \lesssim 0.4$ (95\% CL), with the published timi…
In the present paper we argue that timing irregularities in pulsars, like glitches and timing noise, could be associated with the violation of the weak equivalence principle for vortices in the superfluid core of rotating neutron stars.
The Standard-Model Extension provides a framework to systematically investigate possible violation of the Lorentz symmetry. Concerning gravity, the linearized version was extensively examined. We here cast the first set of experimental bounds on the nonlinear terms in the field equation from the anisotropic cubic curvature couplings. These terms introduce body-dependent accelerations for self-gravitating objects, thus violating the gravitational weak equivalence principle (GWEP). Novel phenomena, that are absent in the linearized gravity, remain experimentally unexplored. We constrain them wit…
Einstein's theory of gravity, general relativity, has passed stringent tests in laboratories, elsewhere in the Solar Sytem, and in pulsar binaries. Nevertheless it is known to be incompatible with quantum mechanics and must differ from the true behaviour of matter in strong fields and at small spatial scales. A key aspect of general relativity to test is the strong equivalence principle (SEP), which states that all freely falling objects, regardless of how strong their gravity, experience the same acceleration in the same gravitational field. Essentially all alternatives to general relativity …
The strong equivalence principle is a cornerstone of general relativity, tested with exquisite accuracy in the Solar system. However, tests in the strong-field regime require a compact object. Currently, PSR J0337+1715 is the unique millisecond pulsar found in a triple stellar system, orbiting two white dwarfs within an area comparable to the orbit of the Earth. This configuration offers the opportunity for a dramatic improvement over previous tests, provided that accurate and regular timing of the pulsar can be achieved. This also requires the development of a new timing model solving numeric…
Three conceptually different masses appear in equations of motion for objects under gravity, namely, the inertial mass, $m_{\cal I}$, the passive gravitational mass, $m_{\cal P}$, and the active gravitational mass, $m_{\cal A}$. It is assumed that, for any objects, $m_{\cal I} = m_{\cal P} = m_{\cal A}$ in the Newtonian gravity, and $m_{\cal I} = m_{\cal P}$ in the Einsteinian gravity, oblivious to objects' sophisticated internal structure. Empirical examination of the equivalence probes deep into gravity theories. We study the possibility of carrying out new tests based on pulsar timing of th…
Max-Planck-Institut für Radioastronomie（马克斯·普朗克射电天文研究所）；Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理学研究所（爱因斯坦研究所））；Leibniz Universität Hannover（汉诺威莱布尼茨大学）；ASTRON, Netherlands Institute for Radio Astronomy（荷兰射电天文研究所）；LUX, Observatoire de Paris, Université PSL, Sorbonne Université, CNRS（巴黎天文台卢森堡联合实验室，巴黎文理研究大学，索邦大学，法国国家科学研究中心）；Jodrell Bank Centre for Astrophysics, University of Manchester（曼彻斯特大学约德雷尔银行天体物理学中心）
Weak Equivalent Principle (WEP) can be tested through the parameterized post-Newtonian parameter $γ$, representing the space curvature produced by unit rest mass. The parameter $γ$ in turn has been constrained by comparing the arrival times of photons originating in distant transient events, such as gamma-ray bursts, fast radio bursts as well as giant pulses of pulsars. Those measurements normally correspond to an individual burst event with very limited energy bands and signal-to-noise ratio (S/N). In this letter, the discrepancy in the pulse arrival times of the Crab Pulsar between different…
Gravitationally bound three-body systems have been studied for hundreds of years and are common in our Galaxy. They show complex orbital interactions, which can constrain the compositions, masses, and interior structures of the bodies and test theories of gravity, if sufficiently precise measurements are available. A triple system containing a radio pulsar could provide such measurements, but the only previously known such system, B1620-26 (with a millisecond pulsar, a white dwarf, and a planetary-mass object in an orbit of several decades), shows only weak interactions. Here we report precisi…
We study the Kozai-Lidov mechanism in a hierarchical triple system in detail by the direct integration of the first-order post Newtonian equations of motion. We analyse a variety of models with a pulsar to evaluate the cumulative shift of the periastron time of a binary pulsar caused by the gravitational wave emission in a hierarchical triple system with Kozai-Lidov mechanism. We compare our results with those by the double-averaging method. The deviation in the eccentricity, even if small, is important in the evaluation of the emission of the gravitational waves. We also calculate the cumulat…
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…
We study a hierarchical triple system with the Kozai-Lidov mechanism, and analyse the cumulative shift of periastron time of a binary pulsar by the emission of gravitational waves. Time evolution of the osculating orbital elements of the triple system is calculated by directly integrating the first-order post-Newtonian equations of motion. The Kozai-Lidov mechanism will bend the evolution curve of the cumulative shift when the eccentricity becomes large. We also investigate the parameter range of mass and semi-major axis of the third companion with which the bending of the cumulative-shift cur…
The timing of millisecond pulsars has long been used as an exquisitely precise tool for testing the building blocks of general relativity, including the strong equivalence principle and Lorentz symmetry. Observations of binary systems involving at least one millisecond pulsar have been used to place bounds on the parameters of Einstein-æther theory, a gravitational theory that violates Lorentz symmetry at low energies via a preferred and dynamical time threading of the spacetime manifold. However, these studies did not cover the region of parameter space that is still viable after the recent b…
Testing Gravity with Binary Pulsars in the SKA Era
Peking University（北京大学）；National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）；Swinburne University of Technology（斯威本科技大学）；University of Cape Town（开普敦大学）；University of Bremen（不来梅大学）；University of Oldenburg（奥尔登堡大学）；Shanghai Astronomical Observatory, Chinese Academy of Sciences（中国科学院上海天文台）；State Key Laboratory of Radio Astronomy and Technology（射电天文与技术国家重点实验室）；University of British Columbia（不列颠哥伦比亚大学）；The University of Manchester（曼彻斯特大学）
Pulsars are precision celestial clocks. When being put in a binary, the ticking conveys the secret of underlying spacetime geometrodynamics. We use pulsars to test if the gravitational interaction possesses a tiny deviation from Einstein's General Relativity (GR). In the framework of Standard-Model Extension (SME), we systematically search for Lorentz-violating operators cataloged by (a) the minimal couplings of mass dimension 4, (b) the CPT symmetry of mass dimension 5, and (c) the gravitational weak equivalence principle (GWEP) of mass dimension 8. No deviation from GR was found yet.
General relativity asserts that: energy and momentum conservation laws are valid, preferred frames do not exist, and the strong equivalence principle is obeyed. In this paper recent progress in testing these important principles using millisecond pulsars is summarised.
Over the last few years, a set of new results from pulsar timing has introduced much tighter constraints on violations of the strong equivalence principle (SEP), either via a direct verification of the universality of free fall for a pulsar in a triple star system, or from tests of the nature of gravitational waves, in particular a search for dipolar gravitational wave emission in a variety of binary pulsars with different masses. No deviations from the SEP have been detected in our experiments. These results introduce some of the most stringent constraints on several classes of alternative th…
I describe a unique, 20-year-long timing program for the binary pulsar B0655+64, the stalwart control experiment for measurements of gravitational radiation damping in relativistic neutron-star binaries. Observed limits on evolution of the B0655+64 orbit provide new bounds on the existence of dipolar gravitational radiation, and hence on violation of the Strong Equivalence Principle.
The Square Kilometre Array (SKA) will use pulsars to enable precise measurements of strong gravity effects in pulsar systems, which yield tests of gravitational theories that cannot be carried out anywhere else. The Galactic census of pulsars will discover dozens of relativistic pulsar systems, possibly including pulsar -- black hole binaries which can be used to test the "cosmic censorship conjecture" and the "no-hair theorem". Also, the SKA's remarkable sensitivity will vastly improve the timing precision of millisecond pulsars, allowing probes of potential deviations from general relativity…
The Strong Equivalence Principle (SEP) demands, besides the validity of the Einstein Equivalence Principle, that all self-gravitating bodies feel the same acceleration in an external gravitational field. It has been found that metric theories of gravity other that than general relativity typically predict a violation of the SEP. In case of the Earth-Moon system (weak field system) this violation is called the Nordtvedt effect. It has been shown by Damour and Schäfer, that small-eccentricity long-orbital-period binary pulsars with a white dwarf companion provide excellent conditions to test the…
The Einstein's equivalence principle can be tested by using parameterized post-Newtonian parameters, of which the parameter $γ$ has been constrained by comparing the arrival times of photons with different energies. It has been constrained by a variety of astronomical transient events, such as gamma-ray bursts (GRBs), fast radio bursts as well as pulses of pulsars, with the most stringent constraint of $Δγ\lesssim 10^{-15}$. In this letter, we consider the arrival times of lights with different circular polarization. For a linearly polarized light, it is the combination of two circularly polar…
Symmetries play important roles in modern theories of physical laws. In this paper, we review several experimental tests of important symmetries associated with the gravitational interaction, including the universality of free fall for self-gravitating bodies, time-shift symmetry in the gravitational constant, local position invariance and local Lorentz invariance of gravity, and spacetime translational symmetries. Recent experimental explorations for post-Newtonian gravity are discussed, of which, those from pulsar astronomy are highlighted. All of these tests, of very different aspects of gr…
Testing Gravity with Binary Pulsars in the SKA Era
Max-Planck-Institut für Radioastronomie（马克斯·普朗克射电天文研究所）；Kavli Institute for Astronomy and Astrophysics, Peking University（北京大学柯利天体物理与天文研究所）；National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）；INAF-Osservatorio Astronomico di Cagliari（意大利国家天体物理研究院卡利亚里天文台）；Center for Astrophysics and Supercomputing, Swinburne University of Technology（斯威本科技大学天体物理学与超级计算中心）；High Energy Physics, Cosmology & Astrophysics Theory (HEPCAT) Group, Department of Mathematics and Applied Mathematics, University of Cape Town（开普敦大学数学与应用数学系高能物理、宇宙学与天体物理理论组）；Center of Applied Space Technology and Microgravity (ZARM), University of Bremen（不来梅大学应用空间技术与微重力中心）；Lohrmann Observatory, Technische Universität Dresden（德累斯顿工业大学洛尔曼天文台）；Department of Astronomy, School of Physics, Peking University（北京大学物理学院天文学系）；Institute of Physics, University of Oldenburg（奥尔登堡大学物理研究所）；Shanghai Astronomical Observatory, Chinese Academy of Sciences（中国科学院上海天文台）
Standard-model extension (SME) is an effective field theory introducing all possible Lorentz-violating (LV) operators to the standard model (SM) and general relativity (GR). In the pure-gravity sector of minimal SME (mSME), nine coefficients describe dominant observable deviations from GR. We systematically implemented twenty-seven tests from thirteen pulsar systems to tightly constrain eight linear combinations of these coefficients with extensive Monte Carlo simulations. It constitutes the first detailed and systematic test of the pure-gravity sector of mSME with the state-of-the-art pulsar …
Highly accurate binary-pulsar timing plays an important role in test of General Relativity. In this Letter, we argue that PSR J0337+1715, a milli-second pulsar in a stellar triple system, could be a very good laboratory for testing the strong equivalence principle (SEP). From the reported orbital parameters of this triple system, we give an uplimited estimation of the Nordtvedt parameter $η_\text{N} < 10^{-4}$ based on the orbital polarization calculation. This result is slightly better than the existed ones. In addition, if based on the observed uncertain value of inner orbital eccentricity, …
The realm of strong classical gravity and perhaps even quantum gravity are waiting to be explored. In this letter we consider the recently detected triple system composed of two stars and a non-accreting black hole. Using published observations of this system we conduct the most sensitive test to date for whether the black hole is actually a wormhole by looking for orbital perturbations due to an object on the other side of the wormhole. The mass limit obtained on the perturber is $\sim4$ orders of magnitude better than for observations of S2 orbiting the supermassive black hole at Sgr A*. We …
This talk reviews the constraints imposed by binary-pulsar data on gravity theories, and notably on "scalar-tensor" theories which are the most natural alternatives to general relativity. Because neutron stars have a strong gravitational binding energy, binary-pulsar tests are qualitatively different from solar-system experiments: They have the capability of probing models which are indistinguishable from general relativity in weak gravitational field conditions. Besides the two most precise binary-pulsar experiments, in the systems B1913+16 and B1534+12, we also present the results of the var…
We review the experimental evidence for Einstein's special and general relativity. A variety of high precision null experiments verify the weak equivalence principle and local Lorentz invariance, while gravitational redshift and other clock experiments support local position invariance. Together these results confirm the Einstein Equivalence Principle which underlies the concept that gravitation is synonymous with spacetime geometry, and must be described by a metric theory. Solar system experiments that test the weak-field, post-Newtonian limit of metric theories strongly favor general relati…
We showed in a previous paper that a wide class of nonmetric theories of gravity encompassed by the $χg$ formalism predict that the speed of light rays depends on the their polarization direction relative to directions singled out by the gravitational field. This gravity-induced birefringence of space is a violation of the Equivalence Principle and is due to the nonmetric coupling between gravity and electromagnetism. In this paper we analyze the propagation of light in the gravitational field of a rotating black hole when nonmetric couplings to curvature are included and compute the time dela…
The relative acceleration between two nearby particles moving along accelerated trajectories is studied, which generalizes the geodesic deviation equation. The polarization content of the gravitational wave in Horndeski theory is investigated by examining the relative acceleration between two self-gravitating particles. It is found out that the longitudinal polarization exists no matter whether the scalar field is massive or not. It would be still very difficult to detect the enhanced longitudinal polarization with the interferometer, as the violation of the strong equivalence principle of mir…
The characterization of nanohertz-frequency gravitational waves (GWs) with pulsar-timing arrays requires a continual expansion of datasets and monitored pulsars. Whereas detection of the stochastic GW background is predicated on measuring a distinctive pattern of inter-pulsar correlations, characterizing the background's spectrum is driven by information encoded in the power spectra of the individual pulsars' time series. We propose a new technique for rapid Bayesian characterization of the stochastic GW background that is fully parallelized over pulsar datasets. This Factorized Likelihood (FL…
In this paper, we review tests of the strong equivalence principle (SEP) derived from pulsar-white dwarf data. The extreme difference in binding energy between both components and the precise measurement of the orbital motion provided by pulsar timing allow the only current precision SEP tests for strongly self-gravitating bodies. We start by highlighting why such tests are conceptually important. We then review previous work where limits on SEP violation are obtained with an ensemble of wide binary systems with small eccentricity orbits. Then we propose a new SEP violation test based on the m…
Binary pulsars provide some of the tightest current constraints on modified theories of gravity and these constraints will only get tighter as radio astronomers continue timing these systems. These binary pulsars are particularly good at constraining scalar-tensor theories in which gravity is mediated by a scalar field in addition to the metric tensor. Scalar-tensor theories can predict large deviations from General Relativity due to the fact that they allow for violation of the strong-equivalence principle through a phenomenon known as scalarization. This effect appears directly in the timing…
The gravitational time delay of light, also called the Shapiro time delay, is one of the four classical tests of Einstein's theory of general relativity. This article derives the Newtonian version of the Shapiro time delay from Einstein's principle of equivalence and the Newtonian description of gravity, in a manner that is accessible to undergraduate students and advanced high-school students. The derivation can be used as a pedagogical tool, similar to the way that simplified derivations of the gravitational deflection of light are used in teaching about general relativity without making use…
General relativity can be formulated either as in its original geometrical version (Einstein, 1915) or as a field theory (Feynman, 1962). In the Feynman presentation of Einstein theory an hypothesis concerning the interaction of gravity to gravity, which was hidden in the original version, becomes explicit. This is nothing but the assumed extension of the validity of the equivalence principle not only for matter-gravity interaction, but also for gravity-gravity. Recently we have presented a field theory of gravity (from here on called the NDL theory) which does not contain such a hypothesis. W…
The recent LIGO detection of gravitational waves from black-hole binaries offers the exciting possibility of testing gravitational theories in the previously inaccessible strong-field, highly relativistic regime. While the LIGO detections are so far consistent with the predictions of General Relativity, future gravitational-wave observations will allow us to explore this regime to unprecedented accuracy. One of the generic predictions of theories of gravity that extend General Relativity is the violation of the strong equivalence principle, i.e. strongly gravitating bodies such as neutron star…
The violation of the weak equivalence principle (EP) in the gravitational field of the Earth, described by the Eötvös parameter $η_\oplus$, was recently constrained to the level $\left|η_\oplus\right| \lesssim 10^{-14}$ by the MICROSCOPE space mission. The Eötvös parameter $η_{\rm DM}$, pertaining to the differential couplings of dark matter (DM) and ordinary matter, was only tested to the level $\left| η_{\rm DM} \right| \lesssim 10^{-5}$ by the Eöt-Wash group and lunar laser ranging. This test is limited by the EP-violating driving force in the Solar neighborhood that is determined by the Ga…
