Testing Lorentz symmetry with planetary orbital dynamics
Aurélien Hees, Quentin G. Bailey, Christophe Le Poncin-Lafitte, Adrien Bourgoin, Attilio Rivoldini, Brahim Lamine, Frédéric Meynadier, Christine Guerlin, Peter Wolf
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12 pages, 2 figures, version accepted for publication in Phys. Rev. D
Planetary ephemerides are a very powerful tool to constrain deviations from the theory of General Relativity using orbital dynamics. The effective field theory framework called the Standard-Model Extension (SME) has been developed in order to systematically parametrize hypothetical violations of Lorentz symmetry (in the Standard Model and in the gravitational sector). In this communication, we use the latest determinations of the supplementary advances of the perihelia and of the nodes obtained by planetary ephemerides analysis to constrain SME coefficients from the pure gravity sector and also from gravity-matter couplings. Our results do not show any deviation from GR and they improve current constraints. Moreover, combinations with existing constraints from Lunar Laser Ranging and from atom interferometry gravimetry allow us to disentangle contributions from the pure gravity sector from the gravity-matter couplings.
The Newton limit of gravity is studied in the presence of Lorentz-violating gravitational operators of arbitrary mass dimension. The linearized modified Einstein equations are obtained and the perturbative solutions are constructed and characterized. We develop a formalism for data analysis in laboratory experiments testing gravity at short range and demonstrate that these tests provide unique sensitivity to deviations from local Lorentz invariance.
The effects of local Lorentz violation on dispersion and birefringence of gravitational waves are investigated. The covariant dispersion relation for gravitational waves involving gauge-invariant Lorentz-violating operators of arbitrary mass dimension is constructed. The chirp signal from the gravitational-wave event GW150914 is used to place numerous first constraints on gravitational Lorentz violation.
We discuss some of the tests of Lorentz symmetry made possible by astrophysical observations of ultrahigh energy cosmic rays, gamma-rays, and neutrinos. These are among the most sensitive tests of Lorentz symmetry violation because they are the highest energy phenomena known to man.
A more complete theoretical model of testing Lorentz violation by the comparison of atomic clocks is developed in the Robertson-Mansouri-Sexl kinematic framework. As this frame postulates the deviation of the coordinate transformation from the Lorentz transformation, from the viewpoint of the transformation violations on time and space, the LI violating effect in the atomic clock comparison can be explained as two parts: time-delay effect $α\frac {v^2}{c^2}$ and structure effect $-\frac {β+2δ}{3} \frac {v^2}{c^2}$. Standard model extension is a widely used dynamic frame to characterize the Lor…
In an earlier paper [1] (hep-ph/0408006), the bound on the Standard Model Extension photon-sector parameter $\tildeκ_{tr}$ [2] (hep-ph/0205211) set by the heavy-ion storage-ring experiment of Saathoff et al. [3] was incorrectly reported. We show that the correct bound on $\tildeκ_{tr}$ which resulted from this experiment is in fact $2.2\times 10^{-7}$.
We have developed an apparatus to test Lorentz invariance in the photon sector by measuring the resonant frequency difference between two counterpropagating directions of an asymmetric optical ring cavity using a double-pass configuration. No significant evidence for the violation was found at the level of $δc /c \lesssim 10^{-14}$. Details of our apparatus and recent results are presented.
Lorentz invariant violation (LIV) test is very important to study in the new physics. All the known astrophysical constraints either have a very small examinable parameter space, or are only suitable for some special theoretical models. Here we suggest that it is possible to detect the time-delay of ultra-high-energy cosmic-rays (UHECRs) directly. We discuss some difficulties in our method, including the intergalactic magnetic fields. It seems that none of them are crucial, hence this method could give a larger examinable parameter space and a stronger constraint on LIV.
In this talk, results from the gravitational sector of the Standard-Model Extension (SME) are discussed. The weak-field phenomenology of the resulting modified gravitational field equations is explored. The application of the results to a variety of modern gravity experiments, including lunar laser ranging, Gravity Probe B, binary pulsars, and Earth-laboratory tests, shows promising sensitivity to gravitational coefficients for Lorentz violation in the SME.
Much research has been done in the latter years on the subject of Lorentz violation induced by Quantum Gravity effects. On the theoretical side it has been shown that both Loop Quantum Gravity and String Theory predict that Lorentz violation can be induced at an energy near to the Planck scale. On the other hand, most of the experimental results in the latter years, have confirmed that the laws of physics are Lorentz invariant at low energy with very high accuracy. The inclusion of one- and two-loop contributions from a Lorentz violating Lagrangian dramatically change the above picture: the lo…
The Weak Equivalence Principle (WEP) and the local Lorentz invariance (LLI) are two major assumptions of General Relativity (GR). The MICROSCOPE mission, currently operating, will perform a test of the WEP with a precision of $10^{-15}$. The data will also be analysed at SYRTE for the purposes of a LLI test realised in collaboration with J. Tasson (Carleton College, Minnesota) and Q. Bailey (Embry-Riddle Aeronautical University, Arizona). This study will be performed in a general framework, called the Standard Model Extension (SME), describing Lorentz violations that could appear at Planck sca…
We study the possibility to constrain deviations from Lorentz invariance in dark matter (DM) with cosmological observations. Breaking of Lorentz invariance generically introduces new light gravitational degrees of freedom, which we represent through a dynamical timelike vector field. If DM does not obey Lorentz invariance, it couples to this vector field. We find that this coupling affects the inertial mass of small DM halos which no longer satisfy the equivalence principle. For large enough lumps of DM we identify a (chameleon) mechanism that restores the inertial mass to its standard value. …
Under the standard model extension (SME) framework, Lorentz invariance is tested in five binary pulsars: PSR J0737-3039, PSR B1534+12, PSR J1756-2251, PSR B1913+16 and PSR B2127+11C. By analyzing the advance of periastron, we obtain the constraints on a dimensionless combination of SME parameters that is sensitive to timing observations. The results imply no evidence for the break of Lorentz invariance at $10^{-10}$ level, one order of magnitude larger than previous estimation.
We present constraints on violations of Lorentz Invariance based on Lunar Laser Ranging (LLR) data. LLR measures the Earth-Moon separation by timing the round-trip travel of light between the two bodies, and is currently accurate to a few centimeters (parts in $10^{11}$ of the total distance). By analyzing archival LLR data under the Standard-Model Extension (SME) framework, we derived six observational constraints on dimensionless SME parameters that describe potential Lorentz-violation. We found no evidence for Lorentz violation at the $10^{-6}$ to $10^{-11}$ level in these parameters.
The Large High Altitude Air Shower Observatory~(LHAASO) recently reported the detection of gamma-ray emissions with energies up to $1.1~\textrm{PeV}$ from the Crab Nebula. Using the absence of vacuum Cherenkov effect by inverse-Compton electrons, we improve previous bounds to linear-order Lorentz invariance violation (LV) in the dispersion relations of electrons by $10^{4}$ times. We show that the LV effect on electrons is severely constrained, compatible with certain type of LV as expected by some models of quantum gravity~(QG), such as the string/D-brane inspired space-time foam. We argue th…
We present the first experimental test of Lorentz invariance using the frequency difference between counter-propagating modes in an asymmetric odd-parity optical resonator. This type of test is $\sim10^{4}$ more sensitive to odd-parity and isotropic (scalar) violations of Lorentz invariance than equivalent conventional even-parity experiments due to the asymmetry of the optical resonator. The disadvantages of odd parity resonators have been negated by the use of counter-propagating modes, delivering a high level of immunity to environmental fluctuations. With a non-rotating experiment our resu…
We investigate experiments that are sensitive to the scalar and parity-odd coefficients for Lorentz violation in the photon sector of the Standard Model Extension (SME). We show that of the classic tests of special relativity, Ives-Stilwell (IS) experiments are sensitive to the scalar coefficient, but at only parts in 10^5 for the state-of-the-art experiment. We then propose asymmetric Mach-Zehnder interferometers with different electromagnetic properties in the two arms, including recycling techniques based on travelling wave resonators to improve the sensitivity. With present technology we e…
We use MCMC to sample the posterior distribution of the mass of the graviton -- assumed here to be manifest through a Yukawa suppression of the Newtonian potential -- by using INPOP planetary ephemerides. The main technical difficulty is the lack of analytical formulation for the forward problem and the cost in term of computation time for its numerical estimation. To overcome these problems we approximate an interpolated likelihood for the MCMC with the Gaussian Process Regression. We also propose a possible way to assess the uncertainty of approximation of the likelihood by mean of some real…
Successful detection of gravitational waves has presented a new avenue to explore the nature of gravity. With the cumulative catalog of detected events, we can perform tests on General Relativity from various aspects with increasing precision. In this work, we focus on Lorentz symmetry during propagation of gravitational waves. Considering the dispersion relation in the gauge-invariant linearized gravity sector of the Standard-Model Extension, the anisotropy, birefringence, and dispersion effects will be induced during propagation of gravitational waves because of the Lorentz violating modific…
We have previously shown that a very small amount of Lorentz invariance violation (LIV), which suppresses photomeson interactions of ultrahigh energy cosmic rays (UHECRs) with cosmic background radiation (CBR) photons, can produce a spectrum of cosmic rays that is consistent with that currently observed by the Pierre Auger Observatory (PAO) and HiRes experiments. Here, we calculate the corresponding flux of high energy neutrinos generated by the propagation of UHECR protons through the CBR in the presence of LIV. We find that LIV produces a reduction in the flux of the highest energy neutrinos…
Violations of both the weak equivalence principle (WEP) and Lorentz invariance can produce vacuum birefringence, which leads to an energy-dependent rotation of the polarization vector of linearly polarized emission from a given astrophysical source. However, the search for the birefringent effect has been hindered by our ignorance concerning the intrinsic polarization angle in different energy bands. Considering the contributions to the observed linear polarization angle from both the intrinsic polarization angle and the rotation angles induced by violations of the WEP and Lorentz invariance, …
Lorentz symmetry violations can be parametrized by an effective field theory framework that contains both general relativity and the standard model of particle physics called the standard-model extension (SME). We present new constraints on pure gravity SME coefficients obtained by analyzing lunar laser ranging (LLR) observations. We use a new numerical lunar ephemeris computed in the SME framework and we perform a LLR data analysis using a set of 20721 normal points covering the period of August, 1969 to December, 2013. We emphasize that linear combination of SME coefficients to which LLR dat…
Testing Local Lorentz Invariance with Laser Tracking of the LAGEOS and LAGEOS II Satellites
Istituto Nazionale di Astrofisica (INAF)（意大利国家天体物理研究所）；Istituto di Astrofisica e Planetologia Spaziali (IAPS)（天体物理学与行星科学研究所）；Istituto Nazionale di Fisica Nucleare (INFN)（意大利国家核物理研究所）；Sezione di Tor Vergata（托尔维尔加塔分部）；Consiglio Nazionale delle Ricerche (CNR)（意大利国家研究委员会）；Istituto di Scienza e Tecnologie della Informazione (ISTI)（信息与科学技术研究所）；Red de Infraestructuras Geodésicas, Instituto Geográfico Nacional（地理国家研究所大地测量基础设施网）；Dipartimento di Fisica, Università di Tor Vergata（托尔维尔加塔大学物理系）
Lorentz symmetry is one of the pillars of both General Relativity and the Standard Model of particle physics. Motivated by ideas about quantum gravity, unification theories and violations of CPT symmetry, a significant effort has been put the last decades into testing Lorentz symmetry. This review focuses on Lorentz symmetry tests performed in the gravitational sector. We briefly review the basics of the pure gravitational sector of the Standard-Model Extension (SME) framework, a formalism developed in order to systematically parametrize hypothetical violations of the Lorentz invariance. Furth…
We analyze the possibility of testing local Lorentz invariance from the observation of tau decays. Future prospects of probing distances below the electroweak characteristic scale are discussed.
Motivated by ideas about quantum gravity, a tremendous amount of effort over the past decade has gone into testing Lorentz invariance in various regimes. This review summarizes both the theoretical frameworks for tests of Lorentz invariance and experimental advances that have made new high precision tests possible. The current constraints on Lorentz violating effects from both terrestrial experiments and astrophysical observations are presented.
Here we explore the possibility of extending to the Solar System scenario the combined residual approach employed for the deterination of the Lense-Thirring effect in the Earth-LAGEOS satellites system. After calculating the secular gravitoelectric advance of the mean anomaly, we propose several linear combinations of the residuals of the nodes, the perihelia and the mean anomalies of some inner planets in order to measure the gravitoelectric advance, the Lense-Thirring effect and the solar quadrupole mass moment. The obtainable accuracies are comparable to those of new complex and expensive m…
It was recently proposed that a giant flare of the blazar PKS B1424-418 at redshift $z=1.522$ is in association with a PeV-energy neutrino event detected by IceCube. Based on this association we here suggest that the flight time difference between the PeV neutrino and gamma-ray photons from blazar flares can be used to constrain the violations of equivalence principle (EP) and the Lorentz invariance for neutrinos. From the calculated Shapiro delay due to clusters or superclusters in the nearby universe, we find that violation of the equivalence principle for neutrinos and photons is constraine…
The recent observation of high-energy astrophysical neutrinos can be used to constrain violations of Lorentz invariance emerging from a quantum theory of gravity. We perform threshold and Cherenkov analyses that improve existing bounds by factors ranging from about a million to 10^{20}.
I discuss some theoretical ideas concerning the representation of quantum gravity as a Lorentz-symmetry-violating `medium' with non-trivial optical properties, which include a refractive index in `vacuo' and stochastic effects associated with a spread in the arrival times of photons, growing linearly with the photon energy. Some of these properties may be experimentally detectable in future satellite facilities (e.g. GLAST or AMS), using as probes light from distant astrophysical sources such as gamma ray bursters. I also argue that such linear violations of Lorentz symmetry may not always be …
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…
The assumption of Lorentz invariance is one of the founding principles of modern physics and violation of that would have deep consequences to our understanding of the universe. Potential signatures of such a violation could range from energy dependent dispersion introduced into a light curve to a change in the photon-photon pair production threshold that changes the expected opacity of the universe. Astronomical sources of Very High Energy (VHE) photons can be used as test beams to probe fundamental physics phenomena, however, such effects would likely be small and need to be disentangled fro…
Short-range experiments testing the gravitational inverse-square law at the submillimeter scale offer uniquely sensitive probes of Lorentz invariance. A combined analysis of results from the short-range gravity experiments HUST-2015, HUST-2011, IU-2012, and IU-2002 permits the first independent measurements of the 14 nonrelativistic coefficients for Lorentz violation in the pure-gravity sector at the level of $10^{-9}$ m$^2$, improving by an order of magnitude the sensitivity to numerous types of Lorentz violation involving quadratic curvature derivatives and curvature couplings.
Optical resonators provide a powerful tool for testing aspects of Lorentz invariance. Here, we present a reanalysis of an experiment where a path asymmetry was created in an optical ring resonator by introducing a dielectric prism in one arm. The frequency difference of the two fundamental counter-propagating modes was then recorded as the apparatus was orientation-modulated in the laboratory. By assuming that the minimal Standard-Model Extension coefficients vanish we are able to place bounds on higher-order parity-odd Lorentz-violating coefficients of the Standard-Model Extension. The result…
The cryogenic sapphire oscillator (CSO) at the Paris Observatory has been continuously compared to various Hydrogen Masers since 2001. The early data sets were used to test Local Lorentz Invariance in the Robertson-Mansouri-Sexl (RMS) framework by searching for sidereal modulations with respect to the Cosmic Microwave Background, and represent the best Kennedy-Thorndike experiment to date. In this work we present continuous operation over a period of greater than six years from September 2002 to December 2008 and present a more precise way to analyze the data by searching the time derivative o…
In the spirit of effective field theory, the Standard-Model Extension (SME) provides a comprehensive framework to systematically probe the possibility of Lorentz/CPT violation. In the pure gravity sector, operators with mass dimension larger than 4, while in general being advantageous to short-range experiments, are hard to investigate with systems of astronomical size. However, there is exception if the leading-order effects are CPT-violating and velocity-dependent. Here we study the lowest-order operators in the pure gravity sector that violate the CPT symmetry with carefully chosen relativi…
Since Stephen Hawking discovered that black holes emit thermal radiation, black holes have become the theoretical laboratories for testing our ideas on quantum gravity. This dissertation is devoted to the study of singularities, the formation of black holes by gravitational collapse and the global structure of spacetime. All our investigations are in the context of a recently proposed approach to quantum gravity, which breaks Lorentz and diffeomorphism symmetries at very high energies.
Explosive astrophysical transients at cosmological distances can be used to place precision tests of the basic assumptions of relativity theory, such as Lorentz invariance, the photon zero-mass hypothesis, and the weak equivalence principle (WEP). Signatures of Lorentz invariance violations (LIV) include vacuum dispersion and vacuum birefringence. Sensitive searches for LIV using astrophysical sources such as gamma-ray bursts, active galactic nuclei, and pulsars are discussed. The most direct consequence of a nonzero photon rest mass is a frequency dependence in the velocity of light propagati…
In this work we outline the two most commonly used test theories (RMS and SME) for testing Local Lorentz Invariance (LLI) of the photon. Then we develop the general framework of applying these test theories to resonator experiments with an emphasis on rotating experiments in the laboratory. We compare the inherent sensitivity factors of common experiments and propose some new configurations. Finally we apply the test theories to the rotating cryogenic experiment at the University of Western Australia, which recently set new limits in both the RMS and SME frameworks [hep-ph/0506074].
Experimental tests of Newton law put stringent constraints on potential deviations from standard theory with ranges from the millimeter to the size of planetary orbits. Windows however remain open for short range deviations, below the millimeter, as well as long range ones, of the order of or larger than the size of the solar system. We discuss here the relation between long range tests of the Newton law and the anomaly recorded on Pioneer 10/11 probes.
Over the last few years the study of possible Planck-scale departures from classical Lorentz symmetry has been one of the most active areas of quantum-gravity research. We now have a satisfactory description of the fate of Lorentz symmetry in the most popular noncommutative spacetimes and several studies have been devoted to the fate of Lorentz symmetry in loop quantum gravity. Remarkably there are planned experiments with enough sensitivity to reveal these quantum-spacetime effects, if their magnitude is only linearly suppressed by the Planck length. Unfortunately, in some quantum-gravity sce…
Extrasolar circumbinary planets are so called because they orbit two stars instead of just one; to date, an increasing number of such planets have been discovered with a variety of techniques. If the orbital frequency of the hosting stellar pair is much higher than the planetary one, the tight stellar binary can be considered as a matter ring current generating its own post-Newtonian stationary gravitomagnetic field through its orbital angular momentum. It affects the orbital motion of a relatively distant planet with Lense-Thirring-type precessional effects which, under certain circumstances,…
We consider the mass-radius bounds for spherically symmetric static compact objects in the de Rham-Gabadadze-Tolley (dRGT) Massive Gravity theories, free of ghosts. In this type of gravitational theories the graviton, the quantum of gravity, may have a small, but non-vanishing mass. We derive the hydrostatic equilibrium and mass continuity equations in the Lorentz-violating Massive gravity in the presence of a cosmological constant and for a non-zero graviton mass. The case of the constant density stars is also investigated by numerically solving the equilibrium equations. The influence of the…
In the present work the thermodynamical properties of bosonic and fermionic gases are analyzed under the condition that a modified dispersion relation is present. This last condition implies a breakdown of Lorentz symmetry. The implications upon the condensation temperature will be studied, as well, as upon other thermodynamical variables such as specific heat, entropy, etc. Moreover, it will be argued that those cases entailing a violation of time reversal symmetry of the motion equations could lead to problems with the concept of entropy. Concerning the fermionic case it will be shown that F…
We study the role of the Barbero-Immirzi parameter $γ$ and the choice of connection in the construction of (a symmetry-reduced version of) loop quantum gravity. We start with the four-dimensional Lorentzian Holst action that we reduce to three dimensions in a way that preserves the presence of $γ$. In the time gauge, the phase space of the resulting three-dimensional theory mimics exactly that of the four-dimensional one. Its quantization can be performed, and on the kinematical Hilbert space spanned by SU(2) spin network states the spectra of geometric operators are discrete and $γ$-dependent…
