A test of general relativity using radio links with the Cassini spacecraft

Testing general relativity: from local to cosmological scales

I summarize various tests of general relativity on astrophysical scales, based on the large-scale structure of the universe but also on other systems, in particular the constants of physics. I emphasize the importance of hypotheses on the geometric structures of our universe while performing such tests and discuss their complementarity as well as their possible extensions.

One gravitational potential or two? Forecasts and tests

The metric of a perturbed Robertson-Walker space-time is characterized by three functions: a scale-factor giving the expansion history and two potentials that generalize the single potential of Newtonian gravity. The Newtonian potential induces peculiar velocities and, from these, the growth of matter fluctuations. Massless particles respond equally to the Newtonian potential and to a curvature potential. The difference of the two potentials, called the gravitational slip, is predicted to be very small in general relativity, but can be substantial in modified gravity theories. The two potentials can be measured, and gravity tested on cosmological scales, by combining weak gravitational lensing or the integrated Sachs-Wolfe effect with galaxy peculiar velocities or clustering.

On the unreasonable effectiveness of the post-Newtonian approximation in gravitational physics

The post-Newtonian approximation is a method for solving Einstein's field equations for physical systems in which motions are slow compared to the speed of light and where gravitational fields are weak. Yet it has proven to be remarkably effective in describing certain strong-field, fast-motion systems, including binary pulsars containing dense neutron stars and binary black hole systems inspiraling toward a final merger. The reasons for this effectiveness are largely unknown. When carried to high orders in the post-Newtonian sequence, predictions for the gravitational-wave signal from inspiraling compact binaries will play a key role in gravitational-wave detection by laser-interferometric observatories.

Varying Constants, Gravitation and Cosmology

Fundamental constants are a cornerstone of our physical laws. Any constant varying in space and/or time would reflect the existence of an almost massless field that couples to matter. This will induce a violation of the universality of free fall. Thus, it is of utmost importance for our understanding of gravity and of the domain of validity of general relativity to test for their constancy. We detail the relations between the constants, the tests of the local position invariance and of the universality of free fall. We then review the main experimental and observational constraints that have been obtained from atomic clocks, the Oklo phenomenon, solar system observations, meteorite dating, quasar absorption spectra, stellar physics, pulsar timing, the cosmic microwave background and big bang nucleosynthesis. At each step we describe the basics of each system, its dependence with respect to the constants, the known systematic effects and the most recent constraints that have been obtained. We then describe the main theoretical frameworks in which the low-energy constants may actually be varying and we focus on the unification mechanisms and the relations between the variation of different constants. To finish, we discuss the more speculative possibility of understanding their numerical values and the apparent fine-tuning that they confront us with.

Solar System tests of Hořava–Lifshitz gravity

In the present paper, we consider the possibility of observationally constraining Hořava gravity at the scale of the Solar System, by considering the classical tests of general relativity (perihelion precession of the planet Mercury, deflection of light by the Sun and the radar echo delay) for the spherically symmetric black hole Kehagias–Sfetsos solution of Hořava–Lifshitz gravity. All these gravitational effects can be fully explained in the framework of the vacuum solution of Hořava gravity. Moreover, the study of the classical general relativistic tests also constrains the free parameter of the solution. From the analysis of the perihelion precession of the planet Mercury, we obtain for the free parameter ω of the Kehagias–Sfetsos solution the constraint ω ≥3.212×10 −26  cm −2 , the deflection of light by the Sun gives ω ≥4.589×10 −26  cm −2 , while the radar echo delay observations can be explained if the value of ω satisfies the constraint ω ≥9.179×10 −26  cm −2 .

Tests of Gravity Using Lunar Laser Ranging

Lunar laser ranging (LLR) has been a workhorse for testing general relativity over the past four decades. The three retroreflector arrays put on the Moon by the Apollo astronauts and the French built arrays on the Soviet Lunokhod rovers continue to be useful targets, and have provided the most stringent tests of the Strong Equivalence Principle and the time variation of Newton's gravitational constant. The relatively new ranging system at the Apache Point 3.5 meter telescope now routinely makes millimeter level range measurements. Incredibly, it has taken 40 years for ground station technology to advance to the point where characteristics of the lunar retroreflectors are limiting the precision of the range measurements. In this article, we review the gravitational science and technology of lunar laser ranging and discuss prospects for the future.

The Pioneer Anomaly

Radio-metric Doppler tracking data received from the Pioneer 10 and 11 spacecraft from heliocentric distances of 20-70 AU has consistently indicated the presence of a small, anomalous, blue-shifted frequency drift uniformly changing with a rate of ∼ 6 × 10-9 Hz/s. Ultimately, the drift was interpreted as a constant sunward deceleration of each particular spacecraft at the level of aP = (8.74 ± 1.33) × 10-10 m/s2. This apparent violation of the Newton's gravitational inverse-square law has become known as the Pioneer anomaly; the nature of this anomaly remains unexplained. In this review, we summarize the current knowledge of the physical properties of the anomaly and the conditions that led to its detection and characterization. We review various mechanisms proposed to explain the anomaly and discuss the current state of efforts to determine its nature. A comprehensive new investigation of the anomalous behavior of the two Pioneers has begun recently. The new efforts rely on the much-extended set of radio-metric Doppler data for both spacecraft in conjunction with the newly available complete record of their telemetry files and a large archive of original project documentation. As the new study is yet to report its findings, this review provides the necessary background for the new results to appear in the near future. In particular, we provide a significant amount of information on the design, operations and behavior of the two Pioneers during their entire missions, including descriptions of various data formats and techniques used for their navigation and radio-science data analysis. As most of this information was recovered relatively recently, it was not used in the previous studies of the Pioneer anomaly, but it is critical for the new investigation.

f(R) Theories

Over the past decade, f(R) theories have been extensively studied as one of the simplest modifications to General Relativity. In this article we review various applications of f(R) theories to cosmology and gravity - such as inflation, dark energy, local gravity constraints, cosmological perturbations, and spherically symmetric solutions in weak and strong gravitational backgrounds. We present a number of ways to distinguish those theories from General Relativity observationally and experimentally. We also discuss the extension to other modified gravity theories such as Brans-Dicke theory and Gauss-Bonnet gravity, and address models that can satisfy both cosmological and local gravity constraints.

Screening long-range forces through local symmetry restoration

We present a screening mechanism that allows a scalar field to mediate a long-range (∼Mpc) force of gravitational strength in the cosmos while satisfying local tests of gravity. The mechanism hinges on local symmetry restoration in the presence of matter. In regions of sufficiently high matter density, the field is drawn towards ϕ = 0 where its coupling to matter vanishes and the ϕ → -ϕ symmetry is restored. In regions of low density, however, the symmetry is spontaneously broken, and the field couples to matter with gravitational strength. We predict deviations from general relativity in the solar system that are within reach of next-generation experiments, as well as astrophysically observable violations of the equivalence principle. The model can be distinguished experimentally from Brans-Dicke gravity, chameleon theories and brane-world modifications of gravity.

Gaia: Relativistic modelling and testing

Gaia is an ambitious space astrometry mission of ESA with a main objective to map the sky in astrometry and photometry down to a magnitude 20 by the end of the next decade. Given its extreme astrometric accuracy and the repeated observations over five years, the observation modelling is done in a fully relativistic framework and several tests of General Relativity or of its extensions can be carried out during the data processing. The paper presents an overview of the current activities in this area and of the expected performances.

Probes and Tests of Strong-Field Gravity with Observations in the Electromagnetic Spectrum

Neutron stars and black holes are the astrophysical systems with the strongest gravitational fields in the universe. In this article, I review the prospect of using observations of such compact objects to probe some of the most intriguing general relativistic predictions in the strong-field regime: the absence of stable circular orbits near a compact object and the presence of event horizons around black-hole singularities. I discuss the need for a theoretical framework, within which future experiments will provide detailed, quantitative tests of gravity theories. Finally, I summarize the constraints imposed by current observations of neutron stars on potential deviations from general relativity.

Testing for Lorentz violation: constraints on standard-model-extension parameters via lunar laser ranging

We present constraints on violations of Lorentz invariance based on archival 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 the equivalent of a few centimeters (parts in 10(11) of the total distance). By analyzing this 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. This work constitutes the first LLR constraints on SME parameters.

Experiments with probe masses

It is reasonable to regard the experiments performed by C. Coulomb and H. Cavendish in the end of the 18th century as the beginning of laboratory experimental physics. These outstanding scientists have measured forces (accelerations) produced by electric charges and by gravitational "charges" on probe masses that were attached to torque balance. Among the variety of different research programs and projects existing today, experiments with probe masses are still playing an important role. In this short review, the achieved and planned sensitivities of very challenging LIGO (Laser Interferometer Gravitational wave Observatory) and LISA (Laser Interferometer Space Antennae) projects are described, and a list of nonsolved problems is discussed as well. The role of quantum fluctuations in high precision measurements is also outlined. Apart from these main topics, the limitations of sensitivity caused by cosmic rays and the prospects of clock frequency stability are presented.

Strongly coupled chameleon fields: new horizons in scalar field theory

We show that, as a result of nonlinear self-interactions, scalar field theories that couple to matter much more strongly than gravity are not only viable but could well be detected by a number of future experiments provided that they are properly designed to do so.

Tests of General Relativity from Timing the Double Pulsar

The double pulsar system PSR J0737-3039A/B is unique in that both neutron stars are detectable as radio pulsars. They are also known to have much higher mean orbital velocities and accelerations than those of other binary pulsars. The system is therefore a good candidate for testing Einstein's theory of general relativity and alternative theories of gravity in the strong-field regime. We report on precision timing observations taken over the 2.5 years since its discovery and present four independent strong-field tests of general relativity. These tests use the theory-independent mass ratio of the two stars. By measuring relativistic corrections to the Keplerian description of the orbital motion, we find that the "post-Keplerian" parameter s agrees with the value predicted by general relativity within an uncertainty of 0.05%, the most precise test yet obtained. We also show that the transverse velocity of the system's center of mass is extremely small. Combined with the system's location near the Sun, this result suggests that future tests of gravitational theories with the double pulsar will supersede the best current solar system tests. It also implies that the second-born pulsar may not have formed through the core collapse of a helium star, as is usually assumed.

Dark energy as a Born-Infeld gauge interaction violating the equivalence principle

We investigate the possibility that dark energy does not couple to gravitation in the same way as ordinary matter, yielding a violation of the weak and strong equivalence principles on cosmological scales. We build a transient mechanism in which gravitation is pushed away from general relativity by a Born-Infeld gauge interaction acting as an abnormally weighting (dark) energy. This mechanism accounts for the Hubble diagram of far-away supernovae by cosmic acceleration and time variation of the gravitational constant while accounting naturally for the present tests on general relativity.

The Confrontation between General Relativity and Experiment

The status of experimental tests of general relativity and of theoretical frameworks for analyzing them is 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. Ongoing 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, and the Nordtvedt effect in lunar motion. Gravitational wave damping has been detected in an amount that agrees with general relativity to better than half a percent using the Hulse-Taylor binary pulsar, and other binary pulsar systems have yielded other tests, especially of strong-field effects. When direct observation of gravitational radiation from astrophysical sources begins, new tests of general relativity will be possible.

Low-Frequency Gravitational Wave Searches Using Spacecraft Doppler Tracking

This paper discusses spacecraft Doppler tracking, the current-generation detector technology used in the low-frequency (∼millihertz) gravitational wave band. In the Doppler method the earth and a distant spacecraft act as free test masses with a ground-based precision Doppler tracking system continuously monitoring the earth-spacecraft relative dimensionless velocity 2Δv/c = Δν/ν0, where Δν is the Doppler shift and ν0 is the radio link carrier frequency. A gravitational wave having strain amplitude h incident on the earth-spacecraft system causes perturbations of order h in the time series of Δν/ν0. Unlike other detectors, the ∼ 1-10 AU earth-spacecraft separation makes the detector large compared with millihertz-band gravitational wavelengths, and thus times-of-flight of signals and radio waves through the apparatus are important. A burst signal, for example, is time-resolved into a characteristic signature: three discrete events in the Doppler time series. I discuss here the principles of operation of this detector (emphasizing transfer functions of gravitational wave signals and the principal noises to the Doppler time series), some data analysis techniques, experiments to date, and illustrations of sensitivity and current detector performance. I conclude with a discussion of how gravitational wave sensitivity can be improved in the low-frequency band.

Massive graviton as a testable cold-dark-matter candidate

We construct a consistent model of gravity where the tensor graviton mode is massive, while linearized equations for scalar and vector metric perturbations are not modified. The Friedmann equation acquires an extra dark-energy component leading to accelerated expansion. The mass of the graviton can be as large as approximately (10(15) cm)(-1), being constrained by the pulsar timing measurements. We argue that nonrelativistic gravitational waves can comprise the cold dark matter and may be detected by the future gravitational wave searches.

Detecting extra dimensions with gravity-wave spectroscopy: the black-string brane world

Using the black string between two branes as a model of a brane-world black hole, we compute the gravity-wave perturbations and identify the features arising from the additional polarizations of the graviton. The standard four-dimensional gravitational wave signal acquires late-time oscillations due to massive modes of the graviton. The Fourier transform of these oscillations shows a series of spikes associated with the masses of the Kaluza-Klein modes, providing in principle a spectroscopic signature of extra dimensions.

Astrophysical Observations: Lensing and Eclipsing Einstein's Theories

Albert Einstein postulated the equivalence of energy and mass, developed the theory of special relativity, explained the photoelectric effect, and described Brownian motion in five papers, all published in 1905, 100 years ago. With these papers, Einstein provided the framework for understanding modern astrophysical phenomena. Conversely, astrophysical observations provide one of the most effective means for testing Einstein's theories. Here, I review astrophysical advances precipitated by Einstein's insights, including gravitational redshifts, gravitational lensing, gravitational waves, the Lense-Thirring effect, and modern cosmology. A complete understanding of cosmology, from the earliest moments to the ultimate fate of the universe, will require developments in physics beyond Einstein, to a unified theory of gravity and quantum physics.

Progress in lunar laser ranging tests of relativistic gravity

Analyses of laser ranges to the Moon provide increasingly stringent limits on any violation of the equivalence principle (EP); they also enable several very accurate tests of relativistic gravity. These analyses give an EP test of Delta(MG/MI)EP=(-1.0+/-1.4) x 10(-13). This result yields a strong equivalence principle (SEP) test of Delta(MG/MI)SEP=(-2.0+/-2.0) x 10(-13). Also, the corresponding SEP violation parameter eta is (4.4+/-4.5) x 10(-4), where eta=4beta-gamma-3 and both beta and gamma are post-Newtonian parameters. Using the Cassini gamma, the eta result yields beta-1=(1.2+/-1.1) x 10(-4). The geodetic precession test, expressed as a relative deviation from general relativity, is Kgp=-0.0019+/-0.0064. The search for a time variation in the gravitational constant results in G /G=(4+/-9) x 10(-13) yr(-1); consequently there is no evidence for local (approximately 1 AU) scale expansion of the solar system.

Measurement of the solar gravitational deflection of radio waves using geodetic very-long-baseline interferometry data, 1979-1999

We used very-long-baseline interferometry (VLBI) to measure the deflection by the Sun of radio waves emanating from distant compact radio sources. This bending is characterized in the parametrized post-Newtonian formalism by gamma, which is unity in general relativity. Using a large geodetic VLBI data set, we obtained gamma=0.9998(3)+/-0.0004(5) (estimated standard error). We found no systematic biases from our analysis of subgroups of data.