The confrontation between general relativity and experiment

We review the experimental evidence for Einstein’s general relativity. Tests of the Einstein equivalence principle support the postulates of curved space-time and bound variations of fundamental constants in space and time, while solar system experiments strongly confirm weak-field general relativity. The binary pulsar provides tests of gravitational wave damping and of strong-field general relativity. Future experiments, such as the gravity probe B gyroscope experiment, a satellite test of the equivalence principle, and tests of gravity at short distance to look for extra spatial dimensions could further constrain alternatives to general relativity. Laser Interferometric Gravitational Wave Observatories on Earth and in space may provide new tests of scalar-tensor gravity and graviton-mass theories via the properties of gravitational waves.     

Towards new tests of strong-field gravity with measurements of surface atomic line redshifts from neutron stars

In contrast to gravity in the weak-field regime, which has been subject to numerous experimental tests, gravity in the strong-field regime is largely unconstrained by observations. We show that gravity theories that pass solar system tests, but that diverge from general relativity in the strong-field regime, predict neutron stars with significantly different properties than their general relativistic counterparts. The range of redshfits of surface atomic lines predicted by such theories is significantly wider than the uncertainty introduced by our lack of knowledge of the equation of state of ultradense matter. Measurements of such lines with x-ray observatories can thus put new constraints on strong-field gravity.     

The confrontation between general relativity and experiment: An update

The status of experimental tests of general relativity to the end of 1983 is reviewed. The experimental support for the Einstein equivalence principle is summarized. If this principle is valid, gravitation must be described by a curved space-time, “metric” theory of gravity. General properties of metric theories are described and the parametrized post-Newtonian (PPN) formalism for treating the weak-field, slow-motion limit of such theories is set up. A zoo of selected metric theories of gravity is presented. Experimental tests of metric theories are then described, including the “classical” tests, tests of the strong equivalence principle, and others. The possibility of using gravitational-wave observations to test metric theories is discussed. A review is presented of the binary pulsar, in which the first evidence for gravitational radiation has been found. Finally cosmological tests of alternative theories are briefly described.     

Extension of loop quantum gravity to f(R) theories

The four-dimensional metric f(R) theories of gravity are cast into connection-dynamical formalism with real su(2) connections as configuration variables. Through this formalism, the classical metric f(R) theories are quantized by extending the loop quantization scheme of general relativity. Our results imply that the nonperturbative quantization procedure of loop quantum gravity is valid not only for general relativity but also for a rather general class of four-dimensional metric theories of gravity.     

Testing Gravity on Astrophysical Scales

We summarize a series of observational tests of the law of gravity on large astrophysical scales. These tests account for testing both the Poisson equation (inverse square law) using weak lensing and the Einstein equivalence principle through the test of the constancy of the constants of Nature. We emphasize the need to test general relativity on cosmological scales in light of the cosmological constant problem and of recent observational claims concerning the variation of fine structure constant.     

Does the planck mass run on the cosmological-horizon scale?

Einstein's theory of general relativity contains a universal value of the Planck mass. However, one may envisage that in alternative theories of gravity the effective value of the Planck mass (or Newton's constant), which quantifies the coupling of matter to metric perturbations, can run on the cosmological-horizon scale. In this Letter, we study the consequences of a glitch in the Planck mass from subhorizon to superhorizon scales. We show that current cosmological observations severely constrain this glitch to less than 1.2%.     

The dynamics of metric-affine gravity

Metric-affine theories of gravity provide an interesting alternative to general relativity: in such an approach, the metric and the affine (not necessarily symmetric) connection are independent quantities. Furthermore, the action should include covariant derivatives of the matter fields, with the covariant derivative naturally defined using the independent connection. As a result, in metric-affine theories a direct coupling involving matter and connection is also present. The role and the dynamics of the connection in such theories is explored. We employ power counting in order to construct the action and search for the minimal requirements it should satisfy for the connection to be dynamical. We find that for the most general action containing lower order invariants of the curvature and the torsion the independent connection does not carry any dynamics. It actually reduces to the role of an auxiliary field and can be completely eliminated algebraically in favour of the metric and the matter field, introducing extra interactions with respect to general relativity. However, we also show that including higher order terms in the action radically changes this picture and excites new degrees of freedom in the connection, making it (or parts of it) dynamical. Constructing actions that constitute exceptions to this rule requires significant fine tuned and/or extra a priori constraints on the connection. We also consider f(R) actions as a particular example in order to show that they constitute a distinct class of metric-affine theories with special properties, and as such they cannot be used as representative toy theories to study the properties of metric-affine gravity.     

The principle of equivalence and theories of gravity

We construct classical theories of gravity on the basis of special relativity and the Einstein-Infeld accelerating-elevator thought experiment. The resulting theories share most of the main features of general relativity, namely the nonlinear character of the theory, the metrical significance of the gravitational potentials and the geodesic equation of particle motion. They differ from general relativity in at most nonlinear terms in the gravitational constant G in their equations of particle motion and field equations.     

Energy conservation and the principle of equivalence

If the equivalence principle is violated, then observers performing local experiments can detect effects due to their position in an external gravitational environment (preferred-location effects) or can detect effects due to their velocity through some preferred frame (preferred-frame effects). We show that the principle of energy conservation implies a quantitative connection between such effects and structure-dependence of the gravitational acceleration of test bodies (violation of the Weak Equivalence Principle). We analyze this connection within a general theoretical framework that encompasses both non-gravitational local experiments and test bodies as well as gravitational experiments and test bodies, and we use it to discuss specific experimental tests of the equivalence principle, including non-gravitational tests such as gravitational redshift experiments, Eötvös experiments, the Hughes-Drever experiment, and the Turner-Hill experiment, and gravitational tests such as the lunar-laser-ranging “Eötvös” experiment, and measurements of anisotropies and variations in the gravitational constant. This framework is illustrated by analyses within two theoretical formalisms for studying gravitational theories: the PPN formalism, which deals with the motion of gravitating bodies within metric theories of gravity, and the TH?μ formalism that deals with the motion of charged particles within all metric theories and a broad class of non-metric theories of gravity.     

Equations of motion of test bodies in a spherically symmetric,static gravitational field

We consider a class of theories of gravity in which the motion of test particles is governed by the path equation (with respect to a general affine connection Г). When we restrict attention to a spherically symmetric, static gravitational field, the path equation is characterized by three arbitrary functions of the gravitational field (as opposed to two in the case of metric theories where Г={ }). We find that there are essentially only two constraints on the three functions by appealing to solar system experiments. Therefore, we must supplement the equation of motion with other physical laws to obtain a value for the third arbitrary function (this, of course, is not necessary in the case of metric theories). If we consider theories in which both Г andg play a physical role we find in certain circumstances that this “third” condition is sufficient to prove that the theories under investigation reduce to their “metric” form.     

Probing Yukawian gravitational potential by numerical simulations. I. Changing N-body codes

In the weak field limit general relativity reduces, as is well known, to the Newtonian gravitation. Alternative theories of gravity, however, do not necessarily reduce to Newtonian gravitation; some of them, for example, reduce to Yukawa-like potentials instead of the Newtonian potential. Since the Newtonian gravitation is largely used to model with success the structures of the universe, such as for example galaxies and clusters of galaxies, a way to probe and constrain alternative theories, in the weak field limit, is to apply them to model the structures of the universe. In the present study, we consider how to probe Yukawa-like potentials using N-body numerical simulations.     

Kerr black holes are not unique to general relativity

Considerable attention has recently focused on gravity theories obtained by extending general relativity with additional scalar, vector, or tensor degrees of freedom. In this Letter, we show that the black-hole solutions of these theories are essentially indistinguishable from those of general relativity. Thus, we conclude that a potential observational verification of the Kerr metric around an astrophysical black hole cannot, in and of itself, be used to distinguish between these theories. On the other hand, it remains true that detection of deviations from the Kerr metric will signify the need for a major change in our understanding of gravitational physics.     

Post-newtonian parameters from alternative theories of gravity

Alternative theories of gravity have been recently studied in connection with their cosmological applications, both in the Palatini and in the metric formalism. The aim of this paper is to propose a theoretical framework (in the Palatini formalism) to test these theories at the solar system level and possibly at the galactic scales. We exactly solve field equations in vacuum and find the corresponding corrections to the standard general relativistic gravitational field. On the other hand, approximate solutions are found in matter cases starting from a Lagrangian which depends on a phenomenological parameter. Both in the vacuum case and in the matter case the deviations from General Relativity are controlled by parameters that provide the Post-Newtonian corrections which prove to be in good agreement with solar system experiments.     

Interpretation of Rotation Curves of Spiral Galaxies in Modified Teleparallel Gravity

There is a significant difference between the calculation based on the theory of general relativity and observation of rotation curves of spiral galaxies. To describe this discrepancy, two distinct theories have been proposed so far： existence of dark matter and modification of underlying gravitational theory. In the absence of dark matter, it is assumed that the theory of general relativity on galactic scales needs to be modified. This letter is devoted to explaining this difference in a modified teleparMIeI gravity. We show that modified teleparallel gravity favors flatness of rotation curves of spiral galaxies much in the same way as observation shows.     

北京光速各向异性实验的广义相对论(及度规理论)预言值

基于广义相对论及度规引力理论的基本原理,计算了北京“光速各向异性检验”实验的预期值。结论是该实验将不可能在广义相对论传统观点和文献[1]提出的观点之间作出判断。     

Interpretation of Rotation Curves of Spiral Galaxies in Modified Teleparallel Gravity

There is a significant difference between the calculation based on the theory of general relativity and observation of rotation curves of spiral galaxies. To describe this discrepancy, two distinct theories have been proposed so far: existence of dark matter and modification of underlying gravitational theory. In the absence of dark matter, it is assumed that the theory of general relativity on galactic scales needs to be modified. This letter is devoted to explaining this difference in a modified teleparallel gravity. We show that modified teleparallel gravity favors flatness of rotation curves of spiral galaxies much in the same way as observation shows.     

Tests of gravitational symmetries with radio pulsars

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 gravity theories, at very different length scales, favor to very high precision the predictions of the strong equivalence principle (SEP) and, in particular, general relativity which embodies SEP completely. As the founding principles of gravity, these symmetries are motivated to be promoted to even stricter tests in future.     

Periodic relativity: basic framework of the theory

An alternative gravity theory is proposed which does not rely on Riemannian geometry and geodesic trajectories. The theory named periodic relativity (PR) does not use the weak field approximation and allows every two body system to deviate differently from the flat Minkowski metric. PR differs from general relativity (GR) in predictions of the proper time intervals of distant objects. PR proposes a definite connection between the proper time interval of an object and gravitational frequency shift of its constituent particles as the object travels through the gravitational field. PR is based on the dynamic weak equivalence principle which equates the gravitational mass with the relativistic mass. PR provides very accurate solutions for the Pioneer anomaly and the rotation curves of galaxies outside the framework of general relativity. PR satisfies Einstein’s field equations with respect to the three major GR tests within the solar system and with respect to the derivation of Friedmann equation in cosmology. This article defines the underlying framework of the theory.     

Probing gravity at cosmological scales by measurements which test the relationship between gravitational lensing and matter overdensity

The standard cosmology is based on general relativity (GR) and includes dark matter and dark energy and predicts a fixed relationship between the gravitational potentials responsible for gravitational lensing and the matter overdensity. Alternative theories of gravity often make different predictions. We propose a set of measurements which can test this relationship, thereby distinguishing between dark energy or matter models and models in which gravity differs from GR. Planned surveys will be able to measure E(G), an observational quantity whose expectation value is equal to the ratio of the Laplacian of the Newtonian potentials to the peculiar velocity divergence, to percent accuracy. This will easily separate alternatives such as the cold dark matter model with a cosmological constant, Dvali-Gabadadze-Porrati, TeVeS, and f(R) gravity.     

Post-Newtonian limit of Finsler space theories of gravity and solar system tests

Finsler geometry is considered as a wider framework for analysing solar system tests of theories of gravity than is afforded by Riemannian geometry. The post-Newtonian limit for the spherically symmetric one-body problem is examined by expanding the Finsler metric about the Minkowski space of Special Relativity for those Finsler spaces whose null surface is Riemannian. In such a framework there are five PPN parameters instead of the three in Riemannian geometry. The classical solar system tests can readily be satisfied leaving two arbitrary parameters. These parameters could be determined from measurements of the second order gravitational red-shift and periodic perturbations in particle orbits, thus providing a consistency check on the Riemannian metric hypothesis of General Relativity. Such an experiment is possible on a satellite on an orbit with perihelion of a few solar radii.