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Experimental Tests of General Relativity: Recent Progress and Future Directions

Slava G. Turyshev

arXiv:0809.3730v2gr-qc

TL;DR

The paper addresses how accurately general relativity has been tested and why new physics beyond it remains worth probing. It reviews the theory’s foundations and experimental progress, then evaluates motivations and proposed space-based gravitational tests. These experiments could improve current-test accuracy by up to several orders of magnitude and advance gravitational research.

  • Problem

    The paper examines whether general relativity remains adequate across gravitational regimes and how higher-precision tests can probe physics beyond it.

  • Method

    The paper reviews general-relativity foundations, recent solar-system tests, theoretical motivations for deviations, and proposed space-based gravitational experiments.

  • Results

    Proposed space-based experiments could improve current-test accuracy by up to several orders of magnitude and significantly advance fundamental-physics research.

  • Takeaways & Limitations

    Space-based laboratories offer controlled, dynamically pure conditions and unique regimes for precision tests of gravitation and fundamental physics.

Abstract

from arXiv · show

Einstein's general theory of relativity is the standard theory of gravity, especially where the needs of astronomy, astrophysics, cosmology and fundamental physics are concerned. As such, this theory is used for many practical purposes involving spacecraft navigation, geodesy and time transfer. Here I review the foundations of general relativity, discuss recent progress in the tests of relativistic gravity, and present motivations for the new generation of high-accuracy tests of new physics beyond general relativity. Space-based experiments in fundamental physics are capable today to uniquely address important questions related to the fundamental laws of nature. I discuss the advances in our understanding of fundamental physics that are anticipated in the near future and evaluate the discovery potential of a number of the recently proposed space-based gravitational experiments.

I. INTRODUCTION

General relativity has passed increasingly precise tests across solar-system and binary-pulsar regimes, becoming the standard theory for practical gravitational applications. The paper reviews these tests, theoretical motivations for deviations, and space-based experiments designed to improve future precision.

  • Experimental status: Very long baseline interferometry produced successive γ measurements, reaching better than approximately 0.045% accuracy through astrometric observations.
  • Experimental status: Lunar laser ranging constrained 4β − γ − 3 to (4.0 ± 4.3) × 10−4, corresponding to approximately 0.011% accuracy in testing general relativity.
  • Experimental status: Cassini constrained the PPN parameter γ−1 to (2.1 ± 2.3) × 10−5, achieving approximately 0.002% accuracy in solar-system gravity tests.
  • Experimental status: General relativity agrees with data from both weak-field solar-system experiments and binary-pulsar tests of stronger-field effects.Binary pulsars provide precision tests of the strong-field regime despite moving in the weak field of a companion.
  • Motivations and outlook: The paper motivates new tests because strong-field theoretical problems, quantum-gravity incompatibility, cosmological observations, and untested large-scale regimes challenge general relativity’s completeness.
  • Motivations and outlook: Space laboratories provide controlled, dynamically pure conditions unavailable on Earth and can exploit variable potentials, large distances, microgravity, and reduced non-gravitational noise.

II. TESTING THE FOUNDATIONS OF GENERAL RELATIVITY

General relativity models gravity as spacetime geometry governed by an action and universally coupled to Standard Model fields. Its field equations connect spacetime curvature with energy-momentum, while coordinate gauge freedom must be fixed to solve them.

  • Foundations: General relativity is a tensor field theory that describes gravity as a universal deformation of flat Minkowski spacetime.
  • Foundations: The gravitational action uses the Ricci scalar, Newton’s constant, the metric determinant, and the spacetime metric to define the theory’s dynamics.
  • Foundations: The metric couples universally and minimally to Standard Model fields by replacing the Minkowski metric throughout their description.
  • Field equations: Solving the field equations requires fixing the theory’s arbitrary coordinate-transformation freedom, for example through harmonic gauge.
  • Field equations: Einstein’s equations link the geometry of four-dimensional spacetime with the energy-momentum contained in that spacetime.

A. Scalar-Tensor Extensions to General Relativity

Scalar-tensor theories extend metric gravity with a scalar field whose coupling can vary with the field. The paper situates these theories within the PPN framework, where deviations from general relativity are encoded in phenomenological parameters.

  • Scalar-tensor theories: Scalar-tensor theories supplement the metric tensor with a scalar field ϕ and allow the gravitational coupling strength to depend on that field.
  • Scalar-tensor theories: Their general action contains field-dependent functions f(ϕ), g(ϕ), V(ϕ), coupling functions q_i(ϕ), and Standard Model matter Lagrangians.
  • Brans–Dicke theory: Brans–Dicke theory is the best-known alternative, with β = 1 and γ = (1 + ω)/(2 + ω), where ω is an unknown dimensionless coupling constant.
  • Brans–Dicke theory: In Brans–Dicke theory, general relativity is recovered as ω →∞, while finite ω represents observational deviations from it.
  • PPN framework: The PPN formalism parameterizes metric theories for slowly moving bodies and weak inter-body gravity, with general relativity as a special case.
  • PPN framework: Under stated assumptions, the metric uses N point-like gravitational sources with μ_j = Gm_j and barycentric positions and separations defining the source geometry.
  • PPN framework: The PPN metric supports derivation of the N-body Lagrangian, equations of motion, and electromagnetic light-time equation used for solar-system experiments.

C. PPN-Renormalized Extension of General Relativity

The PPN-renormalized formulation treats possible departures from general relativity as perturbations around its successful background. It provides equations for metric, dynamics, and light propagation that organize experimental searches for non-Einsteinian effects.

  • PPN-renormalized formulation: Possible deviations are represented by renormalized parameters γ̄ ≡ γ − 1 and β̄ ≡ β − 1, which vanish in general relativity.
  • PPN-renormalized formulation: The PPN metric perturbation δg^PPN_mn is defined relative to the general-relativistic metric and represents a small deformation of that background.
  • Equations of motion: The renormalized equations of motion explicitly include perturbative accelerations in addition to the general-relativistic dynamics.
  • Equations of motion: The framework also accommodates possible violations of equality between gravitational and inertial mass and a varying gravitational constant through additional perturbative terms.
  • Light propagation: The corresponding light-time equation expresses signal travel between transmission and reception events as a general-relativistic contribution plus perturbative terms.
  • Experimental application: Cassini measured γ̄ = (2.1 ± 2.3) × 10−5, while lunar laser ranging yielded β̄ = (1.2 ± 1.1) × 10−4.

III. SEARCH FOR NEW PHYSICS BEYOND GENERAL RELATIVITY

The paper examines why general relativity may require modification despite its empirical success, focusing on quantum-gravity limitations and cosmological evidence for new physics. It motivates high-accuracy experiments to search for predicted deviations.

  • General relativity and the Standard Model successfully describe known fundamental laws, but neither provides a complete account of quantum gravity.
  • Candidate extensions introduce new interactions that may violate the Equivalence Principle, vary fundamental constants, modify the inverse-square law, break Lorentz symmetry, or alter large-scale gravity.
  • Space-based experiments are positioned as opportunities to test these manifestations and search for fundamental discoveries.
  • The paper presents a new generation of gravitational experiments designed to probe non-Einsteinian behavior at sensitivities up to five orders of magnitude beyond current tests.

A. String/M-Theory and Tensor-Scalar Extensions of General Relativity

String/M-theory and tensor-scalar models motivate deviations from general relativity through additional scalar fields and cosmological attractor mechanisms. These models can suppress present-day deviations while retaining experimentally testable residual effects.

  • String/M-theory: Quantum gravity remains incomplete, while string theory supplies candidate frameworks containing gravitons, dilatons, and antisymmetric tensor fields.
  • String/M-theory: The least coupling principle and cosmological attractor mechanism can drive a scalar field toward a coupling minimum, making it approximately decouple from dominant cosmological matter.
  • Tensor-scalar extensions: Current Equivalence Principle limits imply γ̄ ≤ 6 × 10^-9, while Cassini reached 10^-5, leaving insufficient sensitivity to test the CAM in this case.
  • Tensor-scalar extensions: Runaway-dilaton models predict weak-equivalence-principle violations as small as ∆a/a ≃ 10^-18 under solar-system conditions.
  • Tensor-scalar extensions: Attractor dynamics predict post-Einstein parameters that approach, but need not exactly reach, their general-relativistic values.
  • Tensor-scalar extensions: Phantom-energy models face catastrophic ultraviolet instabilities, whereas ghost condensation adds higher-order kinetic terms to stabilize the evolution.

B. Observational Motivations for Higher Accuracy Tests of Gravity

Cosmological observations provide strong motivation for more accurate gravity tests by establishing accelerated expansion and exposing unresolved problems with dark energy and the cosmological constant.

  • CMB, large-scale-structure, and type Ia supernova observations constrain cosmological models and indicate that the universe’s expansion is accelerating.
  • The observed acceleration is independently supported by several hundred type Ia supernovae and CMB observations.
  • The cosmological constant interpretation is troubled because its smallest theoretical estimates exceed the observed value by 55 orders of magnitude.
  • Dynamical scalar fields and modified-gravity models are therefore considered as alternatives to a cosmological constant or dark-energy source.

C. Modified Gravity as an Alternative to Dark Energy

Modified gravity offers an alternative explanation for cosmic acceleration by changing gravity at large distances rather than introducing dark energy. Such models can produce testable planetary effects but face solar-system and theoretical constraints.

  • Some inverse-curvature models recover an acceptable short-distance weak-field limit through screening of extra degrees of freedom.
  • These theories may conflict with solar-system tests or contain ghost-like degrees of freedom that are difficult to reconcile with fundamental theories.
  • Large-distance modifications of gravity, including effects associated with extra spatial dimensions, could account for cosmic acceleration without a dark-energy source.
  • Modified-gravity models can predict deviations in planetary motions, motivating new tests in the solar system.
  • Lunar laser ranging could test an anomalous perihelion shift of ∆φ ∼ 10^-12 against an achieved accuracy of 2.4 × 10^-11.

D. Scalar Field Models as Candidates for Dark Energy

The paper surveys scalar fields as dark-energy candidates, including models motivated by supersymmetry and string/M-theory, and connects their couplings and potentials to cosmological evolution and equivalence-principle tests.

  • D. Scalar Field Models as Candidates for Dark Energy: Scalar fields with extremely low mass and effective potentials are presented as simple candidates for dynamical dark energy.Slowly rolling fields can provide persistent potential energy associated with the late epoch of inflation described in the paper.
  • D. Scalar Field Models as Candidates for Dark Energy: Effective scalar fields arise in supersymmetric field theories and string/M-theory, where dilaton couplings can be represented by scalar-tensor theories.The dilaton’s vacuum expectation value determines the relationship between gauge and gravitational couplings.
  • D. Scalar Field Models as Candidates for Dark Energy: Scaling and tracking quintessence potentials can make scalar-field energy density evolve alongside other matter constituents, but scaling potentials alone do not produce accelerated expansion.The acceleration problem is identified for potentials whose energy density simply scales with the other constituents.
  • D. Scalar Field Models as Candidates for Dark Energy: Couplings between quintessence and dark matter can generate acceleration with a scaling potential while remaining consistent with equivalence-principle tests.The passage also notes that dilaton decoupling from dark matter may proceed more slowly than from gravity and fermions.
  • D. Scalar Field Models as Candidates for Dark Energy: The paper next discusses effects predicted by these theories and proposed dedicated space experiments to test them.The experiments target predictions from the theories and models surveyed above.

1. The Weak Equivalence Principle

The weak equivalence principle states that different compositions undergo the same free-fall acceleration, while experiments seek increasingly precise violations predicted by some extensions of the Standard Model.

  • 1. The Weak Equivalence Principle: The WEP equates gravitational and inertial masses for neutral bodies, implying composition-independent free-fall acceleration in an external gravitational field.Relevant composition differences include nuclear binding, neutron-to-proton ratios, and atomic charges.
  • 1. The Weak Equivalence Principle: New macroscopic-range quantum fields can violate the WEP because their exchange forces couple to generalized charges rather than mass-energy.General relativity and other metric theories assume the WEP is exact.
  • 1. The Weak Equivalence Principle: WEP sensitivity is set by differential-acceleration precision divided by the compositional difference between test bodies.For bodies at equal source distance, the test compares their free-fall accelerations and gravitational-to-inertial mass ratios.
  • 1. The Weak Equivalence Principle: 1.4 × 10^-13 is the most recent reported precision for laboratory WEP tests, with beryllium and titanium yielding Δa/a = (1.0 ± 1.4) × 10^-13.Earlier experiments reached approximately 10^-11 and 10^-12 fractional precision.
  • 1. The Weak Equivalence Principle: Some unified-theory models predict WEP violations at sensitivities accessible to future space-based tests.The proposed missions are motivated by the possibility of probing these predicted deviations from composition-independent acceleration.
  • 1. The Weak Equivalence Principle: Space-based experiments are proposed to reduce non-gravitational noise and improve WEP sensitivity by many orders of magnitude.Proposed targets include 10^-15 for MicroSCOPE, 1 part in 10^16 for QuITE, 1 part in 10^17 for GG, and 1 part in 10^18 for STEP.

2. The Strong Equivalence Principle

The strong equivalence principle extends equivalence to gravitational self-energy and self-gravitating bodies, motivating lunar laser ranging and proposed interplanetary laser-ranging tests.

  • 2. The Strong Equivalence Principle: The SEP covers gravitational properties arising from gravitational energy and concerns the nonlinear behavior of gravity.General relativity assumes the SEP is exact, whereas scalar-field and other alternative metric theories typically violate it.
  • 2. The Strong Equivalence Principle: Unlike the EEP, the SEP applies to self-gravitating objects and requires local experiments to be independent of when and where they occur.It requires a universal gravitational constant and is incompatible with a fifth force.
  • 2. The Strong Equivalence Principle: Planet-sized bodies are required for SEP tests because laboratory bodies have gravitational self-energy ratios near 10^-25.Laboratory WEP accuracy at 1 part in 10^13 is insufficient to test gravitational self-energy contributions.
  • 2. The Strong Equivalence Principle: LLR constrains possible Earth–Moon inequality in gravitational-to-inertial mass ratios to (−0.8 ± 1.3) × 10^-13.The Earth–Moon–Sun system currently provides the best solar-system arena for testing the SEP.
  • 2. The Strong Equivalence Principle: APOLLO’s 1-mm ranging precision is expected to improve SEP accuracy to η ≲ 2 × 10^-5.The same facility is expected to improve WEP tests and inverse-square-law tests at the Earth–Moon distance.
  • 2. The Strong Equivalence Principle: Mars laser ranging could test the SEP at the 2 × 10^-6 level using millimeter-class Earth–Mars ranging.Reliable laser links over tens of millions of kilometers make interplanetary precision ranging feasible.

B. Tests of Local Lorentz Invariance: Search for Physics Beyond the Standard Model

Tests of local Lorentz invariance use kinematic frameworks and increasingly precise laboratory, space-based, and astrophysical measurements to constrain deviations from special relativity. Proposed and anticipated missions extend these searches through controlled space environments, atomic clocks, and high-energy photons.

  • LLI tests examine whether local experimental outcomes depend on apparatus velocity or orientation, requiring an alternative theory to identify violations.
  • The RMS framework parameterizes Lorentz-violation deviations through resonator-frequency changes related to the laboratory’s velocity and orientation relative to a preferred frame.
  • ∆c/c = (2.6 ± 1.7) × 10^-15 was constrained by comparing orthogonal cryogenic optical resonators over approximately one year, with later work improving the bound by another order of magnitude.
  • The RMS framework cannot compare experiments using physically different clocks and rods because it does not specify their dynamics or relation to fundamental particles.
  • δ < 3 × 10^-22 was achieved in Hughes-Drever tests, while reassessment indicated bounds up to 8 orders of magnitude higher.
  • GLAST was expected to probe quantum-gravity effects at δ ≃10^-26 through gamma-ray observations spanning 20 MeV to above 300 GeV.
  • ACES aims to test the SME using atomic clocks in ISS microgravity, with fractional frequency stability and accuracy of a few parts in 10^16.
  • Optical clocks in orbit, combined with accurate time-frequency transfer, could improve present tests of fundamental-constant variation, LLI, and UFF by more than three orders of magnitude.

C. Tests of the Local Position Invariance

Tests of local position invariance assess whether clock rates and gravitational redshift are universal across locations and gravitational potentials. Existing laboratory, space, astronomical, and clock-comparison measurements agree with general relativity, while proposed space experiments target substantially higher precision and possible links to varying constants.

  • LPI tests assess whether a freely falling clock’s rate differs from a standard clock as gravitational potential changes.
  • The Pound–Rebka experiment measured the gravity-induced frequency shift as ∆ν/ν = (2.57 ± 0.26) × 10^-15.
  • Gravity Probe A verified general relativity’s gravitational redshift prediction to 70 ppm and established |µ| < 2 × 10^-4; the current most stringent bound is |µ| < 2.1 × 10^-5.
  • Laboratory, astronomical, atomic-clock, GPS, and binary-pulsar observations agree with general relativity, but their present accuracy cannot distinguish it from other metric theories preserving the EP.
  • 1. Fine-Structure Constant: The Oklo phenomenon constrained long-term fine-structure-constant variation to −0.9 × 10^-7 < αOklo/αtoday −1 < 1.2 × 10^-7 over two billion years.
  • 1. Fine-Structure Constant: Atomic-clock comparisons bounded fine-structure-constant variation at ˙α/α = (−0.9 ± 2.9) × 10^-15 yr^-1.
  • 1. Fine-Structure Constant: ACES is expected to measure fine-structure-constant time variation at approximately 10^-16 yr^-1 using clocks with full ground-and-space accuracy at the 10^-16 level or better.
  • 1. Fine-Structure Constant: Variation of fundamental constants generally entails UFF violation because composition-dependent couplings affect macroscopic-body masses and motion.

2. Gravitational Constant

Space-based ranging and laboratory experiments constrain possible changes to G and deviations from Newton’s inverse-square law, while proposed missions could substantially improve sensitivity to new forces. Current measurements remain broadly compatible with Newtonian gravity.

  • Variability in G: LLR constrains local solar-system expansion to a rate of −(5 ± 6) × 10−13 yr−1, expressed as ˙a/a = −˙G/G.If representative of cosmic history, this implies G changed by less than 1% over 13.4 Gyr.
  • Variability in G: Future LLR and pulsar-timing measurements could reach ˙G/G sensitivities of approximately 1 × 10−14 yr−1 and 3 × 10−15 yr−1, respectively.The quoted MLR estimate is limited by the available timing accuracy.
  • Inverse-square law: Satellite tests probe inverse-square-law ranges of about 10^5 m ≲ λ ≲ 10^7 m and constrain the strength parameter α to approximately 10−7.Other experiments cover shorter laboratory and longer stellar-structure ranges with weaker bounds.
  • Inverse-square law: Ground-based torsion-balance experiments find the inverse-square law holds down to 56 µm, constraining an extra dimension to less than 44 µm.These measurements reach distances below the dark-energy length scale and constrain new short-range forces.
  • Inverse-square law: ISLES could improve ground-based limits on inverse-square-law violations by four to six orders of magnitude below 100 µm and probe extra dimensions down to 5 µm.The proposed experiment combines microgravity with superconducting accelerometers and could also probe axions.
  • Inverse-square law: LLR tests the inverse-square law to 3 × 10−11 of gravitational-field strength at the Earth–Moon distance, while interplanetary ranging could reach 1 × 10−14 at 2 AU.These results and proposals extend precision tests from lunar to interplanetary scales.
  • Anomalies and new forces: Pioneer tracking reported an anomalous sunward acceleration of a_P = (8.74 ± 1.33) × 10−10 m/s2, despite most modern experiments agreeing with Newton’s law.The anomaly was inferred from Doppler drift at heliocentric distances between 20 and 70 AU.

F. Tests of Alternative and Modified-Gravity Theories with Gravitational Experiments in Space

Alternative-gravity theories motivate increasingly precise space experiments targeting the PPN parameter γ and related deviations from general relativity. Proposed missions use laser ranging, interferometry, and drag-free spacecraft to improve existing constraints and search for scalar or other new gravitational interactions.

  • Current constraints: Cassini measured γ̄ = (2.1 ± 2.3) × 10−5, approaching the range where several scalar-tensor theories predict γ̄ ∼ 10−6–10−7.Further improvement could distinguish scalar-tensor gravity from general relativity and test models of cosmological evolution.
  • Current constraints: Future astrometric missions such as Gaia are expected to determine γ with accuracies from 10−6 to 5 × 10−7.These missions improve on the approximately 1 mas astrometric accuracy represented by Hipparcos.
  • Proposed missions: Interplanetary laser ranging to a Mars lander could measure γ to a few parts in 10^7 if the lander’s transponder achieves 1 mm precision.Accuracies beyond this level require a dedicated space experiment.
  • Proposed missions: GTDM proposes drag-free spacecraft and laser ranging near the Sun, with requirements that could enable γ measurements accurate to 2 parts in 10^8.The estimate depends on disturbance compensation, timing transfer, and high-accuracy orbit determination.
  • Proposed missions: LATOR proposes γ accuracy of 1 part in 10^9, a factor of 30000 beyond Cassini’s best result, using redundant optical interferometry and interplanetary laser ranging.Its measurements target light deflection and Shapiro delay around the Sun.
  • Proposed missions: BEACON is designed to reach 1 part in 10^9 sensitivity to γ using four small spacecraft in coordinated Earth orbits and laser metrology links.The mission forms a flexible light-triangle configuration from inter-spacecraft ranging.

V. DISCUSSION AND OUTLOOK

The paper places precision tests of general relativity within broader efforts to understand dark energy, dark matter, cosmological evolution, and possible quantum modifications of gravity. Advances in quantum sensors and space-based experiments could improve current tests by several orders of magnitude.

  • Motivation: Observational cosmology, scalar-tensor extensions, brane-world models, and attempts to modify gravity on large scales motivate searches for deviations from Einstein’s theory.The paper notes that proposed tests target deviations three to five orders of magnitude below current experimental limits.
  • Technology: Ultracold-atom devices, atomic clocks, and quantum inertial sensors enable high-precision tests of quantum physics, the Standard Model, special relativity, gravitation, and general relativity.These technologies improve frequency measurements and monitoring of accelerations and rotations.
  • Outlook: Space-based experiments could improve the accuracy of current tests by up to several orders of magnitude when combined with ground-based laboratories.The paper presents these missions as potential contributors to major advances in fundamental physics over the next decade.
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