The Standard-Model Extension and Gravitational Tests

Construction of Higher-Order Metric Fluctuation Terms in Spacetime Symmetry-Breaking Effective Field Theory

We examined the basic conservation laws for diffeomorphism symmetry in the context of spontaneous diffeomorphism and local Lorentz-symmetry breaking. The conservation laws were used as constraints on a generic series of terms in an expansion around a flat background. We found all such terms for a two-tensor coupling to cubic order in the metric and tensor field fluctuations. The results are presented in a form that can be used for phenomenological calculations. One key result is that if we preserve the underlying diffeomorphism symmetry in a spontaneous-symmetry breaking scenario, one cannot decouple the two-tensor fluctuations from the metric fluctuations at the level of the action, except in special cases of the quadratic actions.

Combined Search for a Lorentz-Violating Force in Short-Range Gravity Varying as the Inverse Sixth Power of Distance

Precision measurements of the inverse-square law via experiments on short-range gravity provide sensitive tests of Lorentz symmetry. A combined analysis of data from experiments at the Huazhong University of Science and Technology and Indiana University sets simultaneous limits on all 22 coefficients for Lorentz violation correcting the Newton force law as the inverse sixth power of distance. Results are consistent with no effect at the level of 10^{-12}  m^{4}.

Lorentz-Violating Gravity Models and the Linearized Limit

Many models in which Lorentz symmetry is spontaneously broken in a curved spacetime do so via a “Lorentz-violating” (LV) vector or tensor field, which dynamically takes on a vacuum expectation value and provides additional local geometric structure beyond the metric. The kinetic terms of such a field will not necessarily be decoupled from the kinetic terms of the metric, and will generically lead to a set of coupled equations for the perturbations of the metric and the LV field. In some models, however, the imposition of certain additional conditions can decouple these equations, yielding an “effective equation” for the metric perturbations alone. The resulting effective equation may depend on the metric in a gauge-invariant way, or it may be gauge-dependent. The only two known models yielding gauge-invariant effective equations involve differential forms; I show in this work that the obvious generalizations of these models do not yield gauge-invariant effective equations. Meanwhile, I show that a gauge-dependent effective equation may be obtained from any “tensor Klein–Gordon” model under similar assumptions. Finally, I discuss the implications of this work in the search for Lorentz-violating gravitational effects.

Relating Noncommutative SO(2,3)☆ Gravity to the Lorentz-Violating Standard-Model Extension

We consider a model of noncommutative gravity that is based on a spacetime with broken local SO(2,3) ☆ symmetry. We show that the torsion-free version of this model is contained within the framework of the Lorentz-violating Standard-Model Extension (SME). We analyze in detail the relation between the torsion-free, quadratic limits of the broken SO(2,3) ☆ model and the Standard-Model Extension. As part of the analysis, we construct the relevant geometric quantities to quadratic order in the metric perturbation around a flat background.

The Muonium Antimatter Gravity Experiment

A direct measurement of the gravitational acceleration of antimatter has the potential to show that we live in a “Dirac-Milne” Universe, which could explain cosmological observations without the need for dark matter, dark energy, inflation, or missing antimatter. Such a measurement would also be sensitive to the possible existence of a fifth force. Cooling antimatter to temperatures where gravitational energies are comparable to thermal energies is challenging for most forms of antimatter, which annihilate upon contact with matter. The exception is the antimuon (μ+), which is easily cooled by stopping in cold matter, but the short muon lifetime poses challenges. Positive muons that stop in material will combine with free electrons to form muonium, a neutral leptonic atom with most of its mass derived from the 2nd-generation antimuon. We are developing the Muonium Antimatter Gravity Experiment (MAGE) to measure the gravitational force on muonium using a novel, monoenergetic, low-velocity, horizontal muonium beam directed at an ultra-precise atom interferometer. If successful, MAGE will measure for the first time the gravitational coupling to a 2nd-generation particle in a system whose antimatter-dominated mass is not predominantly strong-interaction binding energy. The novel MAGE beam production approach could also have important applications to other muonium experiments as well as to the measurement ofg– 2.

Lorentz Symmetry Violations from Matter-Gravity Couplings with Lunar Laser Ranging

The standard-model extension (SME) is an effective field theory framework aiming at parametrizing any violation to the Lorentz symmetry (LS) in all sectors of physics. In this Letter, we report the first direct experimental measurement of SME coefficients performed simultaneously within two sectors of the SME framework using lunar laser ranging observations. We consider the pure gravitational sector and the classical point-mass limit in the matter sector of the minimal SME. We report no deviation from general relativity and put new realistic stringent constraints on LS violations improving up to 3 orders of magnitude previous estimations.

Superconducting-Gravimeter Tests of Local Lorentz Invariance

Superconducting-gravimeter measurements are used to test the local Lorentz invariance of the gravitational interaction and of matter-gravity couplings. The best laboratory sensitivities to date are achieved via a maximum-reach analysis for 13 Lorentz-violating operators, with some improvements exceeding an order of magnitude.

Testing General Relativity with Stellar Orbits around the Supermassive Black Hole in Our Galactic Center

We demonstrate that short-period stars orbiting around the supermassive black hole in our Galactic center can successfully be used to probe the gravitational theory in a strong regime. We use 19 years of observations of the two best measured short-period stars orbiting our Galactic center to constrain a hypothetical fifth force that arises in various scenarios motivated by the development of a unification theory or in some models of dark matter and dark energy. No deviation from general relativity is reported and the fifth force strength is restricted to an upper 95% confidence limit of |α|<0.016 at a length scale of λ=150 astronomical units. We also derive a 95% confidence upper limit on a linear drift of the argument of periastron of the short-period star S0-2 of |ω[over ˙]_{S0-2}|<1.6×10^{-3}  rad/yr, which can be used to constrain various gravitational and astrophysical theories. This analysis provides the first fully self-consistent test of the gravitational theory using orbital dynamic in a strong gravitational regime, that of a supermassive black hole. A sensitivity analysis for future measurements is also presented.