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We investigate leading order deviations from general relativity that violate the Einstein equivalence principle in the gravitational standard model extension. We show that redshift experiments based on matter waves and clock comparisons are equivalent to one another. Consideration of torsion balance tests, along with matter wave, microwave, optical, and Mossbauer clock tests, yields comprehensive limits on spin-independent Einstein equivalence principle-violating standard model extension terms at the $10^{-6}$ level.
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We review matter wave and clock comparison tests of the gravitational redshift. To elucidate their relationship to tests of the universality of free fall (UFF), we define scenarios wherein redshift violations are coupled to violations of UFF (type II), or independent of UFF violations (type III), respectively. Clock comparisons and atom interferometers are sensitive to similar effects in type II and precisely the same effects in type III scenarios, although type III violations remain poorly constrained. Finally, we describe the Geodesic Explorer, a conceptual spaceborne atom interferometer that will test the gravitational redshift with an accuracy 5 orders of magnitude better than current terrestrial redshift experiments for type II scenarios and 12 orders of magnitude better for type III.
General Relativity is today the best theory of gravity addressing a wide range of phenomena. Our understanding of physical laws, from cosmology to local scales, cannot be properly formulated without taking into account it. It is based on one of the most fundamental principles of Nature, the Equivalence Principle, which represents the core of the Einstein theory of gravity. The confirmation of its validity at different scales and in different contexts represents one of the main challenges of modern physics both from the theoretical and the experimental points of view. A major issue related to this principle is the fact that we actually do not know if it is valid at quantum level. Furthermore, recent progress on relativistic theories of gravity have to take into account new issues like Dark Matter and Dark Energy, as well as the validity of fundamental principles like local Lorentz and position invariance. Experiments allow to set stringent constraints on well established symmetry laws, on the physics beyond the Standard Model of particles and interactions, and on General Relativity and its possible extensions. In this review, we discuss precision tests of gravity in General Relativity and alternative theories and their relation with the Equivalence Principle. In the first part, we discuss the Einstein Equivalence Principle according to its weak and strong formulation. We recall some basic topics of General Relativity and the necessity of its extension. Some models of modified gravity are presented in some details. The second part of the paper is devoted to the experimental tests of the Equivalence Principle in its weak formulation. We present the results and methods used in high-precision experiments, and discuss the potential and prospects for future experimental tests.
We propose an experiment to test the Weak Equivalence Principle (WEP) with a test mass consisting of two entangled atoms of different species. In the proposed experiment, a coherent measurement of the differential gravity acceleration between the two atomic species is considered, by entangling two atom interferometers operating on the two species. The entanglement between the two atoms is heralded at the initial beam splitter of the interferometers through the detection of a single photon emitted by either of the atoms, together with the impossibility of distinguishing which atom emitted the photon. In contrast to current and proposed tests of the WEP, our proposal explores the validity of the WEP in a regime where the two particles involved in the differential gravity acceleration measurement are not classically independent, but entangled. We propose an experimental implementation using $^{85}$Rb and $^{87}$Rb atoms entangled by a vacuum stimulated rapid adiabatic passage protocol implemented in a high finesse optical cavity. We show that an accuracy below $10^{-7}$ on the Eotvos parameter can be achieved.
We review the hypothesis of the existence of gravitational magnetic monopoles (H-pole for short) defined in analogy with the Diracs hypothesis of magnetic monopoles in electrodynamics. These hypothetical dual particles violate the equivalence principle and are accelerated by a gravitational field. We propose an expression for the gravitational force exerted upon an H-pole. According to GR ordinary matter (which we call E-poles) follows geodesics in a background metric. The dual H-poles follows geodesics in an effective metric.
We consider the role of the internal kinetic energy of bound systems of matter in tests of the Einstein equivalence principle. Using the gravitational sector of the standard model extension, we show that stringent limits on equivalence principle violations in antimatter can be indirectly obtained from tests using bound systems of normal matter. We estimate the bound kinetic energy of nucleons in a range of light atomic species using Greens function Monte Carlo calculations, and for heavier species using a Woods-Saxon model. We survey the sensitivities of existing and planned experimental tests of the equivalence principle, and report new constraints at the level of between a few parts in $10^{6}$ and parts in $10^{8}$ on violations of the equivalence principle for matter and antimatter.
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