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We present two projects aiming to probe key aspects of the theory of General Relativity with high-precision quantum sensors. These projects use cold-atom interferometry with the aim of measuring gravitational waves and testing the equivalence principle. To detect gravitational waves, a large multi-sensor demonstrator is currently under construction that will exploit correlations between three atom interferometers spread along a 200 m optical cavity. Similarly, a test of the weak equivalence principle is currently underway using a compact and mobile dual-species interferometer, which will serve as a prototype for future high-precision tests onboard an orbiting satellite. We present recent results and improvements related to both projects.
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The quantum field theoretic description of general relativity is a modern approach to gravity where gravitational force is carried by spin-2 gravitons. In the classical limit of this theory, general relativity as described by the Einstein field equations is obtained. This limit, where classical general relativity is derived from quantum field theory is the topic of this thesis. The Schwarzschild-Tangherlini metric, which describes the gravitational field of an inertial point particle in arbitrary space-time dimensions, $D$, is analyzed. The metric is related to the three-point vertex function of a massive scalar interacting with a graviton to all orders in $G_N$, and the one-loop contribution to this amplitude is computed from which the $G_N^2$ contribution to the metric is derived. To understand the gauge-dependence of the metric, covariant gauge is used which introduces the parameter, $xi$, and the gauge-fixing function $G_sigma$. In the classical limit, the gauge-fixing function turns out to be the coordinate condition, $G_sigma=0$. As gauge-fixing function a novel family of gauges, which depends on an arbitrary parameter $alpha$ and includes both harmonic and de Donder gauge, is used. Feynman rules for the graviton field are derived and important results are the graviton propagator in covariant gauge and a general formula for the n-graviton vertex in terms of the Einstein tensor. The Feynman rules are used both in deriving the Schwarzschild-Tangherlini metric from amplitudes and in the computation of the one-loop correction to the metric. The one-loop correction to the metric is independent of the covariant gauge parameter, $xi$, and satisfies the gauge condition $G_sigma=0$ where $G_sigma$ is the family of gauges depending on $alpha$. In space-time $D=5$ a logarithm appears in position space and this phenomena is analyzed in terms of redundant gauge freedom.
Although general relativity (GR) has been precisely tested at the solar system scale, precise tests at a galactic or cosmological scale are still relatively insufficient. Here, in order to test GR at the galactic scale, we use the newly compiled galaxy-scale strong gravitational lensing (SGL) sample to constrain the parameter $gamma_{PPN}$ in the parametrized post-Newtonian (PPN) formalism. We employ the Pantheon sample of type Ia supernovae observation to calibrate the distances in the SGL systems using the Gaussian Process method, which avoids the logical problem caused by assuming a cosmological model within GR to determine the distances in the SGL sample. Furthermore, we consider three typical lens models in this work to investigate the influences of the lens mass distributions on the fitting results. We find that the choice of the lens models has a significant impact on the constraints on the PPN parameter $gamma_{PPN}$. We use the Bayesian information criterion as an evaluation tool to make a comparison for the fitting results of the three lens models, and we find that the most reliable lens model gives the result of $gamma_{PPN}=1.065^{+0.064}_{-0.074}$, which is in good agreement with the prediction of $gamma_{PPN}=1$ by GR. As far as we know, our 6.4% constraint result is the best result so far among the recent works using the SGL method.
During the First World War, the status of energy conservation in general relativity was one of the most hotly debated questions surrounding Einsteins new theory of gravitation. His approach to this aspect of general relativity differed sharply from another set forth by Hilbert, even though the latter conjectured in 1916 that both theories were probably equivalent. Rather than pursue this question himself, Hilbert chose to charge Emmy Noether with the task of probing the mathematical foundations of these two theories. Indirect references to her results came out two years later when Klein began to examine this question again with Noethers assistance. Over several months, Klein and Einstein pursued these matters in a lengthy correspondence, which culminated with several publications, including Noethers now famous paper Invariante Variationsprobleme. The present account focuses on the earlier discussions from 1916 involving Einstein, Hilbert, and Noether. In these years, a Swiss student named R.J. Humm was studying relativity in Gottingen, during which time he transcribed part of Noethers lost manuscript on Hilberts invariant energy vector. By making use of this 9-page manuscript, it is possible to reconstruct the arguments Noether set forth in response to Hilberts conjecture. Her results turn out to be closely related to the findings Klein published two years later, thereby highlighting, once again, how her work significantly deepened contemporary understanding of the mathematical underpinnings of general relativity.
A classic problem in general relativity, long studied by both physicists and philosophers of physics, concerns whether the geodesic principle may be derived from other principles of the theory, or must be posited independently. In a recent paper [Geroch & Weatherall, The Motion of Small Bodies in Space-Time, Comm. Math. Phys. (forthcoming)], Bob Geroch and I have introduced a new approach to this problem, based on a notion we call tracking. In the present paper, I situate the main results of that paper with respect to two other, related approaches, and then make some preliminary remarks on the interpretational significance of the new approach. My main suggestion is that tracking provides the resources for eliminating point particles---a problematic notion in general relativity---from the geodesic principle altogether.
In this note the AKSZ construction is applied to the BFV description of the reduced phase space of the Einstein-Hilbert and of the Palatini--Cartan theories in every space-time dimension greater than two. In the former case one obtains a BV theory for the first-order formulation of Einstein--Hilbert theory, in the latter a BV theory for Palatini--Cartan theory with a partial implementation of the torsion-free condition already on the space of fields. All theories described here are
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