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1. The Case for Nonlocal Modifications of Gravity

   https://doi.org/10.3390/universe4080088  

   Woodard, Richard (August 2018, Universe)

   The huge amounts of undetected and exotic dark matter and dark energy needed to make general relativity work on large scales argue that we should investigate modifications of gravity. The only stable, metric-based and invariant alternative to general relativity is f(R) models. These models can explain primordial inflation, but they cannot dispense with either dark matter or dark energy. I advocate nonlocal modifications of gravity, not as new fundamental theories but rather as the gravitational vacuum polarization engendered by infrared quanta produced during primordial inflation. I also discuss some of the many objections which have been raised to this idea. 

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2. Are General Relativity and Teleparallel Gravity Theoretically Equivalent?

   https://doi.org/10.31389/pop.152  

   Weatherall, James Owen; Meskhidze, Helen (May 2025, Philosophy of Physics)

   Teleparallel gravity shares many qualitative features with general relativity, but differs from it in the following way: whereas in general relativity, gravitation is a manifestation of spacetime curvature, in teleparallel gravity, spacetime is (always) flat. Gravitational effects in this theory arise due to spacetime torsion. It is often claimed that teleparallel gravity is an equivalent reformulation of general relativity. In this paper we question that view. We argue that the theories are not equivalent, by the criterion of categorical equivalence or any stronger criterion, and that teleparallel gravity posits strictly more structure than general relativity. 

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3. Antimatter Free-Fall Experiments and Charge Asymmetry

   https://doi.org/10.3390/sym13071192  

   Jentschura, Ulrich David (July 2021, Symmetry)

   null (Ed.)

   We propose a method by which one could use modified antimatter gravity experiments in order to perform a high-precision test of antimatter charge neutrality. The proposal is based on the application of a strong, external, vertically oriented electric field during an antimatter free-fall gravity experiment in the gravitational field of the Earth. The proposed experimental setup has the potential to drastically improve the limits on the charge-asymmetry parameter ϵ¯q of antimatter. On the theoretical side, we analyze possibilities to describe a putative charge-asymmetry of matter and antimatter, proportional to the parameters ϵq and ϵ¯q, by Lagrangian methods. We found that such an asymmetry could be described by four-dimensional Lorentz-invariant operators that break CPT without destroying the locality of the field theory. The mechanism involves an interaction Lagrangian with field operators decomposed into particle or antiparticle field contributions. Our Lagrangian is otherwise Lorentz, as well as PT invariant. Constraints to be derived on the parameter ϵ¯q do not depend on the assumed theoretical model. 

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4. The Teleparallel Equivalent of Newton-Cartan Gravity

   Teh, N.; Read, J. (August 2018, Classical and quantum gravity)

   We construct a notion of teleparallelization for Newton–Cartan theory, and show that the teleparallel equivalent of this theory is Newtonian gravity; furthermore, we show that this result is consistent with teleparallelization in general relativity, and can be obtained by null-reducing the teleparallel equivalent of a five-dimensional gravitational wave solution. This work thus strengthens substantially the connections between four theories: Newton–Cartan theory, Newtonian gravitation theory, general relativity, and teleparallel gravity. 

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5. A lab-based test of the gravitational redshift with a miniature clock network

   https://doi.org/10.1038/s41467-023-40629-8  

   Zheng, Xin; Dolde, Jonathan; Cambria, Matthew C.; Lim, Hong Ming; Kolkowitz, Shimon (August 2023, Nature Communications)

   Abstract Einstein’s theory of general relativity predicts that a clock at a higher gravitational potential will tick faster than an otherwise identical clock at a lower potential, an effect known as the gravitational redshift. Here we perform a laboratory-based, blinded test of the gravitational redshift using differential clock comparisons within an evenly spaced array of 5 atomic ensembles spanning a height difference of 1 cm. We measure a fractional frequency gradient of [ − 12.4 ± 0. 7_(stat) ± 2. 5_(sys)] × 10⁻¹⁹/cm, consistent with the expected redshift gradient of − 10.9 × 10⁻¹⁹/cm. Our results can also be viewed as relativistic gravitational potential difference measurements with sensitivity to mm scale changes in height on the surface of the Earth. These results highlight the potential of local-oscillator-independent differential clock comparisons for emerging applications of optical atomic clocks including geodesy, searches for new physics, gravitational wave detection, and explorations of the interplay between quantum mechanics and gravity. 

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