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The fundamental symmetries in gravity and gauge theories, formulated using differential forms, are gauge transformations and diffeomorphisms. These symmetries act in distinct ways on different dynamical fields. Yet, the commutator of these symmetries forms a closed, field-independent algebra. This work uncovers a natural correspondence between this algebra and the Lie bracket of some vector fields on the principal fiber bundle associated with the physical theory, providing a geometric interpretation of the symmetry algebra. Furthermore, we demonstrate that the symmetry algebra is independent of the connection. Finally, we analyze an example illustrating how a specific connection, associated with Lorentz-Lie transformations, simplifies the symmetry algebra in the presence of spacetime Killing vector fields.

Unimodular gravity is a compelling modified theory of gravity that offers a natural solution to the cosmological constant problem. However, for unimodular gravity to be considered a viable theory of gravity, one has to show that it has a well-posed initial value formulation. Working in vacuum, we apply Dirac's algorithm to find all the constraints of the theory. Then we prove that, for initial data compatible with these constraints, the evolution is well posed. Finally, we find sufficient conditions for a matter action to preserve the well-posedness of the initial value problem of unimodular gravity. As a corollary, we argue that the "unimodular" restriction on the spacetime volume element can be satisfied by a suitable choice of the lapse function., Comment: 8+1 pages. Accepted in PRD

Energy conservation has the status of a fundamental physical principle. However, measurements in quantum mechanics do not comply with energy conservation. Therefore, it is expected that a more fundamental theory of gravity -- one that is less incompatible with quantum mechanics -- should admit energy nonconservations. This paper begins by identifying the conditions for a theory to have an energy-momentum tensor that is not conserved. Then, the trajectory equation for pointlike particles that lose energy is derived, showing that energy nonconservation produces a particular acceleration. As an example, the unimodular theory of gravity is studied. Interestingly, in spherical symmetry, given that there is a generalized Birkhoff theorem and that the energy-momentum tensor divergence is a closed form, the trajectories of test particles that lose energy can be found using well known methods. Finally, limits on the energy nonconservation parameters are set using Solar system observations., Comment: 13 pages. Accepted in Phys. Rev. D

A method to find the symmetries of a theory in the first order formalism of gravity is presented. This method is applied to the minimal gravity sector of the Standard Model Extension. It is argued that no inconsistencies arise when Lorentz violation is explicit and the relation between Lorentz violation and invariance under (active) diffeomorphisms is clearly exposed., Comment: Presented at the Eighth Meeting on CPT and Lorentz Symmetry, Bloomington, Indiana, May 12-16, 2019

An experiment to test for relativistic frame dragging effects with quantum interferometry is proposed. The idea that the classical trajectories of the interferometer surround a spherical mass source whose angular momentum is perpendicular to the plane containing these trajectories. A simple analysis allows one to find the phase shift for particles traveling in the innermost stable circular orbit; the result can be easily generalized for more realistic orbits. The phase difference goes like the source's angular momentum per mass times the quantum particles' mass. This is a small effect but it can be amplified by making the classical paths go around the source several times. Moreover, this experiment has the advantage that the source's angular momentum can be easily controlled., Comment: Contribution to the 2019 Gravitation session of the 54th Rencontres de Moriond, 3 pages

We develop a framework to test the Equivalence Principle (EP) under conditions where the quantum aspects of nature cannot be neglected, specifically in the context of interference phenomena with unstable particles. We derive the nonrelativistic quantum equation that describes the evolution of the wavefunction of unstable particles under the assumption of the validity of the EP and when small deviations are assumed to occur. As an example, we study the propagation of unstable particles in a COW experiment, and we briefly discuss the experimental implications of our formalism., Comment: To match the published version

We consider a model of Quantum Gravity phenomenology, based on the idea that space-time may have some unknown granular structure that respects the Lorentz symmetry. The proposal involves non-trivial couplings of curvature to matter fields and leads to a well defined phenomenology. In this manuscript, a brief description of the model is presented together with some results obtained using linearized gravity and the Newtonian limit, which could be useful when comparing with real experiments., Comment: 7 pages. Talk presented at "From Quantum to Emergent Gravity: Theory and Phenomenology," June 2007, Trieste, Italy