Lorentz violation is a candidate quantum-gravity signal, and the Standard-Model Extension (SME) is a widely used parametrization of such a violation. In the gravitational SME sector, there is an elusive coefficient for which no effects have been found. This is known as the $t$ puzzle and, to date, it has no compelling explanation. This paper analyzes whether there is a fundamental explanation for the $t$ puzzle. To tackle this question, several approaches are followed. Mainly, redefinitions of the dynamical fields are studied, showing that other SME coefficients can be moved to nongravitational sectors. It is also found that the gravity SME sector can be consistently treated à la Palatini, and that, in the presence of spacetime boundaries, it is possible to correct its action to get the desired equations of motion. Moreover, through a reformulation as a Lanczos-type tensor, some problematic features of the $t$ term, which should arise at the phenomenological level, are revealed. The most important conclusion of the paper is that there is no evidence of a fundamental explanation for the $t$ puzzle, suggesting that it may be linked to the approximations taken at the phenomenological level.

Unimodular gravity is an interesting approach to address the cosmological constant problem, since the vacuum energy density of quantum fields does not gravitate in this framework, and the cosmological constant appears as an integration constant. These features arise as a consequence of considering a constrained volume element 4-form that breaks the diffeomorphisms invariance down to volume preserving diffeomorphisms. In this work, the first-order formulation of unimodular gravity is presented by considering the spin density of matter fields as a source of spacetime torsion. Even though the most general matter Lagrangian allowed by the symmetries is considered, dynamical restrictions arise on their functional dependence. The field equations are obtained and the conservation laws associated with the symmetries are derived. It is found that, analogous to torsion-free unimodular gravity, the field equation for the vierbein is traceless; nevertheless, torsion is algebraically related to the spin density as in standard Einstein-Cartan theory. The particular example of massless Dirac spinors is studied, and comparisons with standard Einstein-Cartan theory are shown.

A recent debate has ensued over the claim by Pikovski et al. [Nat. Phys. 11, 668 (2015)] that systems with internal degrees of freedom undergo a universal, gravity-induced, type of decoherence that explains their quantum-to-classical transition. This decoherence is supposed to arise from the different gravitational redshifts experienced by such systems when placed in a superposition of two wave packets at different heights in a gravitational field. Here we investigate some aspects of the discussion with the aid of simple examples. In particular, we first resolve an apparent conflict between the reported results and the equivalence principle by noting that the static and free-fall descriptions focus on states associated with different hypersurfaces. Next, we emphasize that predictions regarding the observability of interference become relevant only in the context of concrete experimental settings. As a result, we caution against hasty claims of universal validity. Finally, we dispute the claim that, at least in the scenarios discussed by Pikovski et al., gravitation is responsible for the reported results, and we question the alleged ability of decoherence to explain the quantum-to-classical transition. In consequence, we argue against the extraordinary assertion by Pikovski et al. that gravity can account for the emergence of classicality.

Lorentz invariance is one of the fundamental principles of physics, and, as such, it must be experimentally tested. The purpose of this work is to obtain, within the Standard-Model Extension, the dynamics of a Lorentz-violating spinor in a uniform Newtonian gravitational field. This is achieved by treating the spinor as a test particle and introducing the gravitational field through a uniformly accelerated observer. The nonrelativistic Hamiltonian is obtained, and some experimental consequences are discussed. One unexpected outcome of this work is that the gravitational field helps disentangle bounds on coefficients for Lorentz violation.

Lorentz violation is motivated by quantum gravity and it is generically described by nondynamical tensors. In this work a Lorentz violating extension of general relativity is studied where a nondynamical tensor couples to the Weyl tensor. A family of static and spherically symmetric solutions in vacuum is found, confirming that there are consistent solutions with explicit Lorentz violation in dynamical spacetimes. These solutions produce an unconventional dependence of the gravitational redshift, which, in turn, leads to the first bounds on such a nondynamical tensor that do not rely on the physics of the early universe. Moreover, the bounds obtained in this work are competitive with respect to limits on similar nondynamical tensors.

Modified gravity theories are supposed to incorporate low-energy quantum-gravity effects and, at the same time, they could shed light into the dark matter and dark energy problems. Here we study a particular modification of general relativity where local Lorentz invariance is spontaneously broken and whose physical effects, despite a decade-long effort, were unknown. We show that, during inflation, this modification produces anisotropies that would generate measurable effects on the cosmic microwave background. Then, by using empirical constraints on the B-mode polarization spectrum, we can estimate that the “coefficient” components absolute value have to be smaller than ${10}^{-43}$. This is a remarkably strong limit; in fact, it is 29 orders of magnitude better than the best constraints on similar coefficients. Thus, we propose that inflation could stringently test other modified gravity theories.