João Magueijo

Unimodular gravity recasts the cosmological constant as an integration constant, fixed by a constraint on the volume element rather than chosen in the action. We ask what becomes of this constant when matter couples not to the gravitational metric, but to a second metric disformally related to it through a scalar field. Imposing a volume constraint on each metric, we find a theory in which the scalar does not propagate, yet still drives a non-trivial expansion. Written as a single-metric theory, its kinetic term is fixed to a prescribed function of spacetime, and the cosmological constant is replaced by a vacuum contribution that need not be constant. Moreover, we find that this theory admits a phantom crossing through a purely frame-dependent mechanism. This construction, however, rests on a feature invisible with a single metric, and unimodular formalisms that are classically equivalent in that case cease to agree once there are two disformally related metrics.

Quasi-topological theories of gravity are known to resolve black-hole singularities. We investigate whether the same mechanism can remove cosmological singularities. Focusing on non-polynomial curvature quasi-topological gravities in d = 4 dimensions, we find three generic scenarios with the correct infrared limit but without a Big-Bang singularity, for universes filled with pure radiation or other standard matter. The first scenario yields a universe emerging from a de Sitter phase, a case for which the curvature invariants remain finite but the matter density diverges, albeit only at infinite affine distance. The second one corresponds to a bouncing universe, and requires a multi-valued Lagrangian. The third possibility is an asymptotically Minkowski origin, reminiscent of an eternally loitering universe. The matter energy density for this solution is non-singular even at infinite affine distance and does not enter a super-Planckian regime, but is instead approximately constant for the past eternity.

Graviweak theory seeks to unify gravity (specifically in its self-dual formulation) with the weak interaction, preying on their parallel chiral [ ] structures. In this paper, we further this idea by folding it with the concept of spontaneous symmetry breaking. We do this first with a standard Higgs field and potential, starting with a unifying parity-invariant theory which splits into the usual gravity and weak sector under spontaneous symmetry breaking. By rewriting the theory in the two-spin framework, we are then prompted to discuss generalizations, within the generic approach known as MacDowell–Mansouri theories where a larger internal gauge group is broken. One of the predictions of the ensuing construction is a nonminimal coupling in the low-energy broken phase between curvature and the weak gauge fields, translating at the quantum level to a direct channel between the graviton and the weak bosons.

We show that general relativity and other geometrical theories can be viewed as a degenerate Otto cycle with only heat-exchange legs in emergent gravity. Including work-producing legs yields controlled violations of local Lorentz invariance and energy-momentum conservation, which produce late-time cosmological acceleration. Implications for the cosmological constant problem, structure formation, and local observations are discussed.

We consider the path-integral quantization of a minisuperspace cut-and-paste Lorentzian wormhole connecting two Minkowski spacetimes. The dynamics of the throat radius as a function of proper time is governed by a non-polynomial effective action derived by an application of the Israel junction condition formalism. Within a saddle-point approximation of the propagator describing the evolution from an initial to a final throat radius, we show that topology-changing transitions are suppressed by the Hessian determinant. In addition, we analyze the gravitational thermodynamics of the wormhole spacetime by a Wick rotation of the Israel-Lanczos equations in the presence of a thin-shell source. The resulting Euclideanized field equations are assumed to originate from a Euclidean effective gravity-matter action, which enters the path-integral representation of the gravitational canonical partition function. Therefrom we associate a temperature given by the inverse period of solutions, as well as a gravitational entropy as functions of the surface energy density and equation of state parameter of the shell. Both quantities are sourced entirely by the discontinuity of the extrinsic curvature across the junction. We show how this result can be applied to deduce a thermodynamic first law as the differential version of the conservation equation relating the effective mass of the shell to its surface pressure.

We explore the possibility that part of what we call dark matter may be the mark of a preferred frame, revealing a breakdown of diffeomorphism invariance. In the nonrelativistic limit, this appears as a deviant matter source capable of attracting normal matter, but not feeling the attraction from other forms of matter or from itself. While this implies a violation of momentum conservation, no logical inconsistencies arise in this deviant “Newtonian” limit. In contrast, due to Bianchi identities, the relativistic theory must undergo core change, and we discuss a modification of Einstein’s gravity capable of coupling a nonconserved source to gravity. It results from fixing some of the spatial components of the metric, thereby constraining the possible diffeomorphisms and clipping some of the equations. Bianchi identities can always be used to refill the equations, but the effective Stückelberg stresses are so outlandish that this defines symmetry breakdown and violations of local energy-momentum conservation. We work out spherically symmetric solutions with static halos and flat rotation curves, with and without a central black hole. The model has the drawback that it can evade experimental constraints simply by setting to zero the local density of deviant matter (which is a nondynamic input). Its presence, in contrast, would leave inimitable signatures. We briefly discuss the Hamiltonian formulation of these models, where such dark matter appears as a central charge in the Poisson bracket of the Hamiltonian and the momentum.

We show that General Relativity and other geometrical theories can be viewed as a degenerate Otto cycle with only heat-exchange legs in emergent gravity. Including work-producing legs yields controlled violations of local Lorentz invariance and energy-momentum conservation, which produce late-time cosmological acceleration. Implications for the cosmological constant problem, structure formation and local observations are discussed.

We consider the energetics and thermodynamics of spacetimes with no horizons, but endowed with a preferred timelike junction surface. They could arise as a limiting case of the gravastar and other constructions regularizing the interior of the horizon of a black hole, or from the conceptual cutting of a portion of a nonasymptotically flat space and gluing it with flat space. We find that such surfaces can be made to have zero energy, so that the energetics of such spaces is not encumbered by them. They do have a transverse pressure, fixed by the jump in surface gravity. A peculiar matter thermodynamics then follows, with well-defined entropy, temperature, and surface pressure, constrained by specific relations arising from the zero energy condition. This is confirmed by the Euclidean path integral, with the proviso that the Tolman-Ehrenfest temperature should be used. The entropy of the space is then the area of the timelike surface in units of a fundamental area, and the matter temperature is proportional to the transverse pressure and so the jump in surface gravity. However, when the gravitational action is added, the free energy of the surface is also zero. The fact that for some such spaces the temperature comes out negative raises interesting questions regarding the third “law” of thermodynamics.