Salvatore Capozziello

TL;DR: In this paper, the cosmological background of gravitational waves can be tuned by the higher-order corrections to the gravitational Lagrangian, and it can be shown that assuming R 1 + ϵ, where ϵ indicates a generic (eventually small) correction to the Hilbert-Einstein action in the Ricci scalar R, gives a parametric approach to control the evolution and the production mechanism of gravitational wave in the early Universe.

TL;DR: In this paper, the deformation of spacetime metrics as generalized conformal transformations is studied, in particular the equations of motion in deformed spacetime are studied, and some applications are also considered.

TL;DR: In this article, the onset of cosmic acceleration was predicted by an effective cosmographic construction, in the framework of gravity, and the transition time and free parameters of the scenario were derived.

Abstract: Open Quantum Relativity [1] is a theory based on a dynamical unification scheme [2] of fundamental interactions achieved by assuming a 5D space which allows that the conservation laws are always and absolutely valid as a natural necessity. What we usually describe as violations of conservation laws can be described by a process of embedding and dimensional reduction, which gives rise to an induced-matter theory in the 4D space-time by which the usual masses, spins and charges of particles, naturally spring out. At the same time, it is possible to build up a covariant symplectic structure directly related to general conservation laws [3, 4]. Finally, the theory leads to a dynamical explanation of several paradoxes of modern physics (e.g. entanglement of quantum states, quantum teleportation, gamma ray bursts origin, black hole singularities, cosmic primary antimatter absence and a self-consistent fit of all the recently observed cosmological parameters [2, 5, 7, 8, 9]). A fundamental rôle in this approach is the link between the geodesic structure and the field equations of the theory before and after the dimensional reduction process. The emergence of an Extra Force term in the reduction process and the possibility to recover the masses of particles, allow to reinterpret the Equivalence Principle as a dynamical consequence which naturally “selects” geodesics from metric structure and vice-versa the metric structure from the geodesics. It is worth noting that, following Schrödinger [10], in the Einstein General Relativity, geodesic structure is “imposed” by choosing a LeviCivita connection [12] and this fact can be criticized considering a completely “affine” approach like in the Palatini formalism [13]. As we will show below, the dimensional reduction process gives rise to the generation of the masses of particles which emerge both from the field equations and the embedded geodesics. Due to this result, the coincidence of chronological and geodesic structure is derived from the embedding and a new dynamical formulation of the Equivalence Principle is the direct consequence of dimensional reduction. The dynamical structure is further rich since two time arrows and closed time-like paths naturally emerge. This fact leads to a reinterpretation of the standard notion of causality which can be, in this way, always recovered, even in the case in which it is questioned (like in entanglement phenomena and quantum teleportation [5, 6]), because it is generalized to a forward and a backward causation. The layout of the paper is the following. In Sec.2, we sketch the 5D approach while in Sec.3 we discuss the rôle of conservation laws. Sec.4 is devoted to the discussion of geodesic structure and to the emergence of the Extra Force term. The field equations, the masses of the particles and time-like solutions are discussed in Sec.5. Conclusions are drawn in Sec.6.