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In General Relativity, the issue of defining the gravitational energy contained in a given spatial region is still unresolved, except for particular cases of localized objects where the asymptotic flatness holds for a given spacetime. In principle, a theory of gravity is not self-consistent, if the whole energy content is not uniquely defined in a specific volume. Here, we generalize the Einstein gravitational energy–momentum pseudotensor to non-local theories of gravity where analytic functions of the non-local integral operator □ − 1 are taken into account. We apply the Noether theorem to a gravitational Lagrangian, supposed invariant under the one-parameter group of diffeomorphisms, that is, the infinitesimal rigid translations. The invariance of non-local gravitational action under global translations leads to a locally conserved Noether current, and thus, to the definition of a gravitational energy–momentum pseudotensor, which is an affine object transforming like a tensor under affine transformations. Furthermore, the energy–momentum complex remains locally conserved, thanks to the non-local contracted Bianchi identities. The continuity equations for the gravitational pseudotensor and the energy–momentum complex, taking into account both gravitational and matter components, can be derived. Finally, the weak field limit of pseudotensor is performed to lowest order in metric perturbation in view of astrophysical applications. [ABSTRACT FROM AUTHOR]

We review the possible violation of the Equivalence Principle at finite temperature T in the framework of curvature-based Extended Theories of Gravity. Specifically, we first show how it is possible to derive Equivalence Principle violation from Quantum Field Theory at T ≠ 0. Subsequently, we exhibit how this result can be precisely recovered by following an alternative path that envisages the employment of generalized Einstein equations with a temperature-dependent energy-momentum tensor. Finally, we adopt the latter formalism in the context of some Extended Gravity models to quantify the amount of Equivalence Principle violation. Specifically, Brans–Dicke Theory, Standard Model Extension and Conformal Gravity are considered in detail. [ABSTRACT FROM AUTHOR]

We consider the possibility to enlarge the class of symmetries realized in standard local field theories by introducing infinite order derivative operators in the actions, which become nonlocal. In particular, we focus on the Galilean shift symmetry and its generalization in nonlocal (infinite derivative) field theories. First, we construct a nonlocal Galilean model which may be UV finite, showing how the ultraviolet behavior of loop integrals can be ameliorated. We also discuss the pole structure of the propagator which has infinitely many complex conjugate poles, but satisfies tree level unitarity. Moreover, we will introduce the same kind of nonlocal operators in the context of linearized gravity. In such a scenario, the graviton propagator turns out to be ghost-free and the spacetime metric generated by a point-like source is non-singular. [ABSTRACT FROM AUTHOR]

We propose a heuristic derivation of Casimir effect in the context of minimal length theories based on a Generalized Uncertainty Principle (GUP). By considering a GUP with only a quadratic term in the momentum, we compute corrections to the standard formula of Casimir energy for the parallel-plate geometry, the sphere and the cylindrical shell. For the first configuration, we show that our result is consistent with the one obtained via more rigorous calculations in Quantum Field Theory (QFT). Experimental developments are finally discussed. [ABSTRACT FROM AUTHOR]

The propagation of boson particles in a gravitational field described by the Brans-Dicke (BD) theory of gravity is analyzed. We derive the wave function of the scalar particles, and the effective potential experienced by the quantum particles considering the role of the varying gravitational coupling. Besides, we calculate the probability to find the scalar particles near the region where a naked singularity is present. The extremely high energy radiated in such a situation could account for the huge emitted power observed in gamma ray bursts (GRBs). [ABSTRACT FROM AUTHOR]

In this paper, we review the theories of origin of matter-antimatter asymmetry in the universe. The general conditions for achieving baryogenesis and leptogenesis in a CPT conserving field theory have been laid down by Sakharov. In this review, we discuss scenarios where a background scalar or gravitational field spontaneously breaks the CPT symmetry and splits the energy levels between particles and antiparticles. Baryon or Lepton number violating processes in proceeding at thermal equilibrium in such backgrounds gives rise to Baryon or Lepton number asymmetry. [ABSTRACT FROM AUTHOR]

Neutrino (ν) oscillations during the core collapse and bounce of a supernova (SN) are shown to generate the most powerful detectable gravitational wave (GW) bursts. The SN neutronization phase produces mainly electron (νe) neutrinos, the oscillations of which must take place within a few mean-free paths of their resonance surface located near their neutrinosphere. Here we characterize the GW signals produced by spin-flip oscillations inside the fast-rotating protoneutron star in the SN core. In this novel mechanism, the release of both the oscillation-produced νμ's, ντ's and the spin-flip-driven GW pulse provides a unique emission offset $\Delta T_{\rm GW\leftrightarrow \nu}^{\rm emission} = 0$ for measuring the ν travel time to Earth. As massive ν's get noticeably delayed on its journey to Earth with respect to the GW, they generate over the oscillation transient, the accurate measurement of this time-of-flight delay by SNEWS + LIGO, VIRGO, BBO, DECIGO, etc. can assess the absolute ν mass spectrum straightforwardly. [ABSTRACT FROM AUTHOR]

The frequency band used by cellular telephones includes the eigenfrequencies of a dielectric sphere with physical characteristics close to those of a human head. Proceeding from the spatial features of the natural modes of such a sphere, we propose an independent and clear evident accuracy test for the complicated numerical calculations which are conducted when estimating the potential hazard due to the use of cellular telephones, in particular, for the check of the proper handling of the electromagnetic shape resonances of a human head. [ABSTRACT FROM AUTHOR]