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We analyze the dynamics of neutrino Gaussian wave-packets, the damping of flavor oscillations and decoherence effects within the framework of extended theories of gravity. In particular, we show that, when the underlying description of the gravitational interaction admits a violation of the strong equivalence principle, the parameter quantifying such a violation modulates the wave-packet spreading, giving rise to potentially measurable effects.

Under reasonable working assumptions including the polynomial boundedness, one proves the well-known Cerulus-Martin lower bound on how fast an elastic scattering amplitude can decrease in the hard-scattering regime. In this paper we consider two non-trivial extensions of the previous bound. (i) We generalize the assumption of polynomial boundedness by allowing amplitudes to exponentially grow for some complex momenta and prove a more general lower bound in the hard-scattering regime. (ii) We prove a new lower bound on elastic scattering amplitudes in the Regge regime, in both cases of polynomial and exponential boundedness. A bound on the Regge trajectory for negative momentum transfer squared is also derived. We discuss the relevance of our results for understanding gravitational scattering at the non-perturbative level and for constraining ultraviolet completions. In particular, we use the new bounds as probes of non-locality in black-hole formation, perturbative string theory, classicalization, Galileons, and infinite-derivative field theories, where both the polynomial boundedness and the Cerulus-Martin bound are violated., Comment: 48 pages, 4 figures

In this chapter we present a status report of black hole-like solutions in non-local theories of gravity in which the Lagrangians are at least quadratic in curvature and contain specific non-polynomial (i.e., non-local) operators. In the absence of exact black hole solutions valid in the whole spacetime, most of the literature on this topic focus on approximate and simplified equations of motion, which could provide insights on the full non-linear solutions. Therefore, the largest part of this chapter is devoted to the linear approximation. We present results on stationary metric solutions (including both static and rotating cases) and dynamical spacetimes describing the formation of non-rotating mini black holes by the collapse of null shells. Non-local effects can regularize the curvature singularities in both scenarios and, in the dynamical case, there exists a mass gap below which the formation of an apparent horizon can be avoided. In the final part we discuss interesting attempts towards finding non-linear black hole solutions in non-local gravity. Throughout this chapter, instead of focusing on a particular non-local model, we present results valid for large classes of theories (to a feasible extent). This more general approach allows the comparison of similarities and differences of the various types of non-local gravity models., Comment: Invited chapter for the Section "Nonlocal Quantum Gravity" of the "Handbook of Quantum Gravity" (Eds. C. Bambi, L. Modesto and I.L. Shapiro, Springer Singapore, expected in 2023). 29 pages

Neural cells cultures from human embryo brain of 9° - 11°W gestational age have been used to study ERα (Estrogens Receptor α) and to perform toxicity test for Mitomycin C and Methotrexate. Histochemical confirmation of cellular neuronal phenotype was based on histochemical evidence of NSE (Neuron Specific Enolase).The detection of ERα in neuronal cells was performed with a rabbit Monoclonal Antibody. ERα was absent both on neurons grown in vitro and on tissue brain specimens. This finding is apparently in contrast with the positive immunoreactivity of ERα and ERβ reported by other Authors on foetal and adult CNS (Central Nervous System). The absence of nuclear ERα on neurons in culture and in brain tissue specimens in our experiment is not in contrast with the relevant physiologic role of estrogens on nervous central system, but it could be correlated to the embryonic period of life and could represent a protection of male brain from an undue estrogens imprinting. The mitomycin C, alkylation agent, has shown in our experiment a major neurotoxic and cytostatic power in comparison with methotrexate. Our conclusion is that human embryo neuronal culture in vitro is a powerful instrument for physiology and human therapy for cancer and neurodegenerative diseases.