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We focus on viable $f(T)$ teleparallel cosmological models, namely power law, exponential and square-root exponential, carrying out a detailed study of their evolution at all scales. Indeed, these models were extensively analysed in the light of late time measurements, while it is possible to find only upper limits looking at the very early time behavior, i.e. satisfying the Big Bang Nucleosynthesis (BBN) data on primordial abundance of ${}^4He$. Starting from these indications, we perform our analysis considering both background and linear perturbations evolution and constrain, beyond the standard six cosmological parameters, the free parameters of $f(T)$ models in both cases whether the BBN consistency relation is considered or not. We use a combination of Cosmic Microwave Background, Baryon Acoustic Oscillation, Supernovae Ia and galaxy clustering measurements, and find that very narrow constraints on the free parameters of specific $f(T)$ cosmology can be obtained, beyond any previous precision. While no degeneration is found between the helium fraction, $Y_P$, and the free parameter of $f(T)$, we note that these models constrain the current Hubble parameter, $H_0$, {higher extent than the standard model} one, fully compatible with the Riess et al. measurement in the case of power law $f(T)$ model. Moreover, the free parameters are constrained at non-zero values in more than 3-$\sigma$, showing a preference of the observations for extended gravity models., Comment: 13 pages, 5 figures

We present a quantum field theoretical approach to the vacuum neutrino oscillations in curved space, we analyze the non--trivial interplay between quantum field mixing and field quantization in curved space and derive new oscillation formulae. We compute the formulae explicitly in the spatially flat FLRW metrics for universes dominated by a cosmological constant and by radiation. We evaluate the transition probabilities in the Schwarzschild black hole metric, and we show that the Hawking radiation affects the oscillations of neutrinos. We show that our results are consistent with those of previous analyses when the quantum mechanical limit is considered., Comment: 13 pages, no figures

We study the non-relativistic limit of Dirac equation for mixed neutrinos. We demonstrate that such a procedure inevitably leads to a redefinition of the inertial mass. This happens because, in contrast to the case when mixing is absent, the antiparticle sector contribution cannot be neglected for neutrinos with definite flavor. We then show that, when a gravitational interaction is switched on, in the weak-field approximation the mass parameter which couples to gravity (gravitational mass) does not undergo the same reformulation as the inertial mass, thus leading to an apparent breakdown of the weak equivalence principle.

We study quantum corrections at the horizon scale of a black hole induced by a Generalized Uncertainty Principle (GUP) with a quadratic term in the momentum. The interplay between quantum mechanics and gravity manifests itself into a non-zero uncertainty in the location of the black hole radius, which turns out to be larger than the usual Schwarzschild radius. We interpret such an effect as a correction which makes the horizon disappear, as it happens in other models of quantum black holes already considered in literature. We name this kind of horizonless compact objects $GUP stars$. We also investigate some phenomenological aspects in the astrophysical context of binary systems and gravitational wave emission by discussing Love numbers, quasi-normal modes and echoes, and studying their behavior as functions of the GUP deformation parameter. Finally, we preliminarily explore the possibility to constrain such a parameter with future astrophysical experiments., Comment: 8 pages. V2: minor changes, results unchanged, version accepted for publication in EPJC

In this paper we present an iterative method to generate an infinite class of new nonlocal field theories whose propagators are ghost-free. We first examine the scalar field case and show that the pole structure of such generalized propagators possesses the standard two derivative pole and in addition can contain complex conjugate poles which, however, do not spoil at least tree level unitarity as the optical theorem is still satisfied. Subsequently, we define analogous propagators for the fermionic sector which is also devoid of unhealthy degrees of freedom. As a third case, we apply the same construction to gravity and define a new set of theories whose graviton propagators around the Minkowski background are ghost-free. Such a wider class also includes nonlocal theories previously studied, and Einstein's general relativity as a peculiar limit. Moreover, we compute the linearized gravitational potential generated by a static point-like source for several gravitational theories belonging to this new class and show that the nonlocal nature of gravity regularizes the singularity at the origin., Comment: 12 pages, 1 figure

We study decoherence effects on mixing among three generations of neutrinos. We show that in presence of a non--diagonal dissipation matrix, both Dirac and Majorana neutrinos can violate the $CPT$ symmetry and the oscillation formulae depend on the parametrization of the mixing matrix. We reveal the $CP$ violation in the transitions preserving the flavor, for a certain form of the dissipator. In particular, the $CP$ violation affects all the transitions in the case of Majorana neutrinos, unlike Dirac neutrinos which still preserve the $CP$ symmetry in one of the transitions flavor preserving. This theoretical result shows that decoherence effects, if exist for neutrinos, could allow to determine the neutrino nature and to test fundamental symmetries of physics. Next long baseline experiments could allow such an analysis. We relate our study with experiments by using the characteristic parameters and the constraints on the elements of the dissipation matrix of current experiments., Comment: 13 pages, 2 figures

The (inverse) beta-decay of uniformly accelerated protons (p -> n + e+ + ne) has been recently analyzed in the context of two-flavor neutrino mixing and oscillations. It has been shown that the decay rates as measured by an inertial and comoving observer are in agreement, provided that: i) the thermal nature of the accelerated vacuum (Unruh effect) is taken into account; ii) the asymptotic behavior of neutrinos is described through flavor (rather than mass) eigenstates; iii) the Unruh radiation is made up of oscillating neutrinos. Here we extend the above considerations to a more realistic scenario including three generations of Dirac neutrinos. By following the outlined recipe, we find that the equality between the two rates still holds true, confirming that mixing is perfectly consistent with the General Covariance of Quantum Field Theory. Notably, we prove that the analysis of CP violation in neutrino oscillations provides a further solid argument for flavor states as fundamental representation of asymptotic neutrino states. Our approach is finally discussed in comparison with the other treatments appeared in literature., Comment: 12 pages, 5 figures, accepted for publication on EPJC

We study the neutrino pairs annihilation into electron-positron pairs ($\nu+{\bar \nu}\to e^- + e^+$) near the surface of a neutron star. The analysis is performed in the framework of extended theories of gravity. The latter induce a modification of the minimum photon-sphere radius ($R_{ph}$) and the maximum energy deposition rate near to $R_{ph}$, as compared to ones of General Relativity. These results might lead to an efficient mechanism for generating GRBs., Comment: Accepted for pubblication in ApJ

In Cosmology and in Fundamental Physics there is a crucial question like: where the elusive substance that we call Dark Matter is hidden in the Universe and what is it made of?, that, even after 40 years from the Vera Rubin seminal discovery does not have a proper answer. Actually, the more we have investigated, the more this issue has become strongly entangled with aspects that go beyond the established Quantum Physics, the Standard Model of Elementary particles and the General Relativity and related to processes like the Inflation, the accelerated expansion of the Universe and High Energy Phenomena around compact objects. Even Quantum Gravity and very exotic DM particle candidates may play a role in framing the Dark Matter mystery that seems to be accomplice of new unknown Physics. Observations and experiments have clearly indicated that the above phenomenon cannot be considered as already theoretically framed, as hoped for decades. The Special Topic to which this review belongs wants to penetrate this newly realized mystery from different angles, including that of a contamination of different fields of Physics apparently unrelated. We show with the works of this ST that this contamination is able to guide us into the required new Physics. This review wants to provide a good number of these "paths or contamination" beyond/among the three worlds above; in most of the cases, the results presented here open a direct link with the multi-scale dark matter phenomenon, enlightening some of its important aspects. Also in the remaining cases, possible interesting contacts emerges., Comment: 64 pages 16 Figures. In print on Frontiers in Astronomy and Space Sciences, for the Research Topic: "When Planck, Einstein and Vera Rubin Meet. Dark Matter: What is it ? Where is it?"

Modified expansion rates in the early Universe prior to big bang nucleosynthesis are common in modified gravity theories, and can have a significant impact on the generation of dark matter, matter-antimatter asymmetry, primordial black holes and the primordial gravitational wave (PGW) spectrum. Here we study the PGW spectrum in modified gravity theories, in early Universe cosmology. In particular, we consider scalar-tensor and extradimensional scenarios, investigating the detection prospects in current and future GW observatories. For the scalar-tensor case, PGW could be potentially observed by laser interferometers operating in the high-frequency range, while for the extradimensional case they could be detected even at low frequencies with pulsar timing arrays. We find that data from the planned network of several GW detectors operating across various frequency ranges could be able to distinguish between various modified gravity scenarios., Comment: 23 pages, 6 figures, matches the accepted version for publication in JCAP

The gravitino problem is investigated in the framework of Extended Gravity cosmologies. In particular, we consider $f(R)$ gravity, the most natural extension of the Hilbert-Einstein action, and $f(\cal T)$ gravity, the extension of teleparallel equivalent gravity. Since in these theories the expansion laws of the Universe are modified, as compared to the standard $\Lambda$CDM cosmology, it follows that also the thermal history of particles gets modified. We show that $f(R)$ models allow to avoid the late abundance of gravitinos. In particular, we found that for an appropriate choice of the parameters characterizing the $f(R)$ model, the gravitino abundance turns out to be independent of the reheating temperature. A similar behavior is achieved also in the context of $f(\cal T)$ gravity. In this perspective, we can conclude that geometric corrections to standard General Relativity (and to Teleparallel Equivalent of General Relativity) can improve shortcomings both in cosmology and in unified theories beyond the Standard Model of particles., Comment: 7 pages

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. Experimental developments are finally discussed., Comment: 12 pages, 5 figures, to appear in IJMPD

We investigate the structure of the gravity-induced Generalized Uncertainty Principle in three dimensions. The subtleties of lower dimensional gravity, and its important differences with respect to four and higher dimensions, are duly taken into account, by considering different possible candidates for the gravitational radius, $R_g$, that is the minimal length/maximal resolution of the quantum mechanical localization process. We find that the event horizon of the $M \neq 0$ Ba\~{n}ados-Teitelboim-Zanelli micro black hole furnishes the most consistent $R_g$. This allows us to obtain a suitable formula for the Generalized Uncertainty Principle in three dimensions, and also to estimate the corrections induced by the latter on the Hawking temperature and Bekenstein entropy. We also point to the extremal $M=0$ case, and its natural unit of length introduced by the cosmological constant, $\ell = 1 / \sqrt{-\Lambda}$, as a possible alternative to $R_g$, and present a condensed matter analog realization of this scenario., Comment: v2: 26 pages, 4 figures, accepted for publication in Phys.Rev.D

We propose a high precision satellite experiment to further test Einstein's General Relativity and constrain extended theories of gravity. We consider the frequency shift of a photon radially exchanged between two observers located on Earth and on a satellite in circular orbit in the equatorial plane. In General Relativity there exists a peculiar satellite-distance at which the static contribution to the frequency shift vanishes since the effects induced by pure gravity and special relativity compensate, while it can be non-zero in modified gravities, like in models with screening mechanisms. As an experimental device placed on the satellite we choose a system of hydrogen atoms which can exhibit the $1$s spin-flip transition from the singlet (unaligned proton-electron spins) to the triplet (aligned proton-electron spins) state induced by the absorption of photons at $21.1$cm. The observation of an excited state would indicate that the frequency of the emitted and absorbed photon remains unchanged according to General Relativity. On the contrary, a non-zero frequency shift, as predicted in extended theories of gravity, would prevent the spin-flip transition and the hydrogen atoms from jumping into the excited state. Such a detection would signify a smoking-gun signature of new physics beyond special and general relativity., Comment: 7 pages, 2 figures, 1 table. Version accepted for publication in EPJC Letters

We derive the Mandelstam-Tamm time-energy uncertainty relation for neutrino oscillations in a generic stationary curved spacetime. In particular, by resorting to Stodolsky covariant formula of the quantum mechanical phase, we estimate gravity effects on the neutrino energy uncertainty. Deviations from the standard Minkowski result are explicitly evaluated in Schwarzschild, Lense-Thirring and Rindler (uniformly accelerated) geometries. Finally, we discuss how spacetime could affect the characteristic neutrino oscillation length in connection with the recent view of flavor neutrinos as unstable particles., Comment: 13 pages

The study of the decay of an accelerated proton recently provided a theoretical proof of the Unruh effect. On the basis of general covariance of Quantum Field Theory, indeed, it was found that the decay rates in the inertial and comoving frames do coincide only when the thermal nature of the accelerated vacuum is taken into account. Such an analysis was then extended to the case with neutrino mixing. In this Letter, we show that, by further embedding neutrino oscillations in the above framework, general covariance necessarily entails the use of flavor neutrinos as asymptotic states, as well as the occurrence of neutrino oscillations in the Unruh thermal bath.

After a short introduction to the generalized uncertainty principle (GUP), we discuss heuristic derivations of the Casimir effect, first from the usual Heisenberg uncertainty principle (HUP), and then from GUP. Results are compared with those obtained from more standard calculations in Quantum Field Theory (QFT)., Comment: 6 pages, 1 figure

We propose a new approach in the investigation and detection of axion and axion-like particles based on the study of the entanglement for two interacting fermions. We study a system made of two identical fermions with spin-1/2, and we show that fermion-fermion interaction mediated by axions leads to a non-zero entanglement between the fermions. An entanglement measurement can reveal the interaction, providing an indirect evidence of the existence of axions. We discuss how the other interactions affect the entanglement, and how to isolate the axion contribution. Particular care is devoted to the analysis of the magnetic dipole-dipole interaction, which turns out to be, apart from axions, the most relevant contribution to the entanglement, and we show that it can be suppressed by setting opportunely the duration of the observation. We also introduce a two-body correlation function, which could be directly observed in an experiment, and plays the role of an entanglement witness., Comment: 7 pages, 1 figure