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The motion of gravitational axion-like particles (ALP) around a Kerr black hole is analyzed, paying attention to resonance and distribution of spectral radiation. We first discuss the computation of $\sqrt{g}{\tilde R}_{\mu \nu \rho \rho \sigma}R^{\mu \nu \rho \sigma}$ and its implications with Pontryagin's theorem and a detailed analysis of Teukolsky's master equation is done. After carefully analyzing the Teukolsky master equation, we show that this system exhibits resonance when $\omega \gtrsim \mu$ where $\mu$ is the mass of the ALP. A skew-normal distribution can approximate the energy distribution, and we can calculate the mean lifetime of the resonance for black holes with masses between 100 to 1000 $M_{\odot}$. This range corresponds to a duration between $10^{-1}$s and $10^{41}$s, the observation range used in LIGO data., Comment: 23 pages

A cosmological model based on two scalar fields is proposed. The first of these, $\varphi$, has mass $\mu$, while the second, $\chi$, is massless. The pair are coupled through a ``Higgs portal''. First, we show how the model reproduces the Friedmann equations if the square of the mass of the $\varphi$ field is proportional to the cosmological constant and $\chi$ represents the quintessence field. Quantum corrections break the conformal symmetry, and the $\chi$ field acquires a mass equal to $\sqrt{3g\Lambda}$. The perturbative approach with $g\ll 1$ is consistent with the bounds for $m_\chi$; moreover, by using dimensional analysis, we estimate $m_\chi \ll H_0\approx 10^{-33}$ eV, which is in accordance with what is expected in the quintessence scenario. The acceleration of the universe is proportional to $\chi^2$, we conclude that for very long times, the solution of the equation of motion approaches $\langle \chi\rangle \sim {m_\chi}/{{\sqrt\lambda}}$ and the universe continues to accelerate, with a constant acceleration., Comment: Several references were added. To appear in PLB

The multiphoton algebras for one-dimensional Hamiltonians with infinite discrete spectrum, and for their associated kth-order SUSY partners are studied. In both cases, such an algebra is generated by the multiphoton annihilation and creation operators, as well as by Hamiltonians which are functions of an appropriate number operator. The algebras obtained turn out to be polynomial deformations of the corresponding single-photon algebra previously studied. The Barut-Girardello coherent states, which are eigenstates of the annihilation operator, are obtained and their uncertainty relations are explored by means of the associated quadratures., Comment: Last version of the paper, 6 figures

An approach that allows studying the relationship between the neutralization of the cosmological constant and instantons for cosmology coupled to antisymmetric fields is proposed. Using suitable variables, the Lagrangian leading to the FRW equations can be written analogously to a Ginzburg-Landau theory and we show how spontaneous symmetry breaking appears. The approach leads to three possible solutions, if we denote $\Lambda_1$ and $\Lambda_2$ as the cosmological constants that come from gravity ($\Lambda_1$) and antisymmetric fields ($\Lambda_2$), then the solutions, a) $ |\Lambda_2|>|\Lambda_1|$ is consistent with a very small but non-zero $\Lambda_1$, b) $|\Lambda_2|<|\Lambda_1|$, then $\Lambda_1$ is observationally ruled out and, c) $|\Lambda_2|=|\Lambda_1|$ is a solution with finite action and instantons restoring the symmetry $\varphi \to -\varphi$. The third solution is also consistent with neutralization of the cosmological constant in four dimensions., Comment: 7 pages, 1 figure

A relativistic topological insulator model in three spatial dimensions which is a non trivial extension of the non-abelian Landau problem is proposed. The model is exactly soluble and energy levels have both a discrete and a continuous degeneracy. The chromomagnetic field is strong and the fermions are confined in a plane and the physical effects that appear reflects the ${\bm Z}_2$ symmetry., Comment: 9 pages

Following analogies with relativistic point particles, and Schild strings, we show that the Einstein gravity and its strong coupling regime (or the Planck mass going to 0) are related to each other through a Laplace transform. The Feynman propagator of gravity in the strong coupling regime satisfies a functional diffusion equation in the three-metric space with the evolution parameter being the volume of spacetime. We conjecture that the relationship between both regimes is consistent with the existence of an evolution operator in which time is replaced by the volume of spacetime, Comment: 11 pages. Version to be published in special issue of Universe "Beyond Riemannian Geometry in Classical and Quantum Gravity" (Guest eds. Marco Danilo Claudio Torri, Christian Pfeifer and Nicoleta Voicu)

The exploration of the universe has recently entered a new era thanks to the multi-messenger paradigm, characterized by a continuous increase in the quantity and quality of experimental data that is obtained by the detection of the various cosmic messengers (photons, neutrinos, cosmic rays and gravitational waves) from numerous origins. They give us information about their sources in the universe and the properties of the intergalactic medium. Moreover, multi-messenger astronomy opens up the possibility to search for phenomenological signatures of quantum gravity. On the one hand, the most energetic events allow us to test our physical theories at energy regimes which are not directly accessible in accelerators; on the other hand, tiny effects in the propagation of very high energy particles could be amplified by cosmological distances. After decades of merely theoretical investigations, the possibility of obtaining phenomenological indications of Planck-scale effects is a revolutionary step in the quest for a quantum theory of gravity, but it requires cooperation between different communities of physicists (both theoretical and experimental). This review is aimed at promoting this cooperation by giving a state-of-the art account of the interdisciplinary expertise that is needed in the effective search of quantum gravity footprints in the production, propagation and detection of cosmic messengers., Comment: This review was written by participants of the COST Action CA18108. Further information on the review can be found at https://qg-mm.unizar.es/review/, updated to published version

Topological insulators in three dimensions are studied as a problem of supersymmetric quantum mechanics. The spin-orbit coupling is induced as a consequence of the supersymmetrization procedure and we show that it is equivalent to the appearance of a $SU(2)$ connection. The procedure presented in this letter is general and valid for any three-dimensional quantum system. The approach allows -- in principle -- to study a wide range of topological insulators as standard quantum mechanical problems. As an illustration the three-dimensional harmonic oscillator and the Aharonov-Bohm effect are studied in detail., Comment: This is an expanded version, rewritten and includes new results. 18 pages. Comments welcome

A general procedure to describe the coupling $U_A (1) \times U_B (1)$ between antisymmetric gauge fields is proposed. For vector gauge theories the inclusion of magnetic mixing in the hidden sector induces millicharges -- in principle -- observable. We extend the analysis to antisymmetric fields and the extension to higher order monopoles is discussed. A modification of the model discussed in \cite{Ibarra} with massless antisymmetric fields as dark matter is also considered and the total cross section ratio are found and discussed., Comment: new references added

A deformation of the Landau problem based on a modification of Fock algebra is considered. Systems with Hamiltonians f(H) where H is the Landau Hamiltonian in the lowest level are discussed. The case $f(H) = {\alpha} H + b H^2$ is studied and it is shown that in this particular example, parameters of the problem can be fixed by using the quadratic Zeeman effect data and the Breit- Rabi formula. The proposed approach allows to solve exactly Landau-like families of problems not previously discussed in the literature., Comment: 5 pages, no figures

The dynamics of an anapole seen as dark matter at low energies is studied by solving the Schr\"odinger-Pauli equation in a potential involving Dirac-delta and its derivatives in three-dimensions. This is an interesting mathematical problem that, as far as we know, has not been previously discussed. We show how bound states emerge in this approach and the scattering problem is formulated (and solved) directly. The total cross section is in full agreement with independent calculations in the standard model., Comment: One formula and two paragraphs emphasizing physical interpretation are added. To be published in PRD

The Landau problem for inhomogeneous magnetic fields is examined in a very general context and several interesting analogies with the Nielsen-Olesen vortices are established. Firstly we show that the Landau problem with non-homogeneous magnetic fields exhibits Meissner effect that is unstable unless two-body interactions are added and vortices emerge. Using the scaling freedom we can write the Schr\"odinger equation in terms of the scales ratio $\kappa ={ E}/{ m }\propto 1- T/T_c $ where the last identification is realised simply by using the Gizburg-Landau theory. We find our equations are valid in the superconducting regime, and it is not possible for the Cooper pairs amplitude to reach to a constant, non-zero value, and therefore the theory is unstable. The supersymmetric quantum mechanics version, by completeness, is also considered., Comment: 5 pages, two columns, 1 figure. Comments welcomed

We propose a bicosmology model which is the classical analog of noncommutative quantum mechanics. From this point of view the sources of the modified FRW equations are dark energy ones governed by a Chapligyn's equation state. The parameters of noncommutativity $\theta$ and $B$ are interpreted in terms of the Planck area and a like-magnetic field, presumably the magnetic seed of magnetogenesis., Comment: 4 pages

The twin paradox, which evokes from the the idea that two twins may age differently because of their relative motion, has been studied and explained ever since it was first described in 1906, the year after special relativity was invented. The question can be asked: "Is there anything more to say?" It seems evident that acceleration has a role to play, however this role has largely been brushed aside since it is not required in calculating, in a preferred reference frame, the relative age difference of the twins. Indeed, if one tries to calculate the age difference from the point of the view of the twin that undergoes the acceleration, then the role of the acceleration is crucial and cannot be dismissed. In the resolution of the twin paradox, the role of the acceleration has been denigrated to the extent that it has been treated as a red-herring. This is a mistake and shows a clear misunderstanding of the twin paradox., Comment: 16 pages, 5 figures

In the framework of a bimetric model, we discuss a relation between the (modified) Friedmann equations and a mechanical system similar to the quantum Hall effect problem. Firstly, we show how these modified Friedmann equations are mapped to an anisotropic two-dimensional charged harmonic oscillator in the presence of a constant magnetic field, with the frequencies of the oscillator playing the role of the cosmological constants. This problem has two energy scales leading to the identification of two different regimes, namely, one dominated by the cosmological constants, with exponential expansions for the scale factors, and the other dominated by a magnetic seed, which would be responsible for both a component of dark energy and a primordial magnetic field. The latter regime would be described by a (nonperturbative) mapping between the cosmological evolution and the quantum Hall effect., Comment: 4pp

The interaction between two initially causally disconnected regions of the universe is studied using analogies of non-commutative quantum mechanics and deformation of Poisson manifolds. These causally disconnect regions are governed by two independent Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) metrics with scale factors $a$ and $b$ and cosmological constants $\Lambda_a$ and $\Lambda_b$, respectively. The causality is turned on by positing a non-trivial Poisson bracket $[ {\cal P}_{\alpha}, {\cal P}_{\beta} ] =\epsilon_{\alpha \beta}\frac{\kappa}{G}$, where $G$ is Newton's gravitational constant and $\kappa $ is a dimensionless parameter. The posited deformed Poisson bracket has an interpretation in terms of 3-cocycles, anomalies and Poissonian manifolds. The modified FLRW equations acquire an energy-momentum tensor from which we explicitly obtain the equation of state parameter. The modified FLRW equations are solved numerically and the solutions are inflationary or oscillating depending on the values of $\kappa$. In this model the accelerating and decelerating regime may be periodic. The analysis of the equation of state clearly shows the presence of dark energy. By completeness, the perturbative solution for $\kappa \ll1 $ is also studied., Comment: New references added. To appear in Physical Review D

A kinetic mixing term, which generalizes the duality symmetry of Dirac, is studied in a theory with two photons (visible and hidden). This theory can be either CP conserving or CP violating depending on the transformation of fields in the hidden sector. However if CP is violated, it necessarily occurs in the hidden sector. This opens up an interesting possibility of new sources of CP violation., Comment: 3 pages, no figures

We suggest that dark matter may be partially constituted by a dilute 't Hooft-Polyakov monopoles gas. We reach this conclusion by using the Georgi-Glashow model coupled to a dual kinetic mixing term $ F{\tilde {\cal G}}$ where $F$ is the electromagnetic field and ${\cal G}$ the 't Hooft tensor. We show that these monopoles carry both (Maxwell) electric and (Georgi-Glashow) magnetic charges and the electric charge quantization condition is modified in terms of a dimensionless real parameter. This parameter could be determined from milli-charged particle experiments., Comment: 5 pp, no figures

We study two-dimensional Hamiltonians in phase space with noncommutativity both in coordinates and momenta. We consider the generator of rotations on the noncommutative plane and the Lie algebra generated by Hermitian rotationally invariant quadratic forms of noncommutative dynamical variables. We show that two quantum phases are possible, characterized by the Lie algebras $sl(2,\mathbb{R})$ or $su(2)$ according to the relation between the noncommutativity parameters, with the rotation generator related with the Casimir operator. From this algebraic perspective, we analyze the spectrum of some simple models with nonrelativistic rotationally invariant Hamiltonians in this noncommutative phase space, as the isotropic harmonic oscillator, the Landau problem and the cylindrical well potential. PACS: 03.65.-w; 03.65.Fd MSC: 81R05; 20C35; 22E70, Comment: 49 pages. No figures. Version to appear in JPA

The problem of excess gamma radiation in the center of galaxy is discussed assuming that the photon's production is dominated by two kinds of processes, the first one due to the conventional kinetic mixing term and, secondly, due to a kinetic mixing term violating the CP symmetry between dark and visible photons. The CP violation symmetry between dark and visible sectors is not forbidden and, in principle, could be considered as an additional source of CP violation. The conversion probability between dark and visible photons is calculated and compared between both processes. The processes violating CP are less significant but contribute non-trivially to the excess gamma radiation., Comment: 4 pages, no figures

In this article we considered models of particles living in a three-dimensional space-time with a nonstandard noncommutativity induced by shifting canonical coordinates and momenta with generators of a unitary irreducible representation of the Lorentz group. The Hilbert space gets the structure of a direct product with the representation space, where we are able to construct operators which realize the algebra of Lorentz transformations. We study the modified Landau problem for both Schr\"odinger and Dirac particles, whose Hamiltonians are obtained through a kind of non-Abelian Bopp's shift of the dynamical variables from the ones of the usual problem in the normal space. The spectrum of these models are considered in perturbation theory, both for small and large noncommutativity parameters. We find no constraint between the parameters referring to no-commutativity in coordinates and momenta but they rather play similar roles. Since the representation space of the unitary irreducible representations SL(2,R) can be realized in terms of spaces of square-integrable functions, we conclude that these models are equivalent to quantum mechanical models of particles living in a space with an additional compact dimension., Comment: PACS: 03.65.-w; 11.30.Cp; 02.40.Gh, 19 pages, no figures. Version to appear in Physical Review D

The inverse problem of calculus of variations and $s$-equivalence are re-examined by using results obtained from non-commutative geometry ideas. The role played by the structure of the modified Poisson brackets is discussed in a general context and it is argued that classical $s$-equivalent systems may be non-equivalent at the quantum mechanical level. This last fact is explicitly discussed comparing different approaches to deal with the Nair-Polychronakos oscillator., Comment: 7 pages, no figures

A three-dimensional harmonic oscillator with spin non-commutativity in the phase space is considered. The system has a regular symplectic structure and by using supersymmetric quantum mechanics techniques, the ground state is calculated exactly. We find that this state is infinitely degenerate and it has explicit spontaneous broken symmetry. Analyzing the Heisenberg equations, we show that the total angular momentum is conserved., Comment: 6 pages, no figures,references added

The Aharonov-Bohm effect including spin-noncommutative effects is considered. At linear order in $\theta$, the magnetic field is gauge invariant although spatially strongly anisotropic. Despite this anisotropy, the Schr\"odinger-Pauli equation is separable through successive unitary transformations and the exact solution is found. The scattering amplitude is calculated and compared with the usual case. In the noncommutative Aharonov-Bohm case the differential cross section is independent of $\theta$., Comment: 10 pages

A generalization of the Cooper pairing mechanism is proposed which allows for a triplet state of lower energy. This is achieved by incorporating spin into the canonical commutation relations and by modifying the $\delta$ potential contact interaction. The gap equation contain as solutions both singlet and triplet states. It is shown that the triplet state is lower in energy than the singlet state which may explain the spin-triplet superconductivity observed in heavy fermion compound UPt3 and in Sr$_2$RuO$_4$., Comment: 4 pages, 1 figure

A Bose-Einstein condensation theory for any integer spin using noncommutative quantum mechanics methods is considered. The effective potential is derived as a multipolar expansion in the non-commutativity parameter ($\theta$) and, at second order in $\theta$, our procedure yields to the standard dipole-dipole interaction with $\theta^2$ playing the role of the strength interaction parameter. The generalized Gross-Pitaevskii equation containing non-local dipolar contributions is found. For $^{52}$Cr isotopes $\theta = C_{dd}/4\pi$ becomes $\sim 10^{-11}$ cm and, thus for this value of $\theta$ one cannot distinguish interactions coming from non-commutativity or those of dynamical origin., Comment: 6pp

A general three-dimensional noncommutative quantum mechanical system mixing spatial and spin degrees of freedom is proposed. The analogous of the harmonic oscillator in this description contains a magnetic dipole interaction and the ground state is explicitly computed and we show that it is infinitely degenerated and implying a spontaneous symmetry breaking. The model can be straightforwardly extended to many particles and the main above properties are retained. Possible applications to the Bose-Einstein condensation with dipole-dipole interactions are briefly discussed., Comment: New references added, implications with Bose-Einstein condensationare discussed and some portions of the manuscript rewritten