We discuss the motion of spin in inertial and gravitational fields. The coupling of spin with rotation and the gravitomagnetic field has already been extensively studied; therefore, we focus here on the inertial and gravitational spin-orbit couplings. In particular, we investigate the classical and quantum aspects of spin precession and spin-orbit coupling in an arbitrary translationally accelerated frame of reference as well as the exterior Schwarzschild spacetime. Moreover, in connection with Einstein’s principle of equivalence, we clarify the relation between the inertial and gravitational spin-orbit couplings.

A general method for classifying the possible quark models of a multi-Higgs-doublet model, in the presence of Abelian symmetries, is presented. All the possible sets of textures that can be present in a given sector are shown, thus turning the determination of the flavor models into a combinatorial problem. Several symmetry implementations are studied for two and three Higgs doublet models. Some models’ implementations are explored in great detail, with a particular emphasis on models known as Branco-Grimus-Lavoura and nearest-neighbor-interaction. Several considerations on the flavor changing neutral currents of multi-Higgs models are also given.

In this work, we discuss the phase structure of a deformed $\mathcal{N}=1$ supersymmetric nonlinear sigma model in a three-dimensional space-time. The deformation is introduced by a term that breaks supersymmetry explicitly, through imposing a slightly different constraint to the fundamental superfields of the model. Using the tadpole method, we compute the effective potential at leading order in a $1/N$ expansion. From the gap equations, i.e., conditions that minimize the effective potential, we observe that this model presents two phases as the ordinary model, with two remarkable differences: 1) the fundamental fermionic field becomes massive in both phases of the model, which is closely related to the supersymmetry breaking term; 2) the $O(N)$ symmetric phase presents a metastable vacuum.

Following the recent study on the emergent Friedmann equation from the expansion of cosmic space for a flat universe, we apply this method to a nonflat universe, and modify the evolution equation to lead to the Friedmann equation. In order to maintain the same form with the original evolution equation, we have to define the time-dependent Planck length, which shows that the spatial curvature of $k=0$ and $k=1$ is preferable to $k=-1$ since the Planck length of the nonflat open universe is divergent. Finally, we discuss its physical consequences.

Motivated by the holographic study of Fermi surfaces, we develop methods to solve Einstein gravity coupled to fermions and gauge fields, with anti–de Sitter boundary conditions and a chemical potential.

The Bañados-Silk-West effect consists in the possibility to obtain arbitrarily large energy $E_{\mathrm{c}.\mathrm{m}.}$ in the center of mass frame of two colliding particles near the black hole horizon. One of the common beliefs was that the action of force on these particles (say, due to gravitational radiation) should necessarily restrict the growth of $E_{\mathrm{c}.\mathrm{m}.}$. We consider extremal horizons, develop a model-independent approach, and analyze the conditions for the force to preserve or kill the effect, using the frames attached both to observers orbiting the black hole and to ones crossing the horizon. We argue that the aforementioned expectations are not confirmed. Under rather general assumptions, the Bañados-Silk-West effect survives. For equatorial motion it is required only that in the proper frame the radial component of the force be finite, while the azimuthal one tend to zero not too slowly. If the latter condition is violated, we evaluate $E_{\mathrm{c}.\mathrm{m}.}$, which becomes indeed restricted but remains very large for small forces.

We study the complete time evolution of scalar fields propagating in spacetimes of higher-dimensional Lifshitz black holes with the dynamical critical exponent $z=2$, obtained from a theory including the most general quadratic curvature corrections to Einstein-Hilbert gravity in $D$ dimensions. We also computed the quasinormal spectrum after performing a numerical integration and solving exactly the Klein-Gordon equation obeyed by the massive scalar field. We found that quasinormal modes are purely imaginary for all dimensions. Concerning the AdS/CFT correspondence, the results indicate that at higher temperatures, initial fluctuations of the thermal state defined at the boundary are not long-lived.

We evaluate the two-point functions of the electromagnetic field in ($D+1$)-dimensional spatially flat Friedmann–Robertson–Walker universes with a power-law scale factor, assuming that the field is prepared in the Bunch–Davies vacuum state. The range of powers is specified in which the two-point functions are infrared convergent and the Bunch–Davies vacuum for the electromagnetic field is a physically realizable state. The two-point functions are applied for the investigation of the vacuum expectation values of the field squared and the energy-momentum tensor, induced by a single and two parallel conducting plates. Unlike to the case of conducting plates in the Minkowski bulk, in the problem under consideration, the stresses along the directions parallel to the plates are not equal to the energy density. We show that, in addition to the diagonal components, the vacuum energy-momentum tensor has a nonzero off-diagonal component which describes energy flux along the direction normal to the plates. For a single plate, this flux is directed from the plate. The Casimir forces are investigated in the geometry of two plates. At separations between the plates smaller than the curvature radius of the background spacetime, to the leading order, we recover the corresponding result in the Minkowski spacetime, and in this case the forces are attractive. At larger separations, the influence of the curvature on the Casimir forces is essential with different asymptotic behavior for decelerated and accelerated expansions. In particular, for the latter case, there is a range of powers of the expansion law in which the forces become repulsive at large separations between the plates.

We consider planar massless scalar waves impinging upon a Kerr black hole, for general angles of incidence. We compute the absorption cross section via the partial wave approach, and present a gallery of results. In the low-frequency regime, we show that the cross section approaches the horizon area; in the high-frequency regime, we show that the cross section approaches the geodesic capture cross section. In the aligned case, we extend the complex angular momentum method to obtain a “sinc” approximation, which relates the regular high-frequency oscillations in the cross section to the properties of the polar null orbit. In the nonaligned case, we show, via a semianalytic approximation, that the reduction in symmetry generates a richer, less regular absorption cross section. We separate the absorption cross section into corotating and counterrotating contributions, showing that the absorption is larger for counterrotating waves, as expected.

The linearized Einstein equations in $D$ spacetime dimensions can be written as twisted self-duality equations expressing that the linearized curvature tensor of the graviton described by a rank-2 symmetric tensor is dual to the linearized curvature tensor of the “dual graviton” described by a tensor of ($D-3$, 1) Young symmetry type. In the case of four dimensions, both the graviton and its dual are rank-2 symmetric tensors [Young symmetry type (1, 1)], while in the case of 11 spacetime dimensions relevant to M theory, the dual graviton is described by a tensor of (8, 1) Young symmetry type. We provide in this paper an action principle that yields the twisted self-duality conditions as equations of motion, keeping the graviton and its dual on equal footing. In order to construct a local, quadratic, variational principle for the twisted linear self-duality equations, it is necessary to introduce two “prepotentials.” These are also tensors of mixed Young symmetry types and are obtained by solving the Hamiltonian constraints of the Hamiltonian formulation either of the Pauli-Fierz action for the graviton or of the Curtright action for its dual, the resulting actions being identical. The prepotentials enjoy interesting gauge-invariance symmetries, which are exhibited and generalize the gauge symmetries found in $D=4$. A variational principle where the basic variables are the original Pauli-Fierz field and its dual can also be given, but contrary to the prepotential action, the corresponding action is nonlocal in space—while remaining local in time. We also analyze in detail the Hamiltonian structure of the theory and show that the graviton and its dual are canonically conjugate in a sense made precise in the text.

We explore the effects of different boundary conditions and coupling schemes on the response of a particle detector undergoing uniform acceleration in optical cavities. We analyze the thermalization properties of the accelerated detector via nonperturbative calculations. We prove nonperturbatively that if the switching process is smooth enough, the detector thermalizes to the Unruh temperature regardless of the boundary conditions and the form of the coupling considered.

We make a comparative analysis of the various independent methods proposed in the literature for studying the nature of dark energy, using four different mocks of SnIa data. In particular, we explore a generic principal components analysis approach, the genetic algorithms, a series of approximations like Padé power law approximants, and various expansions in orthogonal polynomials, as well as cosmography, and compare them with the usual fit to a model with a constant dark energy equation of state $w$. We find that, depending on the mock data, some methods are more efficient than others at distinguishing the underlying model, although there is no universally better method.

We investigate a simple generalization of the metric exponential $f(R)$ gravity theory that is cosmologically viable and compatible with solar system tests of gravity. We show that, as compared to other viable $f(R)$ theories, its steep dependence on the Ricci scalar $R$ facilitates agreement with structure constraints, opening the possibility of $f(R)$ models with an equation-of-state parameter that could be differentiated from a cosmological constant ($w_{de}=-1$) with future surveys at both background and perturbative levels.

The Planck collaboration has recently published maps of the cosmic microwave background (CMB) radiation, in good agreement with a $\Lambda \mathrm{CDM}$ model, a fit especially valid for multipoles $\ell >40$. We explore here the possibility that dark energy is dynamical and gravitational attraction between dark matter particles is effectively different from the standard one in general relativity: this is the case of coupled dark energy models, where dark matter particles feel the presence of a fifth force, larger than gravity by a factor $2{\beta }^2$, defining an effective gravitational constant $G_{\mathrm{eff}}=G(1+2{\beta }^2)$. We investigate constraints on the strength of the coupling $\beta$ in view of Planck data. Interestingly, we show that a nonzero coupling is compatible with data and find a likelihood peak at $\beta =0.036\pm 0.016$ [$\mathrm{\text{Planck}}+\mathrm{WMAP}\mathrm{\text{polarization}}(\mathrm{WP})+\mathrm{\text{baryonic acoustic oscillations}}(\mathrm{BAO})$] (compatible with zero at $2.2\sigma$). The significance of the peak increases to $\beta =0.066\pm 0.018$ [$\mathrm{\text{Planck}}+\mathrm{WP}+\mathrm{\text{Hubble Space Telescope}}(\mathrm{HST})$] (around $3.6\sigma$ from zero coupling) when Planck is combined to HST data by [16]. This peak comes mostly from the small difference between the Hubble parameter determined with CMB measurements and the one coming from astrophysics measurements and is already present in the combination with BAO. Future observations and further tests of current observations are needed to determine whether the discrepancy is due to systematics in any of the data sets. Our aim here is not to claim new physics but rather to show that a clear understanding of such tension has a considerable impact on dark energy models: it can be used to provide information on dynamical dark energy and modified gravity, allowing us to test the strength of an effective fifth force.

We use the expansion-normalized variables approach to study the dynamics of a nontilted Bianchi type I cosmological model with both a homogeneous magnetic field and a viscous fluid. In our model the perfect magnetohydrodynamic approximation is made, and both bulk and shear viscous effects are retained. The dynamical system is studied in detail through a fixed-point analysis which determines the local sink and source behavior of the system. We show that the fixed points may be associated with Kasner-type solutions, a flat universe Friedmann-LeMaître-Robertson-Walker solution, and interestingly, a new solution to the Einstein field equations involving nonzero magnetic fields and nonzero viscous coefficients. It is further shown that for certain values of the bulk and shear viscosity and equation of state parameters, the model isotropizes at late times.

The $SU(2{)}_A\times U(2{)}_V$-symmetric chiral linear sigma model in the presence of the axial anomaly is studied in the local-potential approximation of the functional renormalization group. The renormalization group flow is investigated in a truncation which reproduces recent results for the $U(2{)}_A\times U(2{)}_V$-symmetric model in the limit of vanishing axial anomaly strength. We search for the conjectured $O(4)$ fixed point in the presence of the $U(1{)}_A$ anomaly and analyze its stability properties.

We propose a model of Dirac neutrino masses generated at one-loop level. The origin of this mass is induced from Peccei-Quinn symmetry breaking which was proposed to solve the so-called strong $CP$ problem in QCD; therefore, the neutrino mass is connected with the QCD scale, ${\Lambda }_{\mathrm{QCD}}$. We also study the parameter space of this model, confronting neutrino oscillation data and leptonic rare decays. The phenomenological implications to leptonic flavor physics, such as the electromagnetic moment of charged leptons and neutrinos, are studied. Axion as the dark matter candidate is one of the byproducts in our scenario. Diphoton and Z-photon decay channels in the LHC Higgs search are investigated. We show that the effects of a singly charged singlet scalar can be distinguished from the general two Higgs doublet model.

The viable window to electroweak baryogenesis in a supersymmetric $U(1{)}^{\prime }$ model is studied in light of the 126 GeV Higgs boson. To investigate the decoupling of the sphaleron process in the broken phase, we evaluate the sphaleron rate and order of the electroweak phase transition. In this model, the electroweak phase transition is strongly first order due to the doublet-singlet Higgs mixing. Consequently, for typical parameter sets the $Z^{\prime }$ boson has to be lighter than (150–300) GeV and thus leptophobic to be consistent with the collider bounds. We also estimate the baryon asymmetry of the Universe based on the closed-time-path formalism and find that the $CP$-violating source term fueled by the $Z^{\prime }$-ino can generate sufficient baryon asymmetry.

We investigate the effects of pairing fluctuations in fermionic superfluids/superconductors where pairing occurs among three species (colors) of fermions. Such color superfluids/superconductors can be realized in three-component atomic Fermi gases and in dense quark matter. The superfluidity/superconductivity is characterized by a three-component order parameter which denotes the pairing among the three colors of fermions. Because of the SU(3) symmetry of the Hamiltonian, one color does not participate in pairing. This branch of fermionic excitation is gapless in the naive BCS mean-field description. In this paper, we adopt a pairing fluctuation theory to investigate the pairing fluctuation effects on the unpaired color in strongly coupled atomic color superfluids and quark color superconductors. At low temperature, a large pairing gap of the paired colors suppresses the pairing fluctuation effects for the unpaired color, and the spectral density of the unpaired color shows a single Fermi-liquid peak, which indicates the naive mean-field picture remains valid. As the temperature is increased, the spectral density of the unpaired color generally exhibits a three-peak structure: The Fermi-liquid peak remains but gets suppressed, and two pseudogaplike peaks appears. At and above the superfluid transition temperature, the Fermi-liquid peak disappears completely and all three colors exhibit pseudogaplike spectral density. The coexistence of Fermi liquid and pseudogap behavior is generic for both atomic color superfluids and quark color superconductors.

We consider the expectation value of a chromomagnetic flux loop in the immediate forward light cone of collisions of heavy nuclei at high energies. Such collisions are characterized by a nonlinear scale $Q_s$ where color fields become strong. We find that loops of area greater than $\sim 1.5/Q_s^2$ exhibit area-law behavior, which determines the scale of elementary flux excitations (“vortices”). We also estimate the magnetic string tension, ${\sigma }_M\simeq 0.12Q_s^2$. By the time $t\sim 1/Q_s$ even small loops satisfy area-law scaling. We describe corrections to the propagator of semihard particles at very early times in the background of fluctuating magnetic fields.