Showing papers on "Scalar potential published in 2014"

Mimetic F(R) gravity: Inflation, dark energy and bounce

Abstract: We propose the mimetic F(R) theory and investigate the early-time and late-time acceleration in such theory. It is demonstrated that inflation consistent with observable data may be realized in such theory. The reconstruction of realistic ΛCDM era is also possible as well as the unification of early-time inflation with late-time acceleration or bounce universe. It is stressed that specific universe evolution is governed by mimetic F(R) theory which is different from convenient F(R) gravity. The corresponding examples are presented. Mimetic F(R) gravity is generalized by the addition of the scalar potential in the formulation of convenient F(R) gravity with specific Lagrange multiplier constraint. It is demonstrated that such theory may admit the arbitrary universe evolution via the corresponding choice of the scalar potential and/or function F(R).

Asymptotically locally AdS and flat black holes in the presence of an electric field in the Horndeski scenario

Abstract: Asymptotically locally anti--de Sitter and asymptotically flat black hole solutions are found for a particular case of the Horndeski action. The action contains the Einstein-Hilbert term with a cosmological constant, a real scalar field with a nonminimal kinetic coupling given by the Einstein tensor, the minimal kinetic coupling, and the Maxwell term. There is no scalar potential. The solution has two integration constants related with the mass and the electric charge. The solution is given for all dimensions. A new class of asymptotically locally flat spherically symmetric black holes is found when the minimal kinetic coupling vanishes and the cosmological constant is present. In this case, we get a solution which represents an electric universe. The electric field at infinity is only supported by $\mathrm{\ensuremath{\Lambda}}$. When the cosmological constant vanishes, the black hole is asymptotically flat.

Vector Potential Electromagnetics with Generalized Gauge for Inhomogeneous Media: Formulation (Invited Paper)

Abstract: The mixed vector and scalar potential formulation is valid from quantum theory to classical electromagnetics. The present rapid development in quantum optics applications calls for electromagnetic solutions that straddle both the quantum and classical physics regimes. The vector potential formulation using A and ' (or A-' formulation) is a good candidate to bridge these two regimes. Hence, there is a need to generalize this formulation to inhomogeneous media. A generalized gauge is suggested for solving electromagnetics problems in inhomogenous media that can be extended to the anistropic case. An advantage of the resulting equations is their absence of catastrophic breakdown at low-frequencies. Hence, the usual difierential equation solvers can be used to solve them over a wide range of scales and bandwidth. It is shown that the interface boundary conditions from the resulting equations reduce to those of classical Maxwell's equations. Also, the classical Green's theorem can be extended to such a formulation, resulting in an extinction theorem and a surface equivalence principle similar to the classical case. Moreover, surface integral equation formulations can be derived for piecewise homogeneous scatterers. Furthermore, the integral equations neither exhibit the low-frequency catastrophe nor the frequency imbalance observed in the classical formulation using E-H flelds. The matrix representation of the integral equation for a PEC (perfect electric conductor) scatterer is given.

Two scalar field cosmology: Conservation laws and exact solutions

Abstract: We consider the two scalar field cosmology in a Friedmann Robertson Walker spatially flat spacetime where the scalar fields interact both in the kinetic part and the potential. We apply the Noether point symmetries in order to define the interaction of the scalar fields. We use the point symmetries in order to write the field equations in the normal coordinates, and we find that the Lagrangian of the field equations which admits at least three Noether point symmetries describes linear Newtonian systems. Furthermore, by using the corresponding conservation laws we find exact solutions of the field equations. Finally, we generalize our results to the case of $N$ scalar fields interacting both in their potential and their kinematic part in a flat Friedmann Robertson Walker background.

Rare region effects dominate weakly disordered three-dimensional Dirac points

Abstract: We study three-dimensional (3D) Dirac fermions with weak finite-range scalar potential disorder. In the clean system, the density of states vanishes quadratically at the Dirac point. Disorder is known to be perturbatively irrelevant, and previous theoretical work has assumed that the Dirac semimetal phase, characterized by a vanishing density of states, survives at weak disorder, with a finite disorder phase transition to a diffusive metal with a nonvanishing density of states. In this paper, we show that nonperturbative effects from rare regions, which are missed by conventional disorder-averaged calculations, instead give rise to a nonzero density of states for any nonzero disorder. Thus, there is no Dirac semimetal phase at nonzero disorder. The results are established both by a heuristic scaling argument and via a systematic saddle-point analysis. We also discuss transport near the Dirac point. At the Dirac point, we argue that transport is diffusive, and proceeds via hopping between rare resonances. As one moves in chemical potential away from the Dirac point, there are interesting intermediate-energy regimes where the rare regions produce scattering resonances that determine the dc conductivity. We derive a scaling theory of transport near disordered 3D Dirac points. We also discuss the interplay of disorder with attractive interactions at the Dirac point and the resulting granular superconducting and Bose glass phases. Our results are relevant for all 3D systems with Dirac points, including Weyl semimetals.

Computing general-relativistic effects from Newtonian N-body simulations: frame dragging in the post-Friedmann approach

Abstract: We present the first calculation of an intrinsically relativistic quantity, the leading-order correction to Newtonian theory, in fully nonlinear cosmological large-scale structure studies. Traditionally, nonlinear structure formation in standard ΛCDM cosmology is studied using N-body simulations, based on Newtonian gravitational dynamics on an expanding background. When one derives the Newtonian regime in a way that is a consistent approximation to the Einstein equations, the first relativistic correction to the usual Newtonian scalar potential is a gravitomagnetic vector potential, giving rise to frame dragging. At leading order, this vector potential does not affect the matter dynamics, thus it can be computed from Newtonian N-body simulations. We explain how we compute the vector potential from simulations in ΛCDM and examine its magnitude relative to the scalar potential, finding that the power spectrum of the vector potential is of the order 10 −5 times the scalar power spectrum over the range of nonlinear scales we consider. On these scales the vector potential is up to two orders of magnitudes larger than the value predicted by second-order perturbation theory extrapolated to the same scales. We also discuss some possible observable effects and future developments.

Scalar Hairy Black Holes in General Dimensions

Abstract: We obtain a class of asymptotic flat or (anti)--de Sitter [(A)dS] hairy black holes in $D$-dimensional Einstein gravity coupled to a scalar with a certain scalar potential. For a given mass, the theory admits both the Schwarzschild-Tangherlini and the hairy black holes with different temperature and entropy, but satisfying the same first law of thermodynamics. For some appropriate choice of parameters, the scalar potential can be expressed in terms of a superpotential, and it can arise in gauged supergravities. In this case, the solutions develop a naked curvature singularity and become the spherical domain walls. Uplifting the solutions to $D=11$ or 10, we obtain solutions that can be viewed as spherical M-branes or D3-branes. We also add electric charges to these hairy black holes. All these solutions contain no scalar charges in that the first law of thermodynamics is unmodified. We also try to construct new AdS black holes carrying scalar charges, with some moderate success in that the charges are pre-fixed in the theory instead of being some continuous integration constants.

The double attractor behavior of induced inflation

Abstract: We describe an induced inflation, which refers to a class of inflationary models with a generalized non-minimal coupling ξg(ϕ)R and a specific scalar potential. The defining property of these models is that the scalar field takes a vev in the vacuum and thus induces an effective Planck mass. We study this model as a function of the coupling parameter ξ. At large ξ, the predictions of the theory are known to have an attractor behavior, converging to a universal result independent on the choice of the function g(ϕ). We find that at small ξ, the theory approaches a second attractor. The inflationary predictions of this class of theories continuously interpolate between those of the Starobinsky model and the predictions of the simplest chaotic inflation with a quadratic potential.

Analysis of an extended scalar sector with S3 symmetry

Abstract: We investigate the scalar potential of a general S3-symmetric three-Higgs-doublet model. The outcome of our analysis does not depend on the fermionic sector of the model. We identify a decoupling limit for the scalar spectrum of this scenario. In view of the recent LHC Higgs data, we show our numerical results only in the decoupling limit. Unitarity and stability of the scalar potential demand that many new scalars must be lurking below 1 TeV. We provide numerical predictions for h→γγ and h→Zγ signal strengths, which can be used to falsify the theory.

Copositive criteria and boundedness of the scalar potential

Abstract: To understand physics beyond the standard model it is important to have the precise knowledge of Higgs boson and top quark masses as well as strong coupling. A recently discovered new boson which is likely to be the standard model Higgs with mass 123--127 GeV has a submissive impact on the stability of the new physics beyond standard model. The beyond standard model scenarios that include many scalar fields posses scalar potential with many quartic couplings. Due to the complicated structures of such scalar potentials it is indeed difficult to adjudge the stability of the vacuum. Thus one needs to formulate a proper prescription for computing the vacuum stability criteria. In this paper we have used the idea of copositive matrices to deduce the conditions that guarantee the boundedness of the scalar potential. We have discussed the basic idea behind the copositivity and then used that to determine the vacuum stability criteria for the left-right symmetric models with doublet and triplet scalars and Type-II seesaw. As this idea is based on the strong mathematical arguments, it helps to compute simple and unique stability criteria embracing the maximum allowed parameter space.

BPS States in Supersymmetric Chiral Models with Higher Derivative Terms

Abstract: We study the higher derivative chiral models with four supercharges and Bogomol'nyi--Prasad--Sommerfield (BPS) states in these models. The off-shell Lagrangian generically includes higher powers of the auxiliary fields $F$, which causes distinct on-shell branches associated with the solutions to the auxiliary fields equation. We point out that the model admits a supersymmetric completion of arbitrary higher derivative bosonic models of a single complex scalar field, and an arbitrary scalar potential can be introduced even without superpotentials. As an example, we present a supersymmetric extension of the Faddeev--Skyrme model without four time derivatives, in contrast to the previously proposed supersymmetric Faddeev--Skyrme-like model containing four time derivatives. In general, higher derivative terms together with a superpotential result in deformed scalar potentials. We find that higher derivative corrections to $1/2$ BPS domain walls and $1/2$ BPS lumps are exactly canceled out, while the $1/4$ BPS lumps (as compact baby Skyrmions) depend on a characteristic feature of the higher derivative models. We also find a new $1/4$ BPS condition for domain wall junctions, which generically receives higher derivative corrections.

Inflation and dark energy from $f(R)$ gravity

Abstract: The standard Starobinsky inflation has been extended to the R + α Rn - β R2-n model to obtain a stable minimum of the Einstein frame scalar potential of the auxiliary field. As a result we have obtained obtain a scalar potential with non-zero value of residual vacuum energy, which may be a source of Dark Energy. Our results can be easily consistent with PLANCK or BICEP2 data for appropriate choices of the value of n.

An H-formulation-based three-dimensional hysteresis loss modelling tool in a simulation including time varying applied field and transport current: the fundamental problem and its solution

Abstract: When analytic solutions are not available, finite-element-based tools can be used to simulate hysteresis losses in superconductors with various shapes. A widely used tool for the corresponding magnetoquasistatic problem is based on the H-formulation, where H is the magnetic field intensity, eddy current model. In this paper, we study this type of tool in a three-dimensional simulation problem. We consider a case where we simultaneously apply both a time-varying external magnetic field and a transport current to a twisted wire. We show how the modelling decisions (air has high finite resistivity and applied field determines the boundary condition) affect the current density distribution along the wire. According to the results, the wire carries the imposed net current only on the boundary of the modelling domain, but not inside it. The current diffuses to the air and back to the boundary. To fix this problem, we present another formulation where air is treated as a region with 0 conductivity. Correspondingly, we express H in the air with a scalar potential and a cohomology basis function which considers the net current condition. As shown in this paper, this formulation does not fail in these so-called AC-AC (time varying transport current and applied magnetic field) simulations.

Measuring the two-Higgs doublet model scalar potential at LHC14

Abstract: After the extraordinary discovery of the Higgs boson at the LHC, the next goal is to pin down its underlying dynamics by measuring the Higgs self-couplings, along with its couplings to gauge and matter particles. As a prototype model of new physics in the scalar sector, we consider the Two Higgs Doublet Model (2HDM) with CP-conservation, and evaluate the prospects for measuring the trilinear scalar couplings among the CP-even Higgs bosons $h$ and $H$ ($\lambda^{hhh}$, $\lambda^{hhH}$, $\lambda^{hHH}$) at LHC14. The continuum and resonant production of CP-even Higgs boson pairs, $hh$ and $hH$, offer complementary probes of the scalar potential away from the light-Higgs decoupling limit. We identify the viable search channels at LHC14 and estimate their expected discovery sensitivities.

Multifield coupled quintessence

Abstract: We study models of quintessence consisting of a number of scalar fields coupled to several dark matter components. In the case of exponential potentials the scaling solutions can be described in terms of a single field. The corresponding effective logarithmic slope and effective coupling can be written in a simple form in terms of the individual slopes and couplings of the original fields. We also investigate solutions where the scalar potential is negligible, in particular those leading to transient matter dominated solutions. Finally, we compute the evolution equations for the linear perturbations which will allow these models to be tested against current and future observational data.

Solution of Klein Gordon Equation for Some Diatomic Molecules with New Generalized Morse-like Potential Using SUSYQM

Abstract: In quantum mechanics, the study of exact solutions of relativistic and non-relativistic equation with different potentials plays a significant role in Physics. The bound state solution of Klein Gordon equation (KGE) is of great important in nuclear and high energy physics. Klein Gordon equation is a relativistic wave equation that describes spinzero particles. It contains of two major objects, the vector potential V(r) and the scalar potential S(r). In D-dimension, the Klein Gordon equation is written as

Intermediate scalings in holographic RG flows and conductivities

Abstract: We construct numerically finite density domain-wall solutions which interpolate between two $AdS_4$ fixed points and exhibit an intermediate regime of hyperscaling violation, with or without Lifshitz scaling. Such RG flows can be realized in gravitational models containing a dilatonic scalar and a massive vector field with appropriate choices of the scalar potential and couplings. The infrared $AdS_4$ fixed point describes a new ground state for strongly coupled quantum systems realizing such scalings, thus avoiding the well-known extensive zero temperature entropy associated with $AdS_2 \times \mathbb{R}^2$. We also examine the zero temperature behavior of the optical conductivity in these backgrounds and identify two scaling regimes before the UV CFT scaling is reached. The scaling of the conductivity is controlled by the emergent IR conformal symmetry at very low frequencies, and by the intermediate scaling regime at higher frequencies.

Inflation in supergravity without Kähler potential

Abstract: We propose a new class of inflation models in supergravity with higher derivative terms. In those models, the Kahler potential does not contain the inflaton multiplet, but a supersymmetric derivative term does. In the models, inflation is effectively driven by a single scalar field with a standard kinetic term and a scalar potential. Remarkably, the so-called η problem does not exist in our models.

Fast-roll inflation

Abstract: A novel class of exact solutions of inflationary dynamics with a specific form of a scalar potential is given based on a "fast-roll" ansatz, where the even-order slow-roll parameters approach to a nonnegligible constants while the odd ones are asymptotically vanishing in the quasi-de Sitter regime. Due to the rapid evolution of the background dynamics, the would-be decaying mode of the linear curvature perturbation may behave as a growing mode depending on the value of the model parameter, while the other mode remains constant. For the parameters giving a slightly red-tilted primordial power spectrum, the unwanted anomalous growth of the curvature perturbation is inevitable, which is similar to the case of the so-called ultra-slow-roll inflation.

A Carleman estimate for infinite cylindrical quantum domains and the application to inverse problems

Abstract: We consider the inverse problem of determining the time-independent scalar potential q of the dynamic Schrodinger equation in an infinite cylindrical domain Ω, from one Neumann boundary observation of the solution. Assuming that q is known outside some fixed compact subset of Ω, we prove that q may be Lipschitz stably retrieved by choosing the Dirichlet boundary condition of the system suitably. Since the proof is by means of a global Carleman estimate designed specifically for the Schrodinger operator acting in an unbounded cylindrical domain, the measurement of the Neumann data is performed on an infinitely extended subboundary of the cylinder.

Foldy–Wouthuysen transformation, scalar potentials and gravity

Abstract: We show that care is required in formulating the nonrelativistic limit of generalized Dirac Hamiltonians which describe particles and antiparticles interacting with static electric and/or gravitational fields. The Dirac–Coulomb and the Dirac–Schwarzschild Hamiltonians, and the corrections to the Dirac equation in a non-inertial frame, according to general relativity, are used as example cases in order to investigate the unitarity of the standard and 'chiral' approaches to the Foldy–Wouthuysen transformation, and spurious parity-breaking terms. Indeed, we find that parity-violating terms can be generated by unitary pseudo-scalar transformations ('chiral' Foldy–Wouthuysen transformations). Despite their interesting algebraic properties, we find that 'chiral' Foldy–Wouthuysen transformations change fundamental symmetry properties of the Hamiltonian and do not conserve the physical interpretation of the operators. Supplementing the discussion, we calculate the leading terms in the Foldy–Wouthuysen transformation of the Dirac Hamiltonian with a scalar potential (of the 1/r-form and of the confining radially symmetric linear form), and obtain compact expressions for the leading higher-order corrections to the Dirac Hamiltonian in a non-inertial rotating reference frame ('Mashhoon term').

Modified Brans–Dicke theory in arbitrary dimensions

Abstract: Within an algebraic framework, used to construct the induced-matter-theory (IMT) setting, in (D + 1)-dimensional Brans–Dicke (BD) scenario, we obtain a modified BD theory (MBDT) in D dimensions. Being more specific, from the (D + 1)-dimensional field equations, a D-dimensional BD theory, bearing new features, is extracted by means of a suitable dimensional reduction onto a hypersurface orthogonal to the extra dimension. In particular, the BD scalar field in such D-dimensional theory has a self-interacting potential, which can be suitably interpreted as produced by the extra dimension. Subsequently, as an application to cosmology, we consider an extended spatially flat FLRW geometry in a (D + 1)-dimensional space–time. After obtaining the power-law solutions in the bulk, we proceed to construct the corresponding physics, by means of the induced MBDT procedure, on the D-dimensional hypersurface. We then contrast the resulted solutions (for different phases of the universe) with those usually extracted from the conventional GR and BD theories in view of current ranges for cosmological parameters. We show that the induced perfect fluid background and the induced scalar potential can be employed, within some limits, for describing different epochs of the universe. Finally, we comment on the observational viability of such a model.

Analytical solutions of the Klein-Fock-Gordon equation with the Manning-Rosen potential plus a Ring-Shaped like potential

Abstract: In this work, on the condition that scalar potential is equal to vector potential, the bound state solutions of the Klein–Fock–Gordon equation of the Manning–Rosen plus ring-shaped like potential are obtained by Nikiforov–Uvarov method. The energy levels are worked out and the corresponding normalized eigenfunctions are obtained in terms of orthogonal polynomials for arbitrary l states. The conclusion also contain central Manning–Rosen, central and noncentral Hulthen potential.

Observational constraints on Tachyon and DBI inflation

Abstract: We present a systematic method for evaluation of perturbation observables in non-canonical single-field inflation models within the slow-roll approximation, which allied with field redefinitions enables predictions to be established for a wide range of models. We use this to investigate various non-canonical inflation models, including Tachyon inflation and DBI inflation. The Lambert function will be used extensively in our method for the evaluation of observables. In the Tachyon case, in the slow-roll approximation the model can be approximated by a canonical field with a redefined potential, which yields predictions in better agreement with observations than the canonical equivalents. For DBI inflation models we consider contributions from both the scalar potential and the warp geometry. In the case of a quartic potential, we find a formula for the observables under both non-relativistic (sound speed cs2 ~ 1) and relativistic behaviour (cs2 1) of the scalar DBI inflaton. For a quadratic potential we find two branches in the non-relativistic cs2 ~ 1 case, determined by the competition of model parameters, while for the relativistic case cs2 → 0, we find consistency with results already in the literature. We present a comparison to the latest Planck satellite observations. Most of the non-canonical models we investigate, including the Tachyon, are better fits to data than canonical models with the same potential, but we find that DBI models in the slow-roll regime have difficulty in matching the data.

Analysis of in situ electric field and specific absorption rate in human models for wireless power transfer system with induction coupling

Abstract: This study investigates the specific absorption rate (SAR) and the in situ electric field in anatomically based human models for the magnetic field from an inductive wireless power transfer system developed on the basis of the specifications of the wireless power consortium. The transfer system consists of two induction coils covered by magnetic sheets. Both the waiting and charging conditions are considered. The transfer frequency considered in this study is 140 kHz, which is within the range where the magneto-quasi-static approximation is valid. The SAR and in situ electric field in the chest and arm of the models are calculated by numerically solving the scalar potential finite difference equation. The electromagnetic modelling of the coils in the wireless power transfer system is verified by comparing the computed and measured magnetic field distributions. The results indicate that the peak value of the SAR averaged over a 10 g of tissue and that of the in situ electric field are 72 nW kg−1 and 91 mV m−1 for a transmitted power of 1 W, Consequently, the maximum allowable transmitted powers satisfying the exposure limits of the SAR (2 W kg−1) and the in situ electric field (18.9 V m−1) are found to be 28 MW and 43 kW. The computational results show that the in situ electric field in the chest is the most restrictive factor when compliance with the wireless power transfer system is evaluated according to international guidelines.