Showing papers on "Scalar potential published in 2021"
TL;DR: In this article, the stability of rotating scalar boson stars with azimuthal number $m=1$ was studied and it was shown that any boson star with $m = 1$ that is sufficiently far into the nonrelativistic regime, where the leading order mass term dominates, will be unstable, independent of the nonlinear scalar selfinteractions.
Abstract: We study the stability of rotating scalar boson stars, comparing those made from a simple massive complex scalar (referred to as mini boson stars), to those with several different types of nonlinear interactions. To that end, we numerically evolve the nonlinear Einstein-Klein-Gordon equations in 3D, beginning with stationary boson star solutions. We show that the linear, non-axisymmetric instability found in mini boson stars with azimuthal number $m=1$ persists across the entire parameter space for these stars, though the timescale diverges in the Newtonian limit. Therefore, any boson star with $m=1$ that is sufficiently far into the nonrelativistic regime, where the leading order mass term dominates, will be unstable, independent of the nonlinear scalar self-interactions. However, we do find regions of $m=1$ boson star parameter space where adding nonlinear interactions to the scalar potential quenches the nonaxisymmetric instability, both on the nonrelativistic, and the relativistic branches of solutions. We also consider select boson stars with $m=2$, finding instability in all cases. For the cases exhibiting instability, we follow the nonlinear development, finding a range of dynamics including fragmentation into multiple unbound nonrotating stars, and formation of binary black holes. Finally, we comment on the relationship between stability and criteria based on the rotating boson star's frequency in relation to that of a spherical boson star or the existence of a corotation point. The boson stars that we find not to exhibit instability when evolved for many dynamical times include rapidly rotating cases where the compactness is comparable to that of a black hole or neutron star.
47 citations
TL;DR: In this paper, a scalar field is coupled to the Gauss-Bonnet term and primordial black holes may be seeded when the scalar potential term and the Bonnet coupling term are nearly balanced.
Abstract: Primordial black holes formed in the early Universe via gravitational collapse of over-dense regions may contribute a significant amount to the present dark matter relic density. Inflation provides a natural framework for the production mechanism of primordial black holes. For example, single field inflation models with a fine-tuned scalar potential may exhibit a period of ultra-slow roll, during which the curvature perturbation may be enhanced to become seeds of the primordial black holes formed as the corresponding scales reenter the horizon. In this work, we propose an alternative mechanism for the primordial black hole formation. We consider a model in which a scalar field is coupled to the Gauss-Bonnet term and show that primordial black holes may be seeded when a scalar potential term and the Gauss-Bonnet coupling term are nearly balanced. Large curvature perturbation in this model not only leads to the production of primordial black holes, but it also sources gravitational waves at the second order. We calculate the present density parameter of the gravitational waves and discuss the detectability of the signals by comparing them with sensitivity bounds of future gravitational wave experiments.
40 citations
TL;DR: The Swampland Distance Conjecture (SDC) restricts the geodesic distances that scalars can traverse in effective field theories as they approach points at infinite distance in moduli space.
Abstract: The Swampland Distance Conjecture (SDC) restricts the geodesic distances that scalars can traverse in effective field theories as they approach points at infinite distance in moduli space We propose that, when applied to the subset of light fields in effective theories with scalar potentials, the SDC restricts the amount of non-geodesicity allowed for trajectories along valleys of the potential This is necessary to ensure consistency of the SDC as a valid swampland criterion at any energy scale across the RG flow We provide a simple description of this effect in moduli space of hyperbolic space type, and products thereof, and obtain critical trajectories which lead to maximum non-geodesicity compatible with the SDC We recover and generalize these results by expressing the SDC as a new Convex Hull constraint on trajectories, characterizing towers by their scalar charge to mass ratio in analogy to the Scalar Weak Gravity Conjecture We show that recent results on the asymptotic scalar potential of flux compatifications near infinity in moduli space precisely realize these critical amounts of non-geodesicity Our results suggest that string theory flux compactifications lead to the most generic potentials allowing for maximum non-geodesicity of the potential valleys while respecting the SDC along them
36 citations
TL;DR: In this article, it was shown that the geometry near the singularity takes a universal Kasner form when the kinetic term of the scalar hair dominates, while novel behaviors different from the Kasner-form are uncovered when scalar potential become important to the background.
Abstract: We establish a no inner-horizon theorem for black holes with charged scalar hairs. Considering a general gravitational theory with a charged scalar field, we prove that there exists no inner Cauchy horizon for both spherical and planar black holes with non-trivial scalar hair. The hairy black holes approach to a spacelike singularity at late interior time. This result is independent of the form of scalar potentials as well as the asymptotic boundary of spacetimes. We prove that the geometry near the singularity takes a universal Kasner form when the kinetic term of the scalar hair dominates, while novel behaviors different from the Kasner form are uncovered when the scalar potential become important to the background. For the hyperbolic horizon case, we show that hairy black hole can only has at most one inner horizon, and a concrete example with an inner horizon is presented. All these features are also valid for the Einstein gravity coupled with neutral scalars.
32 citations
TL;DR: In this article, a simplified Einstein-Gauss-Bonnet inflationary theoretical framework was proposed, which is compatible with the GW170817 observational constraints on the gravitational wave speed.
Abstract: We provide a refined and much more simplified Einstein-Gauss-Bonnet inflationary theoretical framework, which is compatible with the GW170817 observational constraints on the gravitational wave speed. As in previous works, the constraint that the gravitational wave speed is $c_T^2=1$ in natural units, results to a constraint differential equation that relates the coupling function of the scalar field to the Gauss-Bonnet invariant $\xi(\phi)$ and the scalar potential $V(\phi)$. Adopting the slow-roll conditions for the scalar field and the Hubble rate, and in contrast to previous works, by further assuming that $\kappa \frac{\xi '}{\xi''}\ll 1$, which is motivated by slow-roll arguments, we succeed in providing much more simpler expressions for the slow-roll indices and for the tensor and scalar spectral indices and for the tensor-to-scalar ratio. We exemplify our refined theoretical framework by using an illustrative example with a simple power-law scalar coupling function $\xi(\phi)\sim \phi^{
u}$ and as we demonstrate the resulting inflationary phenomenology is compatible with the latest Planck data. Moreover, this particular model produces a blue-tilted tensor spectral index, so we discuss in brief the perspective of describing the NANOGrav result with this model as is indicated in the recent literature.
32 citations
TL;DR: In this paper, it was shown that the roll of a spectator axion on this potential becomes temporarily fast, leading to localized amplification of one helicity state of gauge fields, which can generate observable gravitational waves (GWs) at CMB scales while satisfying the current limits on scalar perturbations.
Abstract: In string theory inspired models of axion-like fields, sub-leading non-perturbative effects, if sufficiently large, can introduce steep cliffs and gentle plateaus onto the underlying scalar potential. During inflation, the motion of a spectator axion $\sigma$ on this potential becomes temporarily fast, leading to localized amplification of one helicity state of gauge fields. In this model, the tensor and scalar correlators sourced by the vector fields exhibit localized peak(s) in momentum space corresponding to the modes that exit the horizon while the roll of $\sigma$ is fast. Thanks to the gravitational coupling of gauge fields with the visible sector and the localized nature of particle production, this model can generate observable gravitational waves (GWs) at CMB scales while satisfying the current limits on scalar perturbations. The resulting GW signal breaks parity and exhibit sizeable non-Gaussianity that can be probed by future CMB B-mode missions. Depending on the initial conditions and model parameters, the roll of the spectator axion can also generate an observably large GW signature at interferometer scales while respecting the bounds on the scalar fluctuations from primordial black hole limits. In our analysis, we carefully investigate bounds on the model parameters that arise through back-reaction and perturbativity considerations to show that these limits are satisfied by the implementations of the model that generate GW signals at CMB and sub-CMB scales.
31 citations
TL;DR: In this article, the authors present the results of a global fit to the Aligned Two-Higgs Doublet Model, assuming that there are no new sources of CP violation beyond the quark mixing matrix.
Abstract: We present the results of a global fit to the Aligned Two-Higgs Doublet Model, assuming that there are no new sources of CP violation beyond the quark mixing matrix. We use the most constraining flavour observables, electroweak precision measurements and the available data on Higgs signal strengths and collider searches for heavy scalars, together with the theoretical requirements of perturbativity and positivity of the scalar potential. The combination of all these constraints restricts the values of the scalar masses, the couplings of the scalar potential and the flavour-alignment parameters. The numerical fits have been performed using the open-source HEPfit package.
31 citations
TL;DR: In this paper, the moduli dependence of perturbative corrections to the 4D scalar potential of type IIB Calabi-Yau orientifold compactifications is investigated.
Abstract: Extracting reliable low-energy information from string compactifications notoriously requires a detailed understanding of the UV sensitivity of the corresponding effective field theories. Despite past efforts in computing perturbative string corrections to the tree-level action, neither a systematic approach nor a unified framework has emerged yet. We make progress in this direction, focusing on the moduli dependence of perturbative corrections to the 4D scalar potential of type IIB Calabi-Yau orientifold compactifications. We proceed by employing two strategies. First, we use two rescaling symmetries of type IIB string theory to infer the dependence of any perturbative correction on both the dilaton and the Calabi-Yau volume. Second, we use F/M-theory duality to conclude that KK reductions on elliptically-fibred Calabi-Yau fourfolds of the M-theory action at any order in the derivative expansion can only generate (α′)even corrections to the 4D scalar potential, which, moreover, all vanish for trivial fibrations. We finally give evidence that (α′)odd effects arise from integrating out KK and winding modes on the elliptic fibration and argue that the leading no-scale breaking effects at string tree-level arise from (α′)3 effects, modulo potential logarithmic corrections.
30 citations
TL;DR: In this paper, the scaling potential of scalar fields in asymptotically safe quantum gravity has been studied and it has been shown that scaling solutions with vanishing relevant parameters can be sufficient for a realistic description of particle physics and cosmology, leading to a cosmological constant or dynamical dark energy.
Abstract: We compute the effective potential for scalar fields in asymptotically safe quantum gravity. A scaling potential and other scaling functions generalize the fixed point values of renormalizable couplings. The scaling potential takes a non-polynomial form, approaching typically a constant for large values of scalar fields. Spontaneous symmetry breaking may be induced by non-vanishing gauge couplings. We strengthen the arguments for a prediction of the ratio between the masses of the top quark and the Higgs boson. Higgs inflation in the standard model is unlikely to be compatible with asymptotic safety. Scaling solutions with vanishing relevant parameters can be sufficient for a realistic description of particle physics and cosmology, leading to an asymptotically vanishing “cosmological constant” or dynamical dark energy.
29 citations
TL;DR: In this article, the authors have shown that certain deformations of the scalar potential in JT gravity can be written as double-scaled matrix models, however, some of the deformations exhibit an apparent breakdown of unitarity in the form of a negative spectral density at disc order.
Abstract: Recent work has shown that certain deformations of the scalar potential in Jackiw-Teitelboim gravity can be written as double-scaled matrix models. However, some of the deformations exhibit an apparent breakdown of unitarity in the form of a negative spectral density at disc order. We show here that the source of the problem is the presence of a multi-valued solution of the leading order matrix model string equation. While for a class of deformations we fix the problem by identifying a first order phase transition, for others we show that the theory is both perturbatively and non-perturbatively inconsistent. Aspects of the phase structure of the deformations are mapped out, using methods known to supply a non-perturbative definition of undeformed JT gravity. Some features are in qualitative agreement with a semi-classical analysis of the phase structure of two-dimensional black holes in these deformed theories.
25 citations
TL;DR: In this article, the Friedmann equation is solved in terms of appropriate statefinder quantities frequently used in the literature, and numerically solved by using physically motivated initial conditions, which is robust against changes in the initial conditions of the scalar field.
Abstract: In this work by using a numerical analysis, we investigate in a quantitative way the late-time dynamics of scalar coupled $f(R,\mathcal{G})$ gravity Particularly, we consider a Gauss-Bonnet term coupled to the scalar field coupling function $\xi(\phi)$, and we study three types of models, one with $f(R)$ terms that are known to provide a viable late-time phenomenology, and two Einstein-Gauss-Bonnet types of models Our aim is to write the Friedmann equation in terms of appropriate statefinder quantities frequently used in the literature, and we numerically solve it by using physically motivated initial conditions In the case that $f(R)$ gravity terms are present, the contribution of the Gauss-Bonnet related terms is minor, as we actually expected This result is robust against changes in the initial conditions of the scalar field, and the reason is the dominating parts of the $f(R)$ gravity sector at late times In the Einstein-Gauss-Bonnet type of models, we examine two distinct scenarios, firstly by choosing freely the scalar potential and the scalar Gauss-Bonnet coupling $\xi(\phi)$, in which case the resulting phenomenology is compatible with the latest Planck data and mimics the $\Lambda$-Cold-Dark-Matter model In the second case, since there is no fundamental particle physics reason for the graviton to change its mass, we assume that primordially the tensor perturbations propagate with the speed equal to that of light's, and thus this constraint restricts the functional form of the scalar coupling function $\xi(\phi)$, which must satisfy the differential equation $\ddot{\xi}=H\dot{\xi}$
TL;DR: In this paper, it was shown that there is no inner Cauchy horizon for both spherical and planar symmetric cases, independent of the scalar potential and nonlinear electrodynamics.
Abstract: We prove a no Cauchy horizon theorem for general nonlinear electrodynamics black holes with charged scalar hairs. By constructing a radially conserved charged, we show that there is no inner Cauchy horizon for both spherical and planar symmetric cases, independent of the form of scalar potential and nonlinear electrodynamics. After imposing the null energy condition, we are also able to rule out the existence of the Cauchy horizon for the hyperbolic black holes. We take the Born-Infeld black hole as a concrete example to study the interior dynamics beyond the event horizon. When the contribution from the scalar potential can be neglected, the asymptotic near-singularity takes a universal Kasner form. We also confirm that the intricate interior dynamics is closely associated with the instability of the inner Cauchy horizon triggered by scalar hairs.
TL;DR: In this article, it was shown that the Reissner-nordstrom black hole (RN black hole) is not stable in the microcanonical ensemble and that the RN black hole will be scalarized by a first order phase transition spontaneously.
Abstract: It has been shown recently that the charged black hole can be scalarized if Maxwell field minimally couples with a complex scalar which has nonnegative nonlinear potential. We first prove that such scalarization cannot be a result of continuous phase transition for general scalar potential. Furthermore, we numerically find that it is possible that the RN black hole will be scalarized by a first order phase transition spontaneously and near extremal Reissner-Nordstr\"om black hole(RN black hole) is not stable in the microcanonical ensemble. In addition, considering a massless scalar perturbation, we compute the quasinormal modes of the scalarized charged black hole and the results do not only imply that the spontaneously scalarized charged black hole is favored in thermodynamics but also suggest that it is kinetically stable against scalar perturbation at linear level. Our numerical results also definitely gives negative answer to Penrose-Gibbons conjecture and two new versions of Penrose inequality in charged case are suggested.
TL;DR: In this article, the wormhole solutions in the background of f(R,φ,X) theory of gravity were investigated, where R is Ricci scalar, φ is scalar potential, and X is the kinetic term.
Abstract: This work aims to investigate the wormhole solutions in the background of f(R,φ,X) theory of gravity, where R is Ricci scalar, φ is scalar potential, and X is the kinetic term. We consider spherica...
TL;DR: In this article, the authors explore the embedding of the phenomenological holographic models describing thermal relativistic ordered conformal phases in R 2, 1 in SUGRA/String theory.
TL;DR: In this article, the authors revisited the astrophysical constraints on a generic light CP-even scalar particle S, mixing with the Standard Model (SM) Higgs boson, from observed luminosities of the Sun, red giants, white dwarfs and horizontal-branch stars.
Abstract: We revisit the astrophysical constraints on a generic light CP-even scalar particle S, mixing with the Standard Model (SM) Higgs boson, from observed luminosities of the Sun, red giants, white dwarfs and horizontal-branch stars. The production of S in the stellar core is dominated by the electron-nuclei bremsstrahlung process e + N → e + N + S. With the S decay and reabsorption processes taken into consideration, we find that the stellar luminosity limits exclude a broad range of parameter space in the S mass-mixing plane, with the scalar mass up to 350 keV and the mixing angle ranging from 7.0 × 10-18 to 3.4 × 10-3. We also apply the stellar limits to a real-singlet scalar extension of the SM, where we can relate the mixing angle to the parameters in the scalar potential. In both the generic scalar case and the real-singlet extension, we show that the stellar limits preclude the scalar interpretation of the recently observed XENON1T excess in terms of the S particles emitted from the Sun.
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TL;DR: In this paper, the Starobinsky model of inflation has been extended with the explicit dependence on fields and parameters in terms of elementary functions, and the scalar potentials, the inflationary observables and the allowed limits on the deformation parameters in all these cases.
Abstract: We propose several extensions of the Starobinsky model of inflation, which obey all observational constraints on the inflationary parameters, by demanding that both the inflaton scalar potential in the Einstein frame and the $F(R)$ gravity function in the Jordan frame have the explicit dependence upon fields and parameters in terms of elementary functions. All our models are continuously connected to the original Starobinsky model via changing the parameters. We modify the Starobinsky $(R+R^2)$ model by adding an $R^3$-term, an $R^4$-term, and an $R^{3/2}$-term, respectively, and calculate the scalar potentials, the inflationary observables and the allowed limits on the deformation parameters in all these cases. We also deform the scalar potential of the Starobinsky model in the Einstein frame, in powers of $y=\exp\left(-\sqrt{\frac{2}{3}}\phi/M_{Pl}\right)$, where $\phi$ is the canonical inflaton (scalaron) field, calculate the corresponding $F(R)$ gravity functions in the two new cases, and find the restrictions on the deformation parameters in the lowest orders with respect to the variable $y$ that is physically small during slow-roll inflation.
TL;DR: In this article, the supersymmetric implementation of Affleck-Dine inflation in the use of two chiral superfields with appropriate superpotential and K\"ahler potential is investigated.
Abstract: Affleck-Dine inflation is a recently proposed model in which a single complex scalar field, nonminimally coupled to gravity, drives inflation and simultaneously generates the baryon asymmetry of universe via Affleck-Dine mechanism. In this paper we investigate the supersymmetric implementation of Affleck-Dine inflation in the use of two chiral superfields with appropriate superpotential and K\"ahler potential. The scalar potential has a similar form to the potential of original Affleck-Dine inflation, and it gives successful inflation and baryogenesis. We also consider the isocurvature perturbation evolving after crossing the horizon, and find that it is ignorable and hence consistent with the observations.
TL;DR: In this article, the moduli dependence of perturbative corrections to the 4D scalar potential of type IIB Calabi-Yau orientifold compactifications is investigated.
Abstract: Extracting reliable low-energy information from string compactifications notoriously requires a detailed understanding of the UV sensitivity of the corresponding effective field theories. Despite past efforts in computing perturbative string corrections to the tree-level action, neither a systematic approach nor a unified framework has emerged yet. We make progress in this direction, focusing on the moduli dependence of perturbative corrections to the 4D scalar potential of type IIB Calabi-Yau orientifold compactifications. We proceed by employing two strategies. First, we use two rescaling symmetries of type IIB string theory to infer the dependence of any perturbative correction on both the dilaton and the Calabi-Yau volume. Second, we use F/M-theory duality to conclude that KK reductions on elliptically-fibred Calabi-Yau fourfolds of the M-theory action at any order in the derivative expansion can only generate $(\alpha')^{\rm even}$ corrections to the 4D scalar potential, which, moreover, all vanish for trivial fibrations. We finally give evidence that $(\alpha')^{\rm odd}$ effects arise from integrating out KK and winding modes on the elliptic fibration and argue that the leading no-scale breaking effects at string tree-level arise from $(\alpha')^3$ effects, modulo potential logarithmic corrections.
TL;DR: In this paper, the cylindrical symmetric solutions in a well-known gravity, namely the $$f(R,\phi )$$ theory of gravity, where R stands for Ricci scalar and $$\phi $$ represents the scalar potential, are discussed.
Abstract: This manuscript is dedicated to discussing the cylindrical symmetric solutions in a well-known gravity, namely the $$f(R,\phi )$$
theory of gravity, where R stands for Ricci scalar and $$\phi $$
represents the scalar potential. For our current study, $$f(R,\phi )=(1+\xi \uplambda ^2 \phi ^2)R$$
gravity model is used to find the exact solutions of field equations. Furthermore, a well-known Levi-Civita solution by considering some parameters has been investigated. We exclusively worked out the expressions of density and pressure terms and analyzed them graphically. Energy conditions especially null energy conditions are examined while discussing the exact solutions of all these cases. It is concluded that the null energy conditions are violated for some specific regions, which is an indication of the existence of cylindrical wormholes. The charming and fascinating feature of this task is two-dimensional and three-dimensional investigation.
TL;DR: In this article, the authors present approximate and analytical solutions of the deformed Klein-Gordon containing an interaction of the equal vector and scalar potential newly generalized modified screened Coulomb plus inversely quadratic Yukawa potential.
Abstract: In this work, we present approximate and analytical solutions of the deformed Klein–Gordon containing an interaction of the equal vector and scalar potential newly generalized modified screened Coulomb plus inversely quadratic Yukawa potential. To overcome the centrifugal barrier, we employed the well-known Greene and Aldrich approximation scheme. This study is realized in the relativistic noncommutative 3-dimensional real space symmetries. This potential is suggested to compute bound-state normalizations and the energy levels of neutral atoms. Furthermore, it is considered a good potential in studying Hydrogen-like atoms. Both ordinary Bopp’s shift method, perturbation theory, and the Greene–Aldrich approximation method of handling centrifugal barriers are surveyed to get generalized excited states energy $$E_{r-nc}^{sip} \left( {V_{0} ,\,V_{1} ,\,k\left( {j,l,s} \right) ,\,\alpha ,\,n,\,j,\,l,\,m,\,s} \right) $$
, as a function of the shift energy, the energy of the modified screened Coulomb plus inversely quadratic Yukawa potential, the discreet atomic quantum numbers $$(j,\,l,\,s,\,m)$$
, the potential parameters (
$$V_{0} ,\,V_{1} ,\,\alpha )$$
and the infinitesimal noncommutativity parameters (
$$\theta $$
and $$\sigma $$
). We have shown that the degeneracy of the initial spectral under the potential in the relativistic commutative quantum mechanics RCQM is broken and replaced by newly degeneracy of energy levels; this gives more precisions in measurement and better off compared to results of ordinary RCQM.
TL;DR: In this article, the authors showed that oscillons formed in the early Universe can be stable on cosmological time scales and thus contribute to the abundance of (ultra)light scalar dark matter.
Abstract: Oscillons are localized states of scalar fields sustained by self interactions. They decay by emitting classical radiation, but their lifetimes are surprisingly large. We revisit the reasons behind their longevity, aiming at how the shape of the scalar potential $V(\phi)$ determines the lifetime. The corpuscular picture, where the oscillon is identified with a bound state of a large number of field quanta, allows to understand lifetimes of order of $10^3$ cycles in generic potentials. At the non-perturbative level, two properties of the scalar potential can substantially boost the lifetime: the flattening of $V(\phi)$ and the positivity of $V''(\phi)$. These properties are realized in the axion monodromy family of potentials. Moreover, this class of models connects continuously with an exceptional potential that admits eternal oscillon solutions. We check these results with a new fast-forward numerical method that allows to evolve in time to stages that cannot be otherwise simulated on a computer. The method exploits the attractor properties of the oscillons and fully accounts for nonlinearities. We find lifetimes up to $10^{14}$ cycles, but larger values are possible. Our work shows that oscillons formed in the early Universe can be stable on cosmological time scales and thus contribute to the abundance of (ultra)light scalar dark matter.
TL;DR: In this article, a magnetic dual-dipolem model was proposed to describe and evaluate the stress concentration in ferromagnetic materials and the contour maps of the magnetic scalar potential showed that there is a magnetic source generated in the damaged area.
Abstract: Experiment shows that the normal component and the amplitude of the spontaneous magnetic signals on the surface of the ferromagnetic part, induced by a stress concentration zone (SCZ) caused by local plastic deformation, have only one peak. These waveform characteristics are precisely opposite of the defect identification criteria proposed by the metal magnetic memory (MMM) method, which include that the normal component of magnetic signals changes to its polarity and the tangential component reaches a peak value. At the beginning, a magnetic dual-dipole model is accordingly proposed to describe and evaluate the stress concentration in ferromagnetic materials. The contour maps of the magnetic scalar potential show that there is a magnetic source generated in the damaged area. This source can be simplified as a dual-dipole. It comes from the two peaks of stress variation at the edges of the SCZ. Furthermore, the maximum potential of magnetic anomalies was obtained. The values are influenced by the applied loading and deflection of the specimen. It decays exponentially with the increase of lift-off values in the air domain. Finally, residual stresses along the scanning line were measured to confirm the theoretical analysis. This dual-dipole model in the MMM technique is feasible to evaluate the stress concentration caused by local plastic deformation.
TL;DR: In this article, the existence of traversable wormhole in the background of f ( R, ϕ, X ) theory of gravity is investigated. But the authors focus on the spherically symmetric space-time.
TL;DR: In this paper, a modified Klein-Fock-Gordon equation for the linear combination of Hulthen and Yukawa potentials is presented, and the relativistic energy eigenvalues and corresponding radial wave functions are obtained from supersymmetric quantum mechanics by applying the shape invariance concept.
Abstract: The relativistic wave equations determine the dynamics of quantum fields in the context of quantum field theory. One of the conventional tools for dealing with the relativistic bound state problem is the Klein-Fock-Gordon equation. In this work, using a developed scheme, we present how to surmount the centrifugal part and solve the modified Klein-Fock-Gordon equation for the linear combination of Hulthen and Yukawa potentials. In particular, we show that the relativistic energy eigenvalues and corresponding radial wave functions are obtained from supersymmetric quantum mechanics by applying the shape invariance concept. Here, both scalar potential conditions, which are whether equal and nonequal to vector potential, are considered in the calculation. The energy levels and corresponding normalized eigenfunctions are represented as a recursion relation regarding the Jacobi polynomials for arbitrary states. Beyond that, a closed form of the normalization constant of the wave functions is found. Furthermore, we state that the energy eigenvalues are quite sensitive with potential parameters for the quantum states. The nonrelativistic and relativistic results obtained within SUSY QM overlap entirely with the results obtained by ordinary quantum mechanics, and it displays that the mathematical implementation of SUSY quantum mechanics is quite perfect.
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TL;DR: In this paper, the authors studied the general structure of 4D scalar potentials at higher orders in the Hodge expansion for arbitrary Hodge numbers and showed the existence of a no-scale structure for odd moduli in the presence of corrections to the Kahler potential.
Abstract: Moduli stabilisation in superstring compactifications on Calabi-Yau orientifolds remains a key challenge in the search for realistic string vacua. In particular, odd moduli arising from the reduction of 2-forms $(B_2,C_2)$ in type IIB are largely unexplored despite their relevance for inflationary model building. This article provides novel insights into the general structure of 4D $\mathcal{N}=1$$F$-term scalar potentials at higher orders in the $\alpha^{\prime}$ and $g_{s}$ expansion for arbitrary Hodge numbers. We systematically examine superpotential contributions with distinct moduli dependences which are induced by fluxes or non-perturbative effects. Initially, we prove the existence of a no-scale structure for odd moduli in the presence of $(\alpha^\prime)^{3}$ corrections to the Kahler potential. By studying a partially $\mathrm{SL}(2,\mathbb{Z})$-completed form of the Kahler potential, we derive the exact no-scale breaking effects at the closed string $1$-loop and non-perturbative D-instanton level. These observations allow us to present rigorous expressions for the $F$-term scalar potential applicable to arbitrary numbers of moduli in type IIB Calabi-Yau orientifold compactifications. Finally, we compute the Hessian for odd moduli and discuss potential phenomenological implications.
TL;DR: In this paper, the authors examined the combined effects of string and f ( R ) gravity corrections on the inflationary dynamics of canonical scalar field inflation, imposing the constraint that the speed of the primordial gravitational waves is equal to that of light's.
TL;DR: In this article, the generalized Klein-Gordon oscillator under the Lorentz symmetry breaking effects was investigated and its behavior was analyzed in the presence of a Cornell-type scalar potential and the solution of the bound state was obtained.
Abstract: We investigate the generalized Klein-Gordon oscillator under the Lorentz symmetry breaking effects where, a linear electric and constant magnetic field is considered and analyze its effects on the relativistic quantum oscillator. Furthermore, the behavior of the quantum oscillator in the presence of a Cornell-type scalar potential is analyzed and the solution of the bound state is obtained. We see that the analytical solution to the generalized Klein-Gordon oscillator can be achieved and the angular frequency of the oscillator depends on the quantum numbers of the system
TL;DR: A Darwin field model is presented, which results in a two-step algorithm, where the discrete representations of the electric scalar potential and the magnetic vector potential are computed consecutively.
Abstract: In the absence of wave propagation, transient electromagnetic fields are governed by a composite scalar/vector potential formulation for the quasi-static Darwin field model Darwin-type field models are capable of capturing inductive, resistive, and capacitive effects To avoid possibly non-symmetric and ill-conditioned fully discrete monolithic formulations, here, a Darwin field model is presented, which results in a two-step algorithm, where the discrete representations of the electric scalar potential and the magnetic vector potential are computed consecutively Numerical simulations show the validity of the presented approach
TL;DR: In this paper, the convergence analysis of the fixed-point method (FPM) to model the nonlinear magnetic characteristics of a 2D magnetostatic problem is presented, and the relative errors between two successive iterations are calculated using different error estimators: the attraction force on the mover, the Fourier coefficients defined in the air gap, the magnetic flux density and the magnetic scalar potential distributions.
Abstract: This article presents the convergence analysis of the fixed-point method (FPM) to model the nonlinear magnetic characteristics of a 2-D magnetostatic problem. In this study, FPM is used as the iterative nonlinear solver of the hybrid analytical modeling (HAM) technique for the accurate computation of the magnetic field distribution. The benchmark consists of a stator with excitation windings, an air gap, and a slotless mover. The relative errors between two successive iterations are calculated using different error estimators: the attraction force on the mover, the Fourier coefficients defined in the air gap, the magnetic flux density, and the magnetic scalar potential distributions. The effect of the number of mesh elements and harmonics on the accuracy and computational cost of the model is investigated for different levels of magnetic saturation. It is observed that the maximum rate of change in the relative difference of attraction force during the iterations is found to be 0.52 under the magnetic saturation. In addition, the absolute error of the attraction force between the developed hybrid model with FPM and the finite element method (FEM) is achieved to be 0.18%, while HAM has approximately three times less number of degrees-of-freedom when compared to FEM.