Self-interaction Potential Research Articles

Stabilization of spherically symmetric static Boson stars by Coleman-Weinberg self-interaction potential

Our motivation in this work is due to the great importance of relativistic boson stars as fierce competitors of black holes. From theoretical perspective, they described by complex Klein Gordon (KG) scalar fields interacting with curved background in general form. In this work we use the Einstein-Klein Gordon (EKG) scalar tensor gravity in presence of the Coleman-Weinberg (CW) self-interaction potential to study formation of a spherically symmetric boson star and situation of its stability. We choose the CW potential because of its important role in description of cosmic inflation.

A cosmological reconstruction of the Higgs vacuum expectation value

We present a simple toy model of cosmic acceleration driven purely by a self-interacting scalar field embedded in theory of grand unification. The scalar self-interaction is Higgs-like and provokes a spontaneous symmetry breaking. The coefficient of the quadratic term in the self-interaction potential has an evolution and it leads to a cosmic variation of proton-to-electron mass ratio, μ. We perform a cosmological reconstruction from the kinematic parameter jerk and discuss a few cosmological consequences of the theory. We also compare the theoretically calculated μ variation with the observations of molecular absorption spectra from Cesium Atomic Clock data.

On the stability of electrovacuum space-times in scalar–tensor gravity

We study the behavior of static, spherically symmetric solutions to the field equations of scalar–tensor theories (STT) of gravity belonging to the Bergmann–Wagoner–Nordtvedt class, in the presence of an electric and/or magnetic charge. This class of theories includes the Brans–Dicke, Barker and Schwinger STT as well as nonminimally coupled scalar fields with an arbitrary parameter ξ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\xi $$\\end{document}. The study is restricted to canonical (nonphantom) versions of the theories and scalar fields without a self-interaction potential. Only radial (monopole) perturbations are considered as the most likely ones to cause an instability. The static background solutions contain naked singularities, but we formulate the boundary conditions in such a way that would preserve their meaning if a singularity is smoothed, for example, due to quantum gravity effects. These boundary conditions look more physical than those used by other authors. Since the solutions of all STT under study are related by conformal transformations, the stability problem for all of them reduces to the same wave equation, but the boundary conditions for perturbations (and sometimes the boundaries themselves) are different in different STT, which affects the stability results. The stability or instability conclusions are obtained for different branches of solutions in the theories under consideration and are presented in a table form.

Quantified asymptotic analysis for the relativistic quantum mechanical system with electromagnetic fields

We study the asymptotic analysis of a relativistic quantum mechanical system interacting with self-consistent electromagnetic fields, with a specific focus on the Maxwell–Klein–Gordon (MKG) system. Firstly, we show that the MKG system is globally well-posed under the Coulomb gauge condition, even in the presence of self-interacting potential. Furthermore, to derive the asymptotic analysis, we consider the non-relativistic and semi-classical regime simultaneously, introducing a single scaling parameter that serves to parameterize both the speed of light and the Planck constant. As the scaling parameter approaches zero, we obtain rigorous and quantified estimates on the asymptotic convergence of the electrostatic MKG system toward the classical Euler–Poisson system. Our analytical framework relies on the modulated energy estimate.

Study on Anisotropic Dark Energy Cosmological Models in Generalized Brans-Dicke Theory

In this present paper, we have investigated the dark energy cosmological model in Bianchi−V I0 spacetime by considering generalised Brans-Dicke theory, self-interacting potential, and a dynamical coupling parameter. For this purpose, we have utilised a hybrid scale factor to approximate the dynamical behaviour of the deceleration parameter. The deceleration parameter should display distinctive flipping behaviour at the transition redshift since the universe is thought to have changed from an early deceleration to a late temporal acceleration. We have studied six alternative transitioning dark energy models on the basis of observational restrictions on the transition redshift. For each model, the behaviour of the dynamical scalarfield, the Brans-Dicke parameter, and the self-interacting potential are examined. On top of that, we used the generalised Brans-Dicke theory to estimate how the Newtonian gravitational constant changes over time.

Quantum Big-Bounce as a phenomenology of RQM in the Mini-superspace

We investigate the emergence of a quantum Big-Bounce in the context of an isotropic Universe, filled by a self-interacting scalar field, which plays the role of a physical clock. The bouncing cosmology is the result of a scattering process, driven by the scalar field potential, which presence breaks down the frequency separation of the Wheeler-DeWitt equation, treated in strict analogy to a relativistic quantum system. Differently from previous analyses, we consider a really perturbative self-interaction potential, affecting the dynamics in a finite range of the time labeled by the scalar clock (and in particular we remove the divergent character previously allowed). The main result of the present analysis is that, when the Relativistic Quantum Mechanics formalism is properly implemented in the Mini-superspace analogy, the probability amplitude for the bounce is, both in the standard and polymerized case, characterized by a maximum in correspondence of the quasi-classical condition of a Universe minimum volume.

Generalized Brans-Dicke cosmology, noether symmetries and quantization

A generalized Brans-Dicke theory of gravitation is applied to investigate a cosmological model for a primordial universe that includes a self-interacting bosonic field as source. This model permits, initially, to consider an arbitrary ω function, not usual for BD formulations. The imposition of Noether symmetries conditions identifies a reduced space for the ω function. This model is shown to present a variety of behaviors consistent with a primordial era, depending on the parameters chosen. We find that the bosonic field is capable of promoting a transition from an initially accelerated to a decelerated regime. The self-interaction potential is also restricted by the Noether conditions, and can be interpreted as a vacuum energy contribution. The model also permits a quantization process, going through a hamiltonian formulation and recognizing the presence of cyclic variables. The Bohm approach shows as result a consistent model with a smooth classical limit as the Universe leaves the Planck era.

Self-interacting scalar field in (2+1) dimensions Einstein gravity with torsion

We study a massless real self-interacting scalar field φ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varphi $$\\end{document} non-minimally coupled to Einstein gravity with torsion in (2+1) space-time dimensions in the presence of a cosmological constant. The field equations with a self-interaction potential V(φ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V(\\varphi )$$\\end{document} including φn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varphi ^{n}$$\\end{document} terms are derived by a variational principle. By numerically solving these field equations with the 4th Runge–Kutta method, the circularly symmetric rotating solutions for (2+1) dimensions Einstein gravity with torsion are obtained. Exact analytical solutions to the field equations are derived for the proposed metric in the absence of both torsion and angular momentum. We find that the self-interacting potential only exists for n=6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n=6$$\\end{document}, as requested by conformal symmetry. We also study the motion of massive and massless particles in (2+1) Einstein gravity with torsion coupled to a self-interacting scalar field. The effect of torsion on the behavior of the effective potentials of the particles is analyzed numerically.

Unfolded dynamics approach and quantum field theory

We study quantization of a self-interacting scalar field within the unfolded dynamics approach. To this end we find and analyze a classical unfolded system describing 4d off-shell scalar field with a general self-interaction potential. Then we systematically construct three different but related unfolded formulations of the corresponding quantum field theory, supporting them with illustrative calculations: an unfolded functional Schwinger-Dyson system, an unfolded system for correlation functions and an unfolded effective system for vertex functions. The most curious feature we reveal is that an unfolded quantum commutator gets naturally regularized: a standard delta-function is replaced with a heat kernel, parameterized by the unfolded proper time. We also identify an auxiliary 5d system, having this proper time as a physical time, which generates 4d scalar action as its on-shell action.

Gravitational collapse of Bose-Einstein condensate dark matter halos with logarithmic nonlinearity

"If dark matter is composed of massive bosons, a Bose-Einstein Condensation process must have occurred during the cosmological evolution. Therefore galactic dark matter may be in a form of a condensate, characterized by a strong self-interaction. One of the interesting forms of the self-interaction potential of the condensate dark matter is the logarithmic form. In the present work we investigate one of the astrophysical implications of the condensate dark matter with logarithmic self-interaction, namely, its gravitational collapse. To describe the condensate dark matter we use the Gross-Pitaevskii equation, and the Thomas-Fermi approximation. By using the hydrodynamic representation of the Gross-Pitaevskii equation we obtain the equation of state of the condensate, which has the form of the ideal gas equation of state, with the pressure proportional to the dark matter density. In the Thomas-Fermi approximation, the evolution equations of the condensate reduce to the classical continuity, and Euler equations of fluid dynamics. We obtain the equations of motion of the condensate radius in spherical symmetry, by assuming certain particular forms for the velocity and density of the condensate. The collapse time required for the formation of a stable macroscopic astrophysical object is obtained in an integral form, and explicit numerical estimations for the formation of astrophysical objects with masses ranging from 106M⊙ to 1012M⊙ are presented."

Thermodynamics of higher-dimensional Brans-Dicke black holes in the presence of a conformal-invariant field inspired by power-Maxwell electrodynamics

Abstract By use of the conformal transformations, in addition to translating the Brans-Dicke (BD) action to the Einstein frame (EF), we introduce an electromagnetic Lagrangian which preserves conformal invariance. We solve the EF field equations, which mathematically are confronted with the problem of indeterminacy, by use of an exponential ansatz function. When the self-interacting potential is absent or is taken constant in the BD action, the exact solution of this theory is just that of Einstein-conformal-invariant theory with a trivial scalar field. This is higher-dimensional (HD) analogues of the same considered in [1]. The EF general solution admits two classes of black holes (BHs) with non-flat and non-AdS asymptotic behavior which can produce extreme and multi-horizon ones. We obtain the exact solutions of BD-conformal-invariant theory, by applying inverse conformal transformations, which show two classes of extreme and multi-horizon BHs too. Based on the fact that thermodynamic quantities remain unchanged under conformal transformations, we show that the first law of BH thermodynamics is valid in the Jordan frame (JF). We analyze thermal stability of the HD BD-conformal-invariant BHs by use of the canonical ensemble method.

Quantum master equation for the vacuum decay dynamics

The quantum master equation required to describe the dynamics of gravity-related vacuum decay is still challenging. We aim to study this issue. Our model consists of the spacetime and scalar field with self-interaction potential. The environment is chosen as spacetime while the system is formed by the vacua of the scalar field. We demonstrate that the quantum dynamics of the vacua can be described by the Redfield equation, which can depict the evolution of both coherence and the comoving volume fraction of the vacuum. Under the Markovian limit, coherence monotonically decreases with time, leading to the initial quantum state to decohere into a classical state. This helps the understanding of the decoherence of the universe. We also highlight that in certain circumstances, the evolution of the vacuum system may display non-Markovian dynamics. In specific scenarios, the classical limit of the quantum master equation is consistent with the classical master equation. In the steady state, the dominant vacuum corresponds to the smallest cosmological constant, and various dS vacua can reach equilibrium states.

Study of Yang–Mills condensate dark energy in the framework of generalized Brans–Dicke theory

The prediction about the accelerating expansion of the universe introduced the concept of dark energy. Since then, a plethora of work has been done to explain the origin and nature of dark energy. This work deals with the possibility of obtaining cosmic acceleration of a new kind of dark energy, viz., Yang–Mills condensate dark energy in generalized Brans–Dicke theory with variable or constant [Formula: see text] (Brans–Dicke parameter) and vanishing and non-vanishing self-interacting potential. We assume the scale factor and scalar field in power law form. Then we investigate the above model to determine whether the universe is accelerating. We obtain a redshift-dependent equation of state parameter, which describes the phase transition of the universe. We notice that the equation of the state parameter meets the [Formula: see text] cold dark matter (CDM) limit in the far future. Then we study the [Formula: see text] analysis to get the thawing or freezing region. We study the stability of the model by studying the square speed of sound. Last, the nature of the scalar field and the potential are analyzed for four cases.

Chains of mini-boson stars

In this paper, we re-investigate the static, soliton-like solutions in the model of the Einstein gravity coupled to a free and complex scalar field, which have been known as mini-boson stars. With the numerical methods, we have discovered a new family of solutions in addition to the typical single mini-boson star solution. These solutions can be interpreted as chains of boson stars, consisting of multiple boson stars along the symmetry axis. We demonstrate the configuration of two types of chains, one with an even number of constituents and the other with an odd number of constituents. Furthermore, we also study the effect of the frequency of the complex scalar field on the ADM mass M and the U(1) scalar charge Q. It is noteworthy that the existence of chains of boson stars does not require the introduction of a complex scalar field with self-interacting potential.

One-loop radiative corrections in bumblebee-Stueckelberg model

This work aims to study the radiative corrections in a vector model with spontaneous Lorentz symmetry violation, known in the literature as the bumblebee model. We consider such a model with self-interaction quadratic smooth potential responsible for spontaneous Lorentz symmetry breaking. The spectrum of this model displays a transversal nonmassive mode, identified as Nambu-Goldstone, and a massive longitudinal mode. Besides the Lorentz symmetry, this model also exhibits gauge symmetry violation. To restore the gauge symmetry, we introduce the Stueckelberg field and calculate the two-point function by employing the principal-value (PV) prescription. The result is nontransversal, leading to a massive excited mode.

Covariant formalism and Noether symmetries on scalar-field cosmologies

In this work, we investigate a cosmological model in the context of the covariant formalism proposed by Canuto et al. where the notion of atomic and gravitational units is invoked. We consider a minimally coupled scalar field as gravitational source, including a self-interacting potential. It is possible to determine the symmetries associated to the correspondent field theory using the Noether procedure, through the Lie derivative construction. This permits to determine the scale function [Formula: see text], present in the covariant formalism, that maps the physics between descriptions in atomic and gravitational units. In gravitational units it is verified that the Klein–Gordon field behaves as a dark constituent. On the other hand, in atomic units what emerges is an initially accelerated universe, with a later incursion into a decelerated one, mirroring the usual matter/radiation age.

Rip behaviour in Brans–Dicke theory

In this work, we present little rip and pseudo rip scenarios in the framework of the generalised Brans–Dicke (GBD) theory where an evolving BD parameter along with a self-interacting potential is considered. The GBD field equations are derived for an anisotropic space time to provide a more general approach to the cosmic expansion. The evolutionary behaviour of the Brans–Dicke (BD) scalar field, dynamical Brans–Dicke parameter and the self interacting potential are studied. It is not possible to separate out the dynamical Brans–Dicke parameter into distinct evolving and non-evolving part for the rip scenarios as is obtained for constant deceleration parameter. While the little rip behaviour requires a positive value for the GBD parameter, a small negative value around −1.33 favours a pseudo rip behaviour.

Interacting quintessence cosmology from Noether symmetries: Comparing theoretical predictions with observational data

In the framework of scalar-tensor gravity, we consider non-flat interacting quintessence cosmology where a scalar field is interacting with dark matter. Such a scalar field can be a standard or a phantom one. We use the Noether Symmetry Approach to obtain general exact solutions for cosmological equations and to select scalar-field self-interaction potentials. It turns out that the found solutions can reproduce the accelerated expansion of the Universe, and are compatible with observational dataset, as the SNeIa Pantheon data, gamma ray bursts Hubble diagram, and direct measurements of the Hubble parameter.

An ab initio investigation of LiCoBO3 as Li-ion battery cathode material

We give a first principles approach for the structural, electronic and magnetic properties of LiCoBO3 and CoBO3 in the monoclinic lattices. Along [001] direction, based on density functional theory approach and using Full Potential Linear Augmented Plane Wave (FP-LAPW) method, Polarized spin and spin–orbit coupling are included in calculations, and major spin was set up. The calculations were carried out using generalized gradient approximation (GGA) + an on-site Coulomb self-interaction correction potential (GGA + U). The magnetic and orbital moments are estimated. The U value was considered to be equal to 6 eV for Co atom. The average equilibrium voltage over a full cycle, of the LiCoBO3 battery is estimated from our FP-LAPW calculations. The capacity of a cell and energy density of LiCoBO3 were calculated. The compound LiCoBO3 is a semiconductor with average intercalation voltage 4.01 V. The voltage difference help promote electrochemical performance, which opens a window for Li-ion battery marketing application.

Mass-varying dark matter from a phase transition

We propose a mass-varying dark matter (MVDM) model consisting of a scalar field and a fermionic field interacting via a simple Yukawa coupling, and containing an exponential self-interaction potential for the scalar field. Analyzing the evolution of this coupled scalar-fermion system in an expanding Universe, we find that it initially behaves like radiation but then undergoes a phase transition after which it behaves like pressureless dark matter. The one free parameter of this model is the temperature at which the phase transition occurs; the mass of the dark matter particle, given by the mass of the fermion, is derived from this. For a phase transition temperature between 10 MeV and $10^7$ GeV, the current dark matter relic density is achieved for a fermion mass in the range of 1 GeV to $10^9$ GeV. In this dark matter model, the scalar becomes a sub-dominant unclustered component of dark matter that can lower the amplitude of structure formation by up to a few percent. Another feature is that the mass-varying fermion component can lead to discrepant measurements of the current dark matter density of about ten percent inferred from early and late-time probes assuming LCDM.