Real Scalar Field Research Articles

On generalized theories of varying fine structure constant

ABSTRACT We work with a class of scalar extended theory of gravity that can drive the present cosmic acceleration as well as accommodate a mild cosmic variation of the fine structure constant α. The motivation comes from a vintage theory developed by Bekenstein, Sandvik, Barrow, and Magueijo. The α variation is introduced by a real scalar field interacting with charged matter. We execute a cosmological reconstruction based on a parametrization of the present matter density of the Universe. Observational consistency is ensured by comparing the theoretical estimates with JLA + OHD + BAO data sets, using a Markov chain Monte Carlo simulation. An analysis of molecular absorption lines from HIRES and UVES spectrographs is considered as a reference for the variation of α at different redshifts. Two examples are discussed. The first explores a field-dependent kinetic coupling of the scalar field interacting with charged matter. The second example is a generalized Brans–Dicke formalism where the varying α is fitted as an effective matter field. This generates a simultaneous variation of the Newtonian constant G and α. The pattern of this variation may have a crucial role in cosmic expansion history.

New class of solutions in the non-minimal O(3)-sigma model

For the study of topological vortices with non-minimal coupling, we built a kind of non-canonical O(3)-sigma model, with a Maxwell term modified by a dielectric function. Through the BPS formalism an investigation is made on possible configurations of vortices in topological sectors of the sigma model and the real scalar field. For a particular ansatz, the solutions of the topological sector of the real scalar field are described by the known kink solutions. On the other hand, when studying the vortices in non-minimal sector of the pure O(3)-sigma model, it is detected the emergence of solutions that generate solitary waves similar to structures derived from a KdV-like theory. We observed that in the study of mixed models, namely, the topological sector of the O(3)-sigma model coupled to the topological sector of the real scalar field, the vortex solutions assume a profile of a step function. Then, when kinks of the topological sector of the scalar field are interacting with the field of the sigma model, it makes the field solutions of the O(3)-sigma model become extremely localized, making the vortice structures non-physical.

Vacuum decay in quadratic gravity

Metastable states decay at zero temperature through quantum tunnelling at an exponentially small rate, which depends on the Coleman–de Luccia instanton, also known as bounce. In some theories, the bounce may not exist or its on-shell action may be ill-defined or infinite, thus hindering the vacuum decay process. In this paper, we test this possibility in modified theories of gravity interacting with a real scalar field. We consider an Einstein–Hilbert term with a non-minimally coupled scalar field and a quadratic Ricci scalar contribution. To tackle the problem, we use a new analytic method, with which we prove that the scalar field on the bounce has a universal behaviour at large Euclidean radii, almost independently of the potential. Our main result is that the quadratic Ricci scalar prevents the decay, regardless of the other terms in the action.

Electroweak phase transition and gravitational waves in a two-component dark matter model

We investigate an extension of the Standard Model (SM) with two candidates for dark matter (DM). One of them is a real scalar field and the other is an Abelian gauge field. Except for these two, there is another beyond SM field which has unit charge under a dark UD(1) gauge symmetry. The model is classically scale invariant and the electroweak symmetry breaks because of the loop effects. Although SM is extended with a new dark symmetry and three fields, because of scale invariance, the parameter space is strictly restricted compared to other two-component DM models. We study both DM phenomenology and electroweak phase transition and show that there are some points in the parameter space of the model consistent with DM relic density and direct detection constraints, while at the same time can lead to first order electroweak phase transition. The gravitational waves produced during the phase transition could be probed by future space-based interferometers such as Laser Interferometer Space Antenna (LISA) and Big Bang Observer (BBO).

Impact of compactlike and asymmetric configurations of thick branes on the scalar\u2013tensor representation of fleft( R,Tright) gravity

In this work we study braneworld models in generalized fleft( R,Tright) gravity theories where the action depends on a function of the Ricci scalar R and the trace of the stress–energy tensor T. We explore the so-called scalar–tensor representation of the theory, where the dependence on R and T are exchanged for two auxiliary real scalar fields. We introduce a first-order formalism to relate the auxiliary fields with the source field of brane and analyze four distinct possibilities of current interest regarding compactification and asymmetry of the brane. We investigate the behavior of the auxiliary fields and their stability in each one of the four cases. For the models where the solution of the source field engenders compact behavior, the auxiliary fields exhibit a hybrid structure, behaving differently inside and outside the compact region described by the source configuration. In particular, we found that the solutions of the auxiliary fields are significantly modified in models where the geometry is strongly influenced by the source field. Moreover, for the model capable of engendering asymmetric features, the two auxiliary fields also respond to modifications on the parameter that controls the asymmetry of the system.

Black Hole and Wormhole Solutions in Einstein–Maxwell Scalar Theory

We classified and studied the charged black hole and wormhole solutions in the Einstein–Maxwell system in the presence of a massless, real scalar field. The possible existence of charged black holes in general scalar–tensor theories was studied in Bronnikov et al., 1999; black holes and wormholes exist for a negative kinetic term for the scalar field. Using a conformal transformation, the static, spherically symmetric possible structures in the minimal coupled system are described. Besides wormholes and naked singularities, only a restricted class of black hole exists, exhibiting a horizon with an infinite surface and a timelike central singularity. The black holes and wormholes defined in the Einstein frame have some specificities with respect to the non-minimal coupling original frame, which are discussed in the text.

2+1 Einstein–Klein–Gordon Black Holes by Gravitational Decoupling

In this work we study the 2+1-Einstein–Klein–Gordon system in the framework of Gravitational Decoupling. We associate the generic matter decoupling sector with a real scalar field so we can obtain a constraint which allows us to close the system of differential equations. The constraint corresponds to a differential equation involving the decoupling functions and the metric of the seed sector and will be independent of the scalar field itself. We show that when the equation admits analytical solutions, the scalar field and the self-interacting potential can be obtained straightforwardly. We found that, in the cases under consideration, it is possible to express the potential as an explicit function of the scalar field only for certain particular cases corresponding to limiting values of the parameters involved.

Motion induced excitation and radiation from an atom facing a mirror

We study quantum dissipative effects due to the nonrelativistic, bounded, accelerated motion of a single neutral atom in the presence of a planar perfect mirror, i.e., a perfect conductor at all frequencies. We consider a simplified model whereby a moving ``scalar atom'' is coupled to a quantum real scalar field, subjected to either Dirichlet or Neumann boundary conditions on the plane. We use an expansion in powers of the departure of the atom with respect to a static average position to compute the vacuum persistence amplitude and the resulting vacuum decay probability. We evaluate transition amplitudes corresponding to the excitation of the atom plus the emission of a particle, and show explicitly that the vacuum decay probabilities match the results obtained by integrating the transition amplitudes over the directions of the emitted particle. We also compute the spontaneous emission rate of an oscillating atom that is initially in an excited state.

Timescape: A Novel Spatiotemporal Modeling Tool

We developed a novel approach in the field of spatiotemporal modeling, based on the spatialisation of time, the Timescape algorithm. It is especially aimed at sparsely distributed datasets in ecological research, whose spatial and temporal variability is strongly entangled. The algorithm is based on the definition of a spatiotemporal distance that incorporates a causality constraint and that is capable of accommodating the seasonal behavior of the modeled variable as well. The actual modeling is conducted exploiting any established spatial interpolation technique, substituting the ordinary spatial distance with our Timescape distance, thus sorting, from the same input set of observations, those causally related to each estimated value at a given site and time. The notion of causality is expressed topologically and it has to be tuned for each particular case. The Timescape algorithm originates from the field of stable isotopes spatial modeling (isoscapes), but in principle it can be used to model any real scalar random field distribution.

Mechanism for baryogenesis via feebly interacting massive particles

We present a simple mechanism which allows the simultaneous generation of the baryon asymmetry of the Universe along with its dark matter content. To this goal, we employ the out-of-equilibrium decays of heavy bath states into a feebly coupled dark matter particle and Standard Model charged fermions. These decays lead to dark matter production via the freeze-in mechanism and, assuming that they further violate $CP$, can generate a viable matter-antimatter asymmetry in the resonant regime. We illustrate this mechanism by studying a particular realization of this general scenario, where the role of the heavy bath particles is played by $SU(3)_{\text{c}}\times SU(2)_{\text{L}}$-singlet vectorlike fermions with a non-zero hypercharge and dark matter is identified with a gauge-singlet real scalar field. We show that in the context of this simple model the cosmological constraints for the dark matter abundance and the baryon asymmetry are satisfied for masses of heavy vectorlike fermion states of a few TeV, potentially within reach of the High-Luminosity Run of the Large Hadron Collider. Dark matter, in turn, is predicted to be rather light, with a mass of a few keV.

The Electro-Weak Phase Transition at Colliders: Discovery Post-Mortem

We explore the capabilities of a future proton collider to probe the nature of the electro-weak phase transition, following the hypothetical discovery of a new scalar particle. We focus on the real singlet scalar field extension of the Standard Model, representing the most minimal, and challenging to probe, framework that can enable a strong first-order electro-weak phase transition. By constructing detailed phenomenological methods for measuring the mass and accessible couplings of the new scalar particle, we find that a 100 TeV proton collider has the potential to explore the parameter space of the real singlet model and provide meaningful constraints on the electro-weak phase transition. We empirically find some necessary conditions for the realization of a strong first order electroweak phase transition and conjecture that additional information, including through multi-scalar processes and gravitational wave detectors, are likely needed to gauge the nature of the cosmological electro-weak transition. This study represents the first crucial step towards solving the inverse problem in the context of the electro-weak phase transition.

From Feynman graphs to Witten diagrams

We investigate the possibility of generalizing Gopakumar’s microscopic derivation of Witten diagrams in large N free quantum field theory [1] to interacting theories. For simplicity we consider a massless, matrix valued real scalar field with Φh interaction in d-dimensions. Using Schwinger’s proper time formulation and organizing the sum over Feynman graphs by the number of loops l, we show that the two-point function can be expressed as a sum over boundary-to-boundary propagators of bulk scalars in AdS d+1 with mass determined by l.This manuscript is intended as a contribution to the festschrift of prof. Tekin Dereli’s on the occasion of his 72nd birthday.1

A Real Scalar Field Unifying the Early Inflation and the Late Accelerating Expansion of the Universe through a Quadratic Equation of State: The Vacuumon

In a previous paper we introduced a cosmological model describing the early inflation, the intermediate decelerated expansion, and the late accelerating expansion of the universe in terms of a single barotropic fluid characterized by a quadratic equation of state. We obtained a scalar field representation of this fluid and determined the potential V(ϕ) connecting the inflaton potential in the early universe to the quintessence potential in the late universe. This scalar field has later been called the ‘vacuumon’ by other authors, in the context of the Running Vacuum model. In this paper, we study how the scalar field potential is modified by the presence of other cosmic components such as stiff matter, black-body radiation, baryonic matter, and dark matter. We also determine the mass m and the self-interaction constant λ of the scalar field given by the second and fourth derivatives of the potential at its extrema. We find that its mass is imaginary in the early universe with a modulus of the order of the Planck mass MP=(ℏc/G)1/2=1.22×1019GeV/c2 and real in the late universe with a value of the order of the cosmon mass mΛ=(Λℏ2/c4)1/2=2.08×10−33eV/c2 predicted by string theory. Although our model is able to describe the evolution of the homogeneous background for all times, it cannot account for the spectrum of fluctuations in the early universe. Indeed, by applying the Hamilton–Jacobi formalism to our model of early inflation, we find that the Hubble hierarchy parameters and the spectral indices lead to severe discrepancies with the observations. This suggests that the vacuumon potential is just an effective classical potential that cannot be directly used to compute the fluctuations in the early universe. A fully quantum field theory may be required to achieve that goal. Finally, we discuss the connection between our model based on a quadratic equation of state and the Running Vacuum model which assumes a variation of the cosmological constant with the Hubble parameter.

BPS equations and solutions for Maxwell–scalar theory

Energy minimizing BPS equations and solutions are obtained for a class of models in Maxwell–scalar theory, where an abelian electric charge is immersed in an effective dielectric of a real scalar field. The first order BPS equations are developed using the straightforward “on-shell method” introduced by Atmaja and Ramadhan. Employment of an auxiliary function of the scalar field allows a scalar potential that displays a tachyonic instability. Consequently, a nontopological scalar soliton is found to form around the charge. Examples and solutions are provided for (1) a point charge or sphere in a flat Minkowski background, and (2) an “overcharged” compact object in a Reissner–Nordstrom background. The solutions presented here for the former (Minkowski) case recover those that have been previously obtained, while the latter solutions are new BPS solutions.

Supersymmetric inhomogeneous field theories in 1+1 dimensions

We study supersymmetric inhomogeneous field theories in 1+1 dimensions which have explicit coordinate dependence. Although translation symmetry is broken, part of supersymmetries can be maintained. In this paper, we consider the simplest inhomogeneous theories with one real scalar field, which possess an unbroken supersymmetry. The energy is bounded from below by the topological charge which is not necessarily nonnegative definite. The bound is saturated if the first-order Bogomolny equation is satisfied. Non-constant static supersymmetric solutions above the vacuum involve in general a zero mode although the system lacks translation invariance. We consider two inhomogeneous theories obtained by deforming supersymmetric sine-Gordon theory and ϕ6 theory. They are deformed either by overall inhomogeneous rescaling of the superpotential or by inhomogeneous deformation of the vacuum expectation value. We construct explicitly the most general supersymmetric solutions and obtain the BPS energy spectrum for arbitrary position-dependent deformations. Nature of the solutions and their energies depend only on the boundary values of the inhomogeneous functions. The vacuum of minimum energy is not necessarily a constant configuration. In some cases, we find a one-parameter family of degenerate solutions which include a non-vacuum constant solution as a special case.

Vector dark matter production from catalyzed annihilation

We provide a simple model of vector dark matter (DM) which can realize the recently proposed freeze-out mechanism with catalyzed annihilation. In our setup, a vector DM field Xμ and a catalyst field Cμ is unified by an SU(2)D gauge symmetry. These gauge fields acquire their masses via spontaneously symmetry breaking triggered by a doublet and a real triplet scalar fields. The catalyst particle is automatically lighter than the DM since it only acquires mass from the vacuum expectation value of the doublet scalar. We also introduce a dimension-5 operator to generate a kinetic mixing term between Cμ and the U(1)Y gauge field Bμ. This mixing term is naturally small due to a suppression with a high UV completion scale, and thus it allows the catalyst to decay after the DM freeze-out. We derive the annihilation cross sections of processes X* + X → 2C and 3C → X* + X and solve the Boltzmann equations for both the DM and the catalyst. We develop the analytical approximate solutions of the equations and find them matching the numerical solutions well. Constraints from relic abundance and indirect detection of DM are considered. We find that the DM with a mass mX ≳ 4.5 TeV survives in the case of a long-living catalyst. On the other hand, if the catalyst decays during the catalyzed annihilation era, then the bound can be released. We also discuss two paradigms which can maintain the kinetic equilibrium of DM until the DM freeze-out. In both cases, the freeze-out temperature of DM is an order of magnitude higher than the original model.

Inflation and dark matter after spontaneous Planck scale generation by hidden chiral symmetry breaking

Dynamical chiral symmetry breaking in a QCD-like hidden sector is used to generate the Planck mass and the electroweak scale including the heavy right-handed neutrino mass. A real scalar field transmits the energy scale of the hidden sector to the visible sectors, playing besides a role of inflaton in the early Universe while realizing a Higgs-inflation-like model. Our dark matter candidates are hidden pions that raise due to dynamical chiral symmetry breaking. They are produced from the decay of inflaton. Unfortunately, it will be impossible to directly detect them, because they are super heavy (109 ∼ 12 GeV), and moreover the interaction with the visible sector is extremely suppressed.

Maxwell-scalar device based on the electric dipole

In this work we study the electric field of a dipole immersed in a medium with permittivity controlled by a real scalar field which is non-minimally coupled to the Maxwell field. We model the system with an interesting function, which allows the presence of exact solutions, describing the possibility of the permittivity to encapsulate the charges at very high values, giving rise to an effect that is not present in the standard situation. The results are of direct interest to applications for emission and absorption of radiation, and may motivate new studies concerning binary stars and black holes in gravity scenarios of current interest.

Scalar-tensor theories within Asymptotic Safety

Asymptotic Safety provides an elegant mechanism for obtaining a consistent high-energy completion of gravity and gravity-matter systems. Following the initial idea by Steven Weinberg, the construction builds on an interacting fixed point of the theories renormalization group (RG) flow. In this work we use the Wetterich equation for the effective average action to investigate the RG flow of gravity supplemented by a real scalar field. We give a non-perturbative proof that the subspace of interactions respecting the global shift-symmetry of the scalar kinetic term is closed under RG transformations. Subsequently, we compute the beta functions in an approximation comprising the Einstein-Hilbert action supplemented by the shift-symmetric quartic scalar self-interaction and the two lowest order shift-symmetric interactions coupling scalar-bilinears to the spacetime curvature. The computation utilizes the background field method with an arbitrary background, demonstrating that the results are manifestly background independent. Our beta functions exhibit an interacting fixed point suitable for Asymptotic Safety, where all matter interactions are non-vanishing. The presence of this fixed point is rooted in the interplay of the matter couplings which our work tracks for the first time. The relation of our findings with previous results in the literature is discussed in detail and we conclude with a brief outlook on potential phenomenological applications.

Asymptotic nonlocality in gauge theories

Asymptotically nonlocal field theories represent a sequence of higher-derivative theories whose limit point is a ghost-free, infinite-derivative theory. Here we extend this framework, developed previously in a theory of real scalar fields, to gauge theories. We focus primarily on asymptotically nonlocal scalar electrodynamics, first identifying equivalent gauge-invariant formulations of the Lagrangian, one with higher-derivative terms and the other with auxiliary fields instead. We then study mass renormalization of the complex scalar field in each formulation, showing that an emergent nonlocal scale (i.e., one that does not appear as a fundamental parameter in the Lagrangian of the finite-derivative theories) regulates loop integrals as the limiting theory is approached, so that quadratic divergences can be hierarchically smaller than the lightest Lee-Wick partner. We conclude by making preliminary remarks on the generalization of our approach to non-Abelian theories, including an asymptotically nonlocal standard model.