Scalar Field Research Articles

Stress Tensor Bounds on Quantum Fields

The singular behaviour of quantum fields in Minkowski space can often be bounded by polynomials of the Hamiltonian H. These so-called H-bounds and related techniques allow us to handle pointwise quantum fields and their operator product expansions in a mathematically rigorous way. A drawback of this approach, however, is that the Hamiltonian is a global rather than a local operator and, moreover, it is not defined in generic curved spacetimes. In order to overcome this drawback we investigate the possibility of replacing H by a component of the stress tensor, essentially an energy density, to obtain analogous bounds. For definiteness we consider a massive, minimally coupled free Hermitean scalar field. Using novel results on distributions of positive type we show that in any globally hyperbolic Lorentzian manifold M for any f,F∈C0∞(M)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f,F\\in C_0^{\\infty }(M)$$\\end{document} with F≡1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$F\\equiv 1$$\\end{document} on supp(f)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{supp}(f)$$\\end{document} and any timelike smooth vector field tμ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$t^{\\mu }$$\\end{document} we can find constants c,C>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$c,C>0$$\\end{document} such that ω(ϕ(f)∗ϕ(f))≤C(ω(Tμνren(tμtνF2))+c)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega (\\phi (f)^*\\phi (f))\\le C(\\omega (T^{\ extrm{ren}}_{\\mu \ u }(t^{\\mu }t^{\ u }F^2))+c)$$\\end{document} for all (not necessarily quasi-free) Hadamard states ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega $$\\end{document}. This is essentially a new type of quantum energy inequality that entails a stress tensor bound on the smeared quantum field. In 1+1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1+1$$\\end{document} dimensions we also establish a bound on the pointwise quantum field, namely |ω(ϕ(x))|≤C(ω(Tμνren(tμtνF2))+c)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$|\\omega (\\phi (x))|\\le C(\\omega (T^{\ extrm{ren}}_{\\mu \ u }(t^{\\mu }t^{\ u }F^2))+c)$$\\end{document}, where F≡1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$F\\equiv 1$$\\end{document} near x.

Comment on “Source of black bounces in Rastall gravity”

In Atazadeh and Hadi (JCAP 01 (2024) 067), the authors proposed that black bounce solutions, such as the Simpson-Visser and the Bardeen-type spacetimes, can be obtained from Rastall gravity. To achieve these spacetimes, the authors consider the presence of a phantom scalar field with nonlinear electrodynamics. However, in this comment, we obtained different electromagnetic Lagrangians from the original work. The most problematic issue is not the incorrect expression of the electromagnetic Lagrangian itself. We show that the method obtains electromagnetic functions that are inconsistent. To obtain the black bounce spacetimes as solutions of Rastall gravity, it is necessary to consider an isotropic fluid, combined with the nonlinear electrodynamics and the phantom scalar field.

Dynamics and Stability via Thin‐Shell of Approximated Black Holes in f(Q)$f(\mathbb {Q})$ Gravity

AbstractThe current study is devoted to exploring the geometrical configuration of a thin‐shell in the background of symmetric teleparallel gravity. For this purpose, the well‐known cut‐and‐paste approach by matching the inner flat and outer newly calculated class of approximated black hole (BH) solutions in symmetric teleparallel gravity are considered, i.e., uncharged, charged, and anti‐de‐Sitter BHs. The dynamical analysis of thin‐shell configuration by adopting the massive and massless scalar field via Klein‐Gordon's equation of motion is discussed. The effective potential and proper time derivative of shell radius for both massive and massless scalar shells are used to discuss the collapse, expansion, and oscillatory behavior. The stable configuration of thin‐shell is observed through the linearized radial perturbation approach with a phantomlike equation of state, i.e., quintessence, dark energy, and phantom energy. It is noted that stable/unstable behavior of thin‐shell is found after the expected position of the event horizon of an exterior manifold. It is concluded that the stability of a thin‐shell is greater for BH with cosmological constant as compared to the uncharged and charged BHs.

Scaling solutions as Early Dark Energy resolutions to the Hubble tension

A wide class of scalar field models including Quintessence and K-essence have the attractive property of tracker regimes, where the energy density stored in the field evolves so as to mimic that of the dominant background component. During this evolution, for a brief period of time, there is an increase in the energy density of the field as it spirals in towards its attractor solution. We show that when the peak of this energy density occurs around the epoch of equality, we can address a key requirement of early dark energy (EDE), postulated as a solution to the Hubble tension. In particular we demonstrate how this can occur in a wide class of Quintessence, axion and K-essence models, before showing that the Quintessence models suffer in that they generally lead to sound speeds incompatible with the requirements of EDE, whereas the K-essence and axion models can do a better job of fitting the data.

Hunting WIMPs with LISA: correlating dark matter and gravitational wave signals

The thermal freeze-out mechanism in its classical form is tightly connected to physics beyond the Standard Model around the electroweak scale, which has been the target of enormous experimental efforts. In this work we study a dark matter model in which freeze-out is triggered by a strong first-order phase transition in a dark sector, and show that this phase transition must also happen close to the electroweak scale, i.e. in the temperature range relevant for gravitational wave searches with the LISA mission. Specifically, we consider the spontaneous breaking of a U(1)′ gauge symmetry through the vacuum expectation value of a scalar field, which generates the mass of a fermionic dark matter candidate that subsequently annihilates into dark Higgs and gauge bosons. In this set-up the peak frequency of the gravitational wave background is tightly correlated with the dark matter relic abundance, and imposing the observed value for the latter implies that the former must lie in the milli-Hertz range. A peculiar feature of our set-up is that the dark sector is not necessarily in thermal equilibrium with the Standard Model during the phase transition, and hence the temperatures of the two sectors evolve independently. Nevertheless, the requirement that the universe does not enter an extended period of matter domination after the phase transition, which would strongly dilute any gravitational wave signal, places a lower bound on the portal coupling that governs the entropy transfer between the two sectors. As a result, the predictions for the peak frequency of gravitational waves in the LISA band are robust, while the amplitude can change depending on the initial dark sector temperature.

Coupled quintessence scalar field model in light of observational datasets

We do a detailed analysis of a well-theoretically motivated interacting dark energy scalar field model with a time-varying interaction term. Using current cosmological datasets from CMB, BAO, Type Ia Supernova, H(z) measurements from cosmic chronometers, angular diameter measurements from Megamasers, growth measurements, and local SH0ES measurements, we found that dark energy component may act differently than a cosmological constant at early times. The observational data also does not disfavor a small interaction between dark energy and dark matter at late times.When using all these datasets in combination, our value of H 0 agrees well with SH0ES results but in 2.5σ tension with Planck results. We also did AIC and BIC analysis, and we found that the cosmological data prefer coupled quintessence model over ΛCDM, although the chi-square per number of degrees of freedom test prefers the latter.

Observational feasibility of 4D Einstein-Gauss-Bonnet cosmology: bouncing and non-bouncing universes

This paper analyzes the possibility of bouncing and non-bouncing universes in the framework of four-dimensional Einstein-Gauss-Bonnet (4D-EGB) gravity,corresponding respectively to negative and positive coupling constants λ of the Gauss-Bonnet term. We also use the Horndeski-type scalar-tensor theory to assess the role of a scalar charge C as a geometrical contribution to the radiation in the Universe.We modify the expansion history of the universe to allow for modifications induced by the 4D-EGB gravity.Using Planck measurements of the cosmic microwave background anisotropies as well as various datasets of baryonic acoustic oscillations, we set the upper bounds λ ≤ 10-16(km/s/Mpc)-2 and λ ≤ 10-30(km/s/Mpc)-2 for the non-bouncing and bouncing scenarios.The upper limit in the latter case is mainly driven by the requirement to conservatively respect the thermal history at energy scales of the standard model of particle physics.We also find that the contribution of the geometrical radiation-like term of the model cannot exceed 10% of the current radiation in the Universe. The possibility of an early inflationary phase produced by a single scalar field is also studied and found to be feasible in both bouncing and non-bouncing scenarios.This study shows the feasibility of a bouncing universe, even with a normal matter sector, in the 4D-EGB gravity. More theoretical investigation is required to further explore possible observational predictions of the model that can distinguish between general relativity and 4D-EGB gravity.

Spontaneous scalarization in Einstein–power–Maxwell–scalar models

We study the spontaneous scalarization of charged black holes in Einstein’s gravity minimally coupled to power–Maxwell electrodynamics which, in turn, is non–minimally coupled to a real scalar field. We point out the existence of a specific power for which the scalarized solution is well-behaved, and entropically preferred in comparison to the scalar-free charged black hole solution.

Effective action approach for preheating

We present a semiclassical non-perturbative approach for calculating the preheating process at the end of inflation. Our method involves integrating out the decayed particles within the path integral framework and subsequently determining world-line instanton solutions in the effective action. This enables us to obtain the effective action of the inflaton, with its imaginary part linked to the phenomenon of particle creation driven by coherent inflaton field oscillations. Additionally, we utilize the Bogoliubov transformation to investigate the evolution of particle density within the medium after multiple inflaton oscillations. We apply our approach to various final state particles, including scalar fields, tachyonic fields, and gauge fields. The non-perturbative approach provides analytical results for preheating that are in accord with previous methods.

Gravitational waves from inflaton decay and bremsstrahlung

The concept of early Universe inflation resolves several problems of hot Big Bang theory and quantitatively explains the origin of the inhomogeneities in the present Universe. However, it is not possible to arrange inflation in a scalar field model with renormalizable potential, such that it would not contradict the recent Planck data. For this reason, inflaton must have also higher derivative couplings suppressed at least by the Planck scale. We show that these couplings may be relevant during reheating and lead to non-negligible production of gravitons. We consider the possibility that the unitarity breaking scale for the model of inflation is lower than the Planck scale and compute production of gravitons during reheating, due to the inflaton decay to two gravitons and graviton bremsstrahlung process. The spectrum of produced gravitons is crucially dependent on reheating temperature and inflaton mass. We find that for low reheating temperature decay to gravitons lead to significant amount of dark radiation. Confronting this result with CMB constraints, we find reheating dependent bounds on the unitarity breaking scale. We also compare the obtained gravitational wave signals with the projected limits of future high frequency gravitational wave experiments.

Cosmological complexity of the modified dispersion relation

Complexity will be more and more essential in high-energy physics. It is naturally extended into the very early universe. Considering the universe as a quantum chaotic system, the curvature perturbation of the scalar field is identified with the two-mode squeezed state. By solving the Schrödinger equation, one can obtain the numerical solutions of the angle parameter and squeezing parameter. The solution of the squeezing parameter mainly determines the evolution of complexity. Our numeric indicates that the complexity of the modified dispersion relation will have a non-linear pattern after the horizon exits. Meanwhile, its corresponding Lyapunov index is also larger compared with the standard case. During the inflationary period, the complexity will irregularly oscillate and its scrambling time is also shorter compared with the standard case. Since the modified dispersion relation can be dubbed as the consequences of various frameworks of quantum gravity, it could be applicable to these frameworks. Finally, one can expect the framework of quantum gravity will lead to the fruitful evolution of complexity, which guides us in distinguishing various inflationary models.

Reconstruction of F(T,TG) gravity model with scalar fields

In this paper, we investigate the scalar field dark energy (DE) models within the context of [Formula: see text] gravity. Scalar field models are known for their dynamic nature. Parameters in the dynamical equation of state are responsible for the acceleration of the cosmos in recent epochs. We determined that the power-law cosmology fits the OHD and Pantheon data nicely. Using the Bayesian analysis and likelihood function in conjunction with the Markov Chain Monte Carlo (MCMC) method, we examine the three sets of the model parameters [Formula: see text] [Formula: see text] obtained by 57 points of the [Formula: see text] data, [Formula: see text] [Formula: see text] 1048 points of the Pantheon data and [Formula: see text] [Formula: see text] by using joint data ([Formula: see text]), respectively. We solved the modified Einstein’s field equations by taking the bulk-viscosity component [Formula: see text]. We also establish a correspondence between the [Formula: see text] gravity model and scalar field DE models such as quintessence, [Formula: see text]-essence, and DBI-essence. The nature of scalar fields and their corresponding potentials are being graphically analyzed. To check the validity of [Formula: see text] gravity model, we also analyze the behavior of energy conditions.

Modeling the deterioration of the stiffness and of the collagen fibril distribution in a discrete model of the cornea microstructure

We present a stochastic approach to model the mechanical deterioration of the reinforcing microstructure of the human cornea. The fundamental structural micro-components of the stroma, collagen and crosslinks, are assembled deterministically into an elementary trusswork cell, multiply repeated and distorted to form a three-dimensional shell with the shape of a cornea. The spatial orientation of the collagen-like elements of each cell is thus characterized stochastically with a non correlated random angle field, obeying an assigned probability density function, leading to a non-deterministic structural stiffness. It follows that the mechanical response of the model to the action of deterministic forces equivalent to the intraocular pressure is stochastic due to the random spatial orientation of collagen fibers. The deterioration of the mechanical stiffness of the collagen components is described through a scalar variable field, evolving in space and in time, representative of a progressive damage which causes heterogeneity and asymmetric behavior. The damage variable acts in two ways on the global stiffness: (i) by reducing the stiffness of the collagen components; (ii) by modifying the dispersion coefficient of the probability density function. The equilibrium equations of the damaging model are solved at discrete time steps, with a fully explicit solution scheme, by means of the stochastic finite element improved perturbation method. The results show that when the collagen fibril stiffness reduces to 10% of the healthy value, as expected in the case of the vision-impairing condition known as keratoconus, the displacement field due to intraocular pressure is significantly affected in terms of both average and variance distributions. This effect confers a typical conical shape to the cornea. In particular, the analysis shows that high values of the response variances are confined in the keratoconus area, which agrees with a high level of uncertainties due to loss of fibril organization and thickness reduction under pathologic conditions.

Multibranch Elastic Bound States in the Continuum.

Constructing a highly localized wave field by means of bound states in the continuum (BICs) promotes enhanced wave-matter interaction and offers approaches to high-sensitivity devices. Elastic waves can carry complex polarizations and thus differ from electromagnetic waves and other scalar mechanical waves in the formation of BICs, which is yet to be fully explored and exploited. Here, we report the investigation of local resonance modes supported by a Lamb waveguide side-branched with two pairs of resonant pillars and show the emergence of two groups of elastic BICs with different polarizations or symmetries. Particularly, the two groups of BICs exhibit distinct responses to external perturbations, based on which a label-free sensing scheme with enhanced-sensitivity is proposed. Our study reveals the rich properties of BICs arising from the complex wave dynamics in elastic media and demonstrates their unique functionality for sensing and detection.

Field theory in Rindler frame and more on the correspondence with thermal field theory formalisms

Considering two accelerated observers with same acceleration in two timelike wedges of Rindler frame we calculate the Feynman-like propagators for a real scalar field in a thermal bath with respect to the Minkowski vacuum. Only the same wedge correlators are symmetric under the exchange of the real thermal bath and Unruh thermal bath, while the cross-wedge ones are not. Interestingly, they contain a cross term which is a collective effects of acceleration and thermal nature of field. Particularly the zero temperature description along with no analytic continuation between coordinates in right and left Rindler wedges, as expected, corresponds to usual thermofield-double formalism. However, unlike in later formulation, the two fields are now parts of the original system. Moreover it bears the features of a spacial case of closed-time formalism (CTP) where the Keldysh contour is along the increasing Rindler time in the respective Rindler wedges. Interestingly, we observe a new feature that the analytic continuation between the wedges provides the two more spacial cases of CTP. Hence Rindler-frame-field theory seems to be a viable candidate to deal thermal theory of fields and may illuminate the search for a bridge between the usual existing formalisms.

Generalized Lagrangian for canonical and non-canonical scalar field

In this paper, we proposed a generalized Lagrangian for three different classes of scalar fields namely quintessence ([Formula: see text]), phantom ([Formula: see text]) and tachyonic ([Formula: see text]) parameterized by [Formula: see text]. These three scalar fields can be described by a common single Lagrangian called generalized scalar field Lagrangian (GSL). We obtain mathematically consistent forms of generalized equations of motion parameterized by [Formula: see text]. It can recover the individual equation of motion of quintessence, phantom and tachyon scalar fields from generalized equation of motion of the unified scalar field.

Scalar field perturbation around a rotating hairy black hole: quasinormal modes, quasibound states and superradiant instability

We consider the quasinormal modes, quasibound states and superradiant instability of a rotating hairy black hole, which possesses a Horndeski hair as deviation from Kerr black hole, under the perturbation of massive scalar field. With the use of the matrix method, we mainly calculate the eigenfrequencies related to those modes of the perturbation. Under the perturbation of the massless scalar field, the Horndeski hair and spin parameter have significant influences on the quasinormal frequency, but its imaginary part is always finite negative and no unstable mode is found. Under the perturbation of the massive scalar field, we focus on the eigenfrequencies of quasibound states and find the modes of which the imaginary part of eigenfrequencies is positive, indicating that the black hole undergoes superradiant instability. Then we scan the parameters and figure out a diagram in the space of Horndeski hair and spin parameters to distinguish the rotating hairy black hole with superradiant instability from the stable one.

Quazinormal modes and greybody factor of black hole surrounded by a quintessence in the S-V-T modified gravity as well as shadow

The purpose of this study is to investigate the quasinormal modes (QNMs), greybody factors (GFs) and shadows in a plasma of a black hole (BH) surrounded by an exotic fluid of quintessence type in a scalar-vector-tensor modified gravity. The effects of a quintessence scalar field and the modified gravity (MOG) field on the QNM, GF, and shadow are examined. Using the sixth-order WKB approach, we investigate the QNMs of massless scalar and electromagnetic perturbations. Our findings show that as the quintessence and the MOG parameter (ϵ and α) increase, the oscillation frequencies decrease significantly. Gravitational wave damping, on the other hand, decreases with increasing ϵ and α. In addition, we obtain an analytical solution for the transmission coefficients (GF) and demonstrate that more thermal radiation reaches the observer at spatial infinity as both the ϵ and α parameters increase. We also investigate the effect of the plasma background on the BH shadow and show that as the plasma background parameter increases, the shadow radius slightly shrinks. Nevertheless, the shadow radius increases as α and ϵ increase. Particularly intriguing is the fact that increasing ϵ has a greater impact on the shadow radius than increasing α, indicating that the quintessence parameter has a greater impact than the MOG parameter.

Integrated study of dark matter and dark energy models

Dark matter and dark energy are used as two important concepts in cosmology to explain some of the observed phenomena in the universe. Dark matter is one of the most dominant constituents of the Universe, and it influences the structural formation of the Universe through gravity, including the formation and evolution of galaxies, clusters, and the large-scale structure of the Universe. Dark energy is believed to be one of the causes of the accelerated expansion of the Universe, and its presence explains the observed phenomenon of the accelerating rate of expansion of the Universe. Although their existence has not been directly observed, people understand through the study of the structure and evolution of the universe that they play an important role in the universe. This paper first introduces the background knowledge of dark matter and its related properties and explains the reasons why three types of models, namely WIMP, axion, and sterile neutrino, are candidates for dark matter in the light of existing observations. The paper then discusses the relevant properties of dark energy and analyses the mainstream dark energy models. For the cosmological constant mode, the fine-tuning problem and cosmic coincidence problem it faces are analysed in detail. The evolution of the dark energy equation of state from the past >-1 to the present <-1 is then explained, and this is used to introduce the scalar field model involving dynamic, the Chaplygin gas model, the holographic dark energy model, and the interacting dark energy model.

Motion of rotating black holes in homogeneous scalar fields: A general case

Motion of rotating black holes in homogeneous scalar fields: A general case