Scalar Field Research Articles

Weak cosmic censorship with excited scalar fields and bound on charge-to-mass ratio

Abstract Recent study in [1] discovered that introducing a massive charged scalar field and requiring the Weak Gravity Conjecture (WGC) to hold can eliminate a class of Weak Cosmic Censorship Conjecture (WCCC) counterexamples in anti-de Sitter spacetime, indicating a potential connection between WCCC and WGC. In this paper, we extend the study to the case of excited-state scalar fields, and numerically construct the static solutions of excited massive charged scalar fields coupled to the Einstein-Maxwell field in four dimensional spacetime with asymptotically anti-de Sitter boundary conditions. In the absence of scalar field, there is a class of counterexamples to cosmic censorship. However, after adding the scalar field with sufficiently large charge, the original counterexamples can be removed and cosmic censorship is preserved. We find this conclusion also applies to the excited-state of scalar field. There is a minimum value $$ {q}_c^{\textrm{bound}} $$ q c bound . When the charge of the excited scalar field is larger than this minimum value, for sufficiently large boundary electric amplitude a, there will not appear a region with arbitrarily large curvature. That means there exists lower bound on the charge for excited state fields which protects cosmic censorship from being violated.

Majoron-driven leptogenesis in gauged U(1)Lμ−Lτ model

We propose a novel leptogenesis scenario in the gauged U(1)Lμ−Lτ model. Achieving successful leptogenesis in the U(1)Lμ−Lτ symmetric phase is challenging due to the absence of a CP phase, caused by restriction from the gauge symmetry. To overcome this issue, we introduce an additional global symmetry, U(1)B−L, and a scalar field Φ responsible for breaking this symmetry. Through the kinetic misalignment mechanism, the Majoron field associated with U(1)B−L symmetry breaking has a kinetic motion in the early Universe. Subsequently, time-dependent Majoron field background induces the background CP phase dynamically, leading to successful leptogenesis in the U(1)Lμ−Lτ symmetric phase. Furthermore, Majoron itself serves as a dark matter candidate in this scenario. As one of the phenomenological applications, we consider the model that can also explain the muon g−2 anomaly. Published by the American Physical Society 2024

On the role of fiducial structures in minisuperspace reduction and quantum fluctuations in LQC

Abstract In spatially non-compact homogeneous minisuperpace models, spatial integrals in the Hamiltonian and symplectic form must be regularised by confining them to a finite volume Vo , known as the fiducial cell. As this restriction is unnecessary in the complete field theory before homogeneous reduction, the physical significance of the fiducial cell has been largely debated, especially in the context of (loop) quantum cosmology. Understanding the role of Vo is in turn essential for assessing the minisuperspace description’s validity and its connection to the full theory. In this work we present a systematic procedure for the field theory reduction to spatially homogeneous and isotropic minisuperspaces within the canonical framework and apply it to both a massive scalar field theory and gravity. Our strategy consists in implementing spatial homogeneity via second-class constraints for the discrete field modes over a partitioning of the spatial slice into countably many disjoint cells. The reduced theory’s canonical structure is then given by the corresponding Dirac bracket. Importantly, the latter can only be defined on a finite number of cells homogeneously patched together. This identifies a finite region, the fiducial cell, whose physical size acquires then a precise meaning already at the classical level as the scale over which homogeneity is imposed. Additionally, the procedure allows us to track the information lost during homogeneous reduction and how the error depends on Vo . We then move to the quantisation of the classically reduced theories, focusing in particular on the relation between the theories for different Vo , and study the implications for statistical moments, quantum fluctuations, and semiclassical states. In the case of a quantum scalar field, a subsector of the full quantum field theory where the results from the ‘first reduced, then quantised’ approach can be reproduced is identified and the conditions for this to be a good approximation are also determined.

JWST observations constrain the time evolution of fine structure constants and dark energy-electromagnetic coupling

Abstract It was hypothesized in the literature that some physical parameters may be time-evolving and the astrophysical data can serve as a probe. Recently, James Webb Space Telescope (JWST) have released its early observations. In this work, we select the JWST spectroscopic observations of the high redshift ($z>7.1$) galaxies with strong [\ion{O}{III}] ($\lambda=4959$\AA \,and $5007$\AA \,in the rest frame) emission lines to constraint the evolution of the fine structure constant ($\alpha$). With the spectra from two galaxies at redshifts of $7.19$ and $8.47$, the deviation of $\alpha$ to its fiducial value is found to be as small as $0.44^{+8.4+1.7}_{-8.3-1.7} \times 10^{-4}$ and $-10.0^{+18+1.5}_{-18-1.5} \times 10^{-4}$, respectively (the first error is statistical and the latter is systematic). The combination of our results with the previous data reveals that $\frac{1}{\alpha} \frac{d \alpha}{dt} = 0.30^{+4.5}_{-4.5} \times 10^{-17}~{\rm yr^{-1}}$. Clearly, there is no evidence for a cosmic evolution of $\alpha$. The prospect of further constraining the time evolution of $\alpha$ is also discussed. The scalar field of dark energy is hypothesized to drive the acceleration of the universe's expansion through an interaction with the electromagnetic field. By integrating the observational data of the fine-structure constant variation, $\frac{\Delta\alpha}{\alpha}(z)$, we have established a stringent upper limit on the coupling strength between dark energy and electromagnetism. Our analysis yields $\zeta \leq 3.92 \times 10^{-7}$ at the 95\% confidence level, representing the most stringent bound to date.

Double Copy From Tensor Products of Metric BV■‐Algebras

AbstractField theories with kinematic Lie algebras, such as field theories featuring color–kinematics duality, possess an underlying algebraic structure known as BV■‐algebra. If, additionally, matter fields are present, this structure is supplemented by a module for the BV■‐algebra. The authors explain this perspective, expanding on our previous work and providing many additional mathematical details. The authors also show how the tensor product of two metric BV■‐algebras yields the action of a new syngamy field theory, a construction which comprises the familiar double copy construction. As examples, the authors discuss various scalar field theories, Chern–Simons theory, self‐dual Yang–Mills theory, and the pure spinor formulations of both M2‐brane models and supersymmetric Yang–Mills theory. The latter leads to a new cubic pure spinor action for 10‐dimensional supergravity. A homotopy‐algebraic perspective on colour–flavour‐stripping is also given, obtain a new restricted tensor product over a wide class of bialgebras, and it is also show that any field theory (even one without colour–kinematics duality) comes with a kinematic ‐algebra.

Simultaneous solution of implicitly defined curved, linear Timoshenko beams in two‐dimensional bulk domains

AbstractA novel formulation of curved Timoshenko beams which are defined by all level sets of a scalar function in a two‐dimensional bulk domain is presented, including a corresponding finite element method for the simultaneous solution of these beams. The required geometrical setup and differential operators are introduced and the model is defined in strong form. The weak form for the simultaneous solution involves the co‐area formula. A crucial aspect is how the difference vector, describing the rotational deformation in this model, is discretized wherefore two different approaches are shown in this paper. Higher‐order convergence studies in the residual errors confirm that the proposed method is valid and achieves expected convergence rates.

Charged critical behavior and nonperturbative continuum limit of three-dimensional lattice SU(Nc) gauge Higgs models

We consider three-dimensional (3D) lattice SU(Nc) gauge Higgs theories with multicomponent (Nf>1) degenerate scalar fields and U(Nf) global symmetry, focusing on systems with Nc=2, to identify critical behaviors that can be effectively described by the corresponding 3D SU(Nc) gauge Higgs field theory. The field-theoretical analysis of the RG flow allows one to identify a stable charged fixed point for large values of Nf, that would control transitions characterized by the global symmetry-breaking pattern U(Nf)→SU(2)⊗U(Nf−2). Continuous transitions with the same symmetry-breaking pattern are observed in the SU(2) lattice gauge model for Nf≥30. Here we present a detailed finite-size scaling analysis of the Monte Carlo data for several large values of Nf. The results are in substantial agreement with the field-theoretical predictions obtained in the large-Nf limit. This provides evidence that the SU(Nc) gauge Higgs field theories provide the correct effective description of the 3D large-Nf continuous transitions between the disordered and the Higgs phase, where the flavor symmetry breaks to SU(2)⊗U(Nf−2). Therefore, at least for large enough Nf, the 3D SU(Nc) gauge Higgs field theories with multicomponent scalar fields can be nonperturbatively defined by the continuum limit of lattice discretized models with the same local and global symmetries. Published by the American Physical Society 2024

Locality and entanglement harvesting in covariantly bandlimited scalar fields

Locality and entanglement harvesting in covariantly bandlimited scalar fields

The two stages of inflation with non-canonical scalar fields

The two stages of inflation with non-canonical scalar fields

Irreducible cosmological backgrounds of a real scalar with a broken symmetry

We explore the irreducible cosmological implications of a singlet real scalar field. Our focus is on theories with an approximate and spontaneously broken Z2 symmetry where quasistable domain walls can form at early times. This seemingly simple framework bears a wealth of phenomenological implications that can be tackled by means of different cosmological and astrophysical probes. We elucidate the connection between domain wall dynamics and the production of dark matter and gravitational waves. In particular, we identify three main benchmark scenarios. The gravitational wave signal observed by pulsar timing arrays can be generated by the domain walls if the mass of the singlet is ms∼PeV. For lower masses, but with ms≳10 GeV, scalars produced in the annihilation of the domain walls can be dark matter with a distinctive feature in their power spectrum. Finally, the thermal bath provides an unavoidable source of unstable scalars via the freeze-in mechanism whose subsequent decays can be tested by their imprints on cosmological and terrestrial observables. Published by the American Physical Society 2024

Modularity in d > 2 free conformal field theory

We derive new closed form expressions for the partition functions of free conformally-coupled scalars on S2D−1 × S1 which resum the exact high-temperature expansion. The derivation relies on an identification of the partition functions, analytically continued in chemical potentials and temperature, with multiple elliptic Gamma functions. These functions satisfy interesting modular properties, which we use to arrive at our expressions. We describe a geometric interpretation of the modular properties of multiple elliptic Gamma functions in the context of superconformal field theory. Based on this, we suggest a geometric interpretation of the modular property in the context of the free scalar CFT in even dimensions and comment on extensions to odd dimensions and free fermions.

Einstein’s spacetime curvature and gravitational waves: Elucidating the gradient flow of scalar invariants, variations in the Ricci scalar, and gravitational wave propagation

In the general theory of relativity initially rationalized by Einstein, the gravity is considered as an occurrence ensuing from the spacetime curvature, which is in turn triggered by the presence of mass. This article provides a detailed analysis of spacetime curvature and gravitational waves, enhancing our understanding of general relativity and astrophysics. Using both analytical and numerical methods, we examined the gradient flow of scalar invariants, variations in the Ricci scalar, and gravitational wave propagation. New findings include the identification of unique curvature patterns around rotating black holes, a detailed comparison of gradient flow behavior in different spacetime geometries, and the discovery of a correlation between scalar invariant fluctuations and gravitational wave amplitudes. These findings validate numerical techniques and reveal how different parameters affect gravitational wave characteristics. While simplified models are used, the present study offers a robust framework for future research. Our work aligns with previous studies but also reveals unique aspects of wave behavior, with implications for quantum gravity and cosmology.

Perturbations of classical fields by gravitational shockwaves

Gravitational shockwaves are geometries where components of the transverse curvature have abrupt behaviour across null hypersurfaces, which are fronts of the waves. We develop a general approach to describe classical field theories on such geometries in a linearized approximation, by using free scalar fields as a model. Perturbations caused by shockwaves exist above the wave front and are solutions to a characteristic Cauchy problem with initial data on the wave front determined by a supertranslation of ingoing fields. A special attention is paid to perturbations of fields of point-like sources generated by plane-fronted gravitational shockwaves. One has three effects: conversion of non-stationary perturbations into an outgoing radiation, a spherical scalar shockwave which appears when the gravitational wave hits the source, and a plane scalar shockwave accompanying the initial gravitational wave. Our analysis is applicable to gravitational shockwaves of a general class including geometries sourced by null particles and null branes.

Cutkosky rules and 1-loop κ -deformed amplitudes

In this paper, we show that the Cutkosky cutting rules are still valid term by term in the expansion in powers of κ of the κ-deformed 1-loop correction to the propagator of the κ-deformed complex scalar field. We first present a general argument which relates each term in the expansion to a nondeformed amplitude containing additional propagators with mass M>κ. We then show the same thing more pragmatically, by reducing the singularity structure of the coefficients in the expansion of the κ-deformed amplitude, to the singularity structure of nondeformed loop amplitudes, by using algebraic and analytic identities. We will explicitly show this up to second order in 1/κ, but the technique can be generalized to higher orders in 1/κ. Both the abstract and the more direct approach easily generalize to different deformed theories. We will then compute the full imaginary part of the κ-deformed 1-loop correction to the propagator in a specific model, up to second order in the expansion in 1/κ, highlighting the usefulness of the approach for the phenomenology of deformed models. This explicitly confirms previous qualitative arguments concerning the behavior of the decay width of unstable particles in the considered model. Published by the American Physical Society 2024

Primordial magnetogenesis in a bouncing model with dark energy

We investigate primordial magnetogenesis within a quantum bouncing model driven by a scalar field, focusing on various non-minimal couplings between the electromagnetic field and the scalar field. We test three cases: no coupling, a Cauchy coupling with gradual decay, and a Gaussian coupling with rapid fall-off. By exploring these scenarios, we assess a wide range of coupling strengths across different scales. The scalar field, with an exponential potential, behaves as pressureless matter in the asymptotic past of the contracting phase, as stiff matter around the bounce, and as dark energy during the expanding phase. Our findings reveal that, among the tested cases, only the Gaussian coupling can explain the generation of primordial magnetic fields on cosmological scales.

Gravitationally dominated instantons and instability of dS, AdS and Minkowski spaces

We study the decay of the false vacuum in the regime where the quantum field theory analysis is not valid, since gravitational effects become important. This happens when the height of the barrier separating the false and the true vacuum is large, and it has implications for the instability of de Sitter, Minkowski and anti-de Sitter vacua. We carry out the calculations for a scalar field with a potential coupled to gravity, and work within the thin-wall approximation, where the bubble wall is thin compared to the size of the bubble. We show that the false de Sitter vacuum is unstable, independently of the height of the potential and the relative depth of the true vacuum compared to the false vacuum. The false Minkowski and anti-de Sitter vacua can be stable despite the existence of a lower energy true vacuum. However, when the relative depth of the true and false vacua exceeds a critical value, which depends on the potential of the false vacuum and the height of the barrier, then the false Minkowski and anti-de Sitter vacua become unstable. We calculate the probability for the decay of the false de Sitter, Minkowski and anti-de Sitter vacua, as a function of the parameters characterizing the field potential.

Probing Krylov complexity in scalar field theory with general temperatures

Krylov complexity characterizes the operator growth in the quantum many-body systems or quantum field theories. The existing literatures have studied the Krylov complexity in the low temperature limit in the quantum field theories. In this paper, we extend and systematically study the Krylov complexity and Krylov entropy in a scalar field theory with general temperatures. To this end, we propose a new method to calculate the Wightman power spectrum which allows us to compute the Lanczos coefficients and subsequently to study the Krylov complexity (entropy) in general temperatures. We find that the Lanczos coefficients and Krylov complexity (entropy) in the high temperature limit will behave somewhat differently from those studies in the low temperature limit. We give an explanation of why the Krylov complexity does not oscillate in the high-temperature region. Moreover, we uncover the transition temperature that separates the oscillating and monotonic increasing behavior of Krylov complexity.

Gravitational waves of nonextremal Kerr black holes from conformal symmetry

In the low-energy limit, the near region of a generic Kerr black hole has been conjectured to be holographically dual to a two-dimensional conformal field theory. In this paper, we consider a test object orbiting in the near region of a nonextremal Kerr black hole. We first couple it to a massless scalar field. The resulting scalar radiation at the horizon is computed from the perspectives of gravity and dual conformal field theory. Considering the influence of nonzero temperature, the agreement of both computations is found. Then, we generalize the analysis to the gravitational radiation and find agreement again. The agreement supports the conjectured holography and provides a potential theoretical tool for gravitational wave computations. Published by the American Physical Society 2024

Chuprov invariant for vector-scalar fields of multipole sources in a shallow sea

A computational and theoretical study of the properties of the well-known waveguide invariant S.D. Chuprova (IC) was carried out in a plane-parallel Pekeris waveguide. Unlike earlier works, in which predominantly non-directional (monopole) sources were used as a source, and sound pressure fields (scalar fields) were studied, in this work not only scalar, but also vector fields formed in the waveguide by directional - combined multipole sources with directivity in both horizontal and vertical planes. A differential equation has been obtained that makes it possible to fairly accurately calculate the IC values under different conditions of signal propagation and different depths of sources and receivers. This makes it possible, in a simpler way than “full computer modeling,” to predict the invariance (stability) of the IC when varying both the hydrophysical conditions in the waveguide and the geometry of the experiment. It is shown that the directionality of sources in the horizontal plane has virtually no effect on the properties of the IC, and the directionality in the vertical plane leads to a shift in the fan structure of the signal amplitude fields, but has little effect on the IC values. The properties of the fan structure change in a similar way when using vertical projections of the oscillatory velocity vector - despite the fact that another analytical relation, different from scalar fields, is used to calculate the IC, the IC value is close to (+1) at all frequencies and distances, except those at which new modes or dislocations arise. At these frequencies and in these zones, alternating emissions with different signs and magnitudes occur. It is concluded that the stability of IC allows the application of signal processing algorithms developed for scalar fields and non-directional sources to vector-scalar fields generated, including using directional sources.

Stability of Cauchy horizon in Einstein–Power–Maxwell–de Sitter black holes

We investigated the Strong Cosmic Censorship (SCC) conjecture in Einstein–Power–Maxwell–de Sitter (EPMdS) black holes by analyzing the quasinormal modes (QNMs) of a massless neutral scalar field perturbation. Using the pseudospectral method, we calculated the QNM frequencies across various cosmological constants and nonlinear electromagnetic parameters. Our results show that for black holes far from extremality, the lowest QNM frequency -Im(ω)/κ-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$-\ ext {Im} (\\omega )/\\kappa _-$$\\end{document} remains below 1/2. However, as the black holes approach extremality, the lowest mode’s -Im(ω)/κ-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$-\ ext {Im} (\\omega )/\\kappa _-$$\\end{document} consistently exceeds 1/2, leading to a violation of SCC. Moreover, with a fixed cosmological constant, as the nonlinearity parameter α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} increases, the interval of SCC violation under the charge extremality ratio narrows. Considering that k=1/2+1/α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k = 1/2 + 1/\\alpha $$\\end{document} is inversely proportional to α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}, our results indicate that increasing the order k of the non-linear electromagnetic field can effectively mitigate SCC violations.