Scalar Field Research Articles

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.

Phase transitions, critical behavior and microstructure of the FRW universe in the framework of higher order GUP

In this paper, we explore the phase transition, critical behavior and microstructure of the FRW in the framework of a new higher order generalized uncertainty principle (GUP). Our initial step involves deriving the equation of state by defining the work density W from GUP corrected Friedmann equations as the thermodynamic pressure P. Based on the modified equation of state, we conduct an analysis of the P−V phase transition in the FRW universe. Subsequently, we obtain the critical exponents and coexistence curves for the small and large phases of the FRW universe around the critical point. Finally, employing Ruppeiner geometry, we derive the thermodynamic curvature scalar RN, investigating its sign-changing curve and spinodal curve. The results reveal distinctive thermodynamic properties for FRW universes with positive and negative GUP parameters β. In the case of β>0, the phase transition, critical behavior and microstructure of FRW universe are like those of Van der Waals system and charged AdS. Conversely, for β<0, the results resemble those obtained through effective scalar field theory. These findings underscore the capacity of quantum gravity to induce phase transitions in the universe, warranting further in-depth exploration.

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&gt;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.

A speed limit on tachyon fields from cosmological and fine-structure data

The rolling tachyon is a non-canonical scalar field model well motivated in string theory which naturally predicts variations of the fine-structure constant. Such variations can in principle lead to interesting observable consequences, but they can also lead to extremely tight constraints on these kinds of models. In this work we subject the rolling tachyon model evolving in a variety of potentials to current data and show that most cosmologically interesting evolutions are already strongly excluded. We find |1 + w 0| < 10-3 from cosmological data and |1 + w 0| < 10-9 from fine-structure data, leaving the rolling tachyon to either play a role almost entirely equivalent to a cosmological constant or that of a test field. We also find that in most of the allowed parameter space the field evolves very slowly, allowing its evolution to be approximated as an equivalent canonical scalar field.

Optical Singularities in Photonic Microstructures with Rosette Symmetries: A Unified Theoretical Scheme

Optical singularities are topological defects of electromagnetic fields; they include phase singularity in scalar fields, polarization singularity in vector fields, and three-dimensional (3D) singularities such as optical skyrmions. The exploitation of photonic microstructures to generate and manipulate optical singularities has attracted wide research interest in recent years, with many photonic microstructures having been devised to this end. Accompanying these designs, scattered phenomenological theories have been proposed to expound the working mechanisms behind individual designs. In this work, instead of focusing on a specific type of microstructure, we concentrate on the most common geometric features of these microstructures—namely, symmetries—and revisit the process of generating optical singularities in microstructures from a symmetry viewpoint. By systematically employing the projection operator technique in group theory, we develop a widely applicable theoretical scheme to explore optical singularities in microstructures with rosette (i.e., rotational and reflection) symmetries. Our scheme agrees well with previously reported works and further reveals that the eigenmodes of a symmetric microstructure can support multiplexed phase singularities in different components, such as out-of-plane, radial, azimuthal, and left- and right-handed circular components. Based on these phase singularities, more complicated optical singularities may be synthesized, including C points, V points, L lines, Néel- and bubble-type optical skyrmions, and optical lattices, to name a few. We demonstrate that the topological invariants associated with optical singularities are protected by the symmetries of the microstructure. Lastly, based on symmetry arguments, we formulate a so-called symmetry matching condition to clarify the excitation of a specific type of optical singularity. Our work establishes a unified theoretical framework to explore optical singularities in photonic microstructures with symmetries, shedding light on the symmetry origin of multidimensional and multiplexed optical singularities and providing a symmetry perspective for exploring many singularity-related effects in optics and photonics.

Relativistic interacting fluids in cosmology

Motivated by cosmological applications for interacting matters, an extensionof the action functional for relativistic fluids is proposed to incorporate thephysics of non-adiabatic processes and chemical reactions. The formerare characterised by entropy growth, while the latter violateparticle number conservation.The relevance of these physics is demonstrated in the contexts ofself-interacting fluids, fluids interacting with scalar fields, andhyperhydrodynamical interactions with geometry. The possible cosmologicalapplications range from early-universe phase transitions to astrophysicalphenomena, and from matter creation inflationary alternatives to interactingdark sector alternatives to the ΛCDM model that aim to address its tensions.As an example of the latter, a single fluid model of a unified dark sector is presented. The simple action of the model features one field and one parameter, yet it can both reproduce the ΛCDM cosmology and predict new phenomenology.

Influence of GUP corrected Casimir energy on zero tidal force wormholes in modified teleparallel gravity with matter coupling

In recent times, the study of the Casimir effect in quantum field theory has garnered increasing attention because of its potential to be an ideal source of exotic matter needed for stabilizing traversable wormholes. It has been confirmed through experimental evidence that this phenomenon involves fluctuations in the vacuum field, leading to a negative energy density. Motivated by the above, we have investigated Casimir wormholes with corrections from the Generalized Uncertainty Principle (GUP) within the framework of matter-coupled teleparallel gravity. Our analysis includes three well-known GUP models: the Kempf, Mangano, and Mann (KMM) model, the Detournay, Gabriel, and Spindel (DGS) model, and a third model called Model II. For a broader analysis, we have considered two well-known model functions for the teleparallel theory: a linear f(T,T)=αT+βT\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(T,\\mathcal {T})=\\alpha T+\\beta \\mathcal {T}$$\\end{document} and a quadratic model f(T,T)=ηT2+χT\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(T,\\mathcal {T})=\\eta T^2+\\chi \\mathcal {T}$$\\end{document}. The shape function solutions corresponding to both models are examined in the absence of tidal forces in spacetime. We also demonstrate the crucial role played by the parameters of the f(T,T)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(T,\\mathcal {T})$$\\end{document} models in the violation of the energy conditions. With the increasing interest in detecting gravitational waves from astrophysical objects, we have thoroughly discussed the perturbation of the wormhole solutions in the scalar, electromagnetic, axial gravitational, and Dirac field backgrounds. We employ the 3rd order WKB expansion to find the complex frequencies associated with the quasinormal modes of energy dissipation. Additionally, we also calculate the active mass and total gravitational energy for the wormhole geometry. The amount of exotic matter involved in sustaining these wormholes is also found in this paper. Furthermore, the physical stability of such Casimir wormholes is examined using the Tolman–Oppenheimer–Volkoff equation.

Robust, Secure, and Private Cache-Aided Scalar Linear Function Retrieval From Distributed System With Blind and Adversarial Servers

Robust, Secure, and Private Cache-Aided Scalar Linear Function Retrieval From Distributed System With Blind and Adversarial Servers

Existence of ground state sign-changing solutions for a class of quasilinear scalar field equations originating from nonlinear optics

This paper is mainly concerned with the existence of ground state sign-changing solutions for a class of second order quasilinear elliptic equations in bounded domains, which derived from nonlinear optics models. Combining a non-Nehari manifold method due to Tang and Cheng [J. Differ. Equations 261, 2384–2402 (2016)] and a quantitative deformation lemma with Miranda theorem, we obtain that the problem has at least one ground state solution and one ground state sign-changing solution with two precise nodal domains and we present the concrete lower bounds of ground state solution and ground state energy. We also obtain that any weak solution of the problem has C1,σ-regularity for some σ ∈ (0, 1). With the help of Maximum Principle, we reach the conclusion that the energy of the ground state sign-changing solutions is strictly larger than twice that of the ground state solutions.

Alleviating H 0 and S 8 Tensions Simultaneously in K-essence Cosmology

The present work begins by examining the early-Universe inflationary epoch of a special K-essence model, which incorporates a linear coupling term between the scalar field potential and the canonical Lagrangian. For the power-law potential, we both numerically and analytically prove that the inflationary parameters such as the spectral index and tensor-to-scalar ratio are compatible with the recent BICEP/Keck observations. Continuing this work, our analysis based on comparing early-Universe observations with late-Universe measurements indicates that the tension on the Hubble parameter H 0 and the growth of structure parameter S 8 can be alleviated simultaneously. More precisely, compared to the standard ΛCDM model, our model can reduce H 0 tension to roughly 2.2σ, and the S 8 discrepancy diminishes to 0.82σ.