Scalar Field Lagrangian Research Articles

Phase-space analysis in non-minimal symmetric-teleparallel dark energy

We modify the symmetric-teleparallel dark energy through the addition of a further Yukawa-like term, in which the non-metricity scalar, Q, is non-minimally coupled to a scalar field Lagrangian where the phion acts as quintessence, describing dark energy. We investigate regions of stability and find late-time attractors. To do so, we conduct a stability analysis for different types of physical potentials describing dark energy, namely the power-law, inverse power-law, and exponential potentials. Within these choices, we furthermore single out particular limiting cases, such as the constant, linear and inverse potentials. For all the considered scenarios, regions of stability are calculated in terms of the signs of the coupling constant and the exponent, revealing a clear degeneracy among coefficients necessary to ensure stability. We find that a generic power-law potential with α>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha > 0$$\\end{document} is not suitable as a non-minimal quintessence potential and we put severe limits on the use of inverse potential, as well. In addition, the equations of state of each potential have been also computed. We find the constant potential seems to be favored than other treatments, since the critical point appears independent of the non-minimal coupling.

Wormholes inside stars and black holes

We construct models of two exotic objects: (i) a wormhole whose throat is hidden by a stellar object like a neutron star; and (ii) a wormhole inside a black hole. We work within Einstein’s gravity coupled to two scalar fields with a specific choice of the scalar field Lagrangian. In general, the model contains ghosts, but they are eliminated using the constraints given by the Lagrange multiplier fields. The constraints are a generalization of the mimetic constraint, where nondynamical dark matter effectively appears. As a result, in our model, instead of the nondynamical dark matter, nondynamical exotic matter like a phantom effectively arises. For the mixed wormhole-plus-star system, we find the corresponding mass-radius relation and show that it is possible to get characteristics comparable to those of ordinary neutron stars. For the wormhole inside the black hole, we find an extremal limit where the radius of the throat coincides with the radius of the event horizon and demonstrate that the Hawking temperature vanishes in this limit. Published by the American Physical Society 2024

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.

Dissipative quintessence and its cosmological implications

We consider a generalization of the quintessence type scalar field cosmological models, by adding a multiplicative dissipative term in the scalar field Lagrangian, which generally is represented in an exponential form. The generalized dissipative Klein-Gordon equation is obtained in a general covariant form in Riemann geometry, from the variational principle with the help of the Euler-Lagrange equations. The energy-momentum tensor of the dissipative scalar field is also obtained from the dissipative Lagrangian, and its properties are discussed in detail. Several applications of the general formalism are presented for the case of the cosmological Friedmann-Lema\^{\i}tre-Robertson-Walker metric. The generalized Friedmann equations in the presence of the dissipative scalar field are obtained for a specific form of dissipation, with the dissipation exponent represented as the time integral of the product of the Hubble function, and of a function describing the dissipative properties of the scalar field. For this case the Friedmann equations reduce to a system of differential-integral equations, which, by means of some appropriate transformation, can be represented in the redshift space as a first order dynamical system. Several cosmological models, corresponding to different choices of the dissipation function, and of the scalar field potential, are considered in detail. For the different values of the model parameters the evolution of the cosmological parameters (scale factor, Hubble function, deceleration parameter, the effective density and pressure of the scalar field, and the parameter of the dark energy equation of state, respectively) is considered in detail by using both analytical and numerical techniques. A comparison with the observational data for the Hubble function and with the predictions of the standard $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ paradigm is presented for each dissipative scalar field model. In the large time limit the model describes an accelerating universe, with the effective negative pressure induced by the dissipative effects associated with the scalar field. Accelerated expansion in the absence of the scalar field potential is also possible, with the kinetic term dominating the expansionary evolution. The dissipative scalar field models describe well the data, with the model free parameters obtained by a trial and error method. The obtained results show the dissipative scalar field model offers an effective dynamical possibility for replacing the cosmological constant and for explaining the recent cosmological observational data.

Double field theory with matter and the generalized Bergshoeff–de Roo identification

The scalar field-perfect fluid (sf-pf) correspondence shows that the energy-momentum tensor of a scalar field is in correspondence with the dynamics of a perfect fluid. In this work we generalize this concept to study the higher-derivative structure of double field theory with statistical matter. Using the generalized Bergshoeff--de Roo identification we find nontrivial higher-derivative corrections for the generalized scalar field Lagrangian. However, these contributions are removed to any desired order using field redefinitions at the supergravity level. By virtue of the generalized sf-pf correspondence we obtain the higher-derivative dynamics for the perfect fluid in the double geometry, which is also trivialized at the supergravity level. These results imply that the well-known ${\ensuremath{\alpha}}^{\ensuremath{'}}$-corrections obtained by this procedure only correct the effective vacuum Lagrangian, while the sf-pf Lagrangian coupled to the supergravity background remains uncorrected to all orders. Our findings apply for a general (bosonic-heterotic-type II-HSZ) supergravity background.

Natural TeV cutoff of the Higgs field from a multiplicative Lagrangian

The various types of the non-standard Lagrangian can be added to the standard Lagrangian with the invariant of the equation of motion in the low energy limit. In this paper, we construct the multiplicative Lagrangian of a complex scalar field giving the approximated Klein-Gordon equation from the inverse problem of the calculus of variation. Then, this multiplicative Lagrangian with arbitrary high cutoff is applied to the toy model of the Higgs mechanism in U(1)-gauge symmetry in order to study the simple effects in the Higgs physics. We show that, after spontaneous symmetry breaking happens, the Higgs vev is free from the Fermi-coupling constant and the Higgs field gets the natural cutoff in TeV scale. The other relevant coupling constants, the UV-sensitivity of Higgs mass due to the loop correction, some applications on the strong CP problem as well as anomalous small fermion mass, and the cosmological constant problem are also discussed.

A p-Adic Matter in a Closed Universe

In this paper, we introduce a new type of matter that has origin in p-adic strings, i.e., strings with a p-adic worldsheet. We investigate some properties of this p-adic matter, in particular its cosmological aspects. We start with crossing symmetric scattering amplitudes for p-adic open strings and related effective nonlocal and nonlinear Lagrangian which describes tachyon dynamics at the tree level. Then, we make a slight modification of this Lagrangian and obtain a new Lagrangian for non-tachyonic scalar field. Using this new Lagrangian in the weak field approximation as a matter in Einstein gravity with the cosmological constant, one obtains an exponentially expanding FLRW closed universe. At the end, we discuss the obtained results, i.e., computed mass of the scalar p-adic particle, estimated radius of related closed universe and noted p-adic matter as a possible candidate for dark matter.

Anisotropic spacetimes in chiral scalar field cosmology

Study the behaviour and the evolution of the cosmological field equations in an homogeneous and anisotropic spacetime with two scalar fields coupled in the kinetic term. Specifically, the kinetic energy for the scalar field Lagrangian is that of the Chiral model and defines a two-dimensional maximally symmetric space with negative curvature. For the background space we assume the locally rotational spacetime which describes the Bianchi I, the Bianchi III and the Kantowski-Sachs anisotropic spaces. We work on the $H$% -normalization and we investigate the stationary points and their stability. For the exponential potential we find a new exact solution which describes an anisotropic inflationary solution. The anisotropic inflation is always unstable, while future attractors are the scaling inflationary solution or the hyperbolic inflation. For scalar field potential different from the exponential, the de Sitter universe exists.

Local Existence of Classical Solutions to Scalar Field Equation on Spatially Compact Spacetime as a Background

The goal of this paper is to prove the wellposedness of scalar field equation on spatially compact spacetime of Riemannian manifold. We construct the equation of motion from the Lagrangian of scalar field with non-minimal coupling, where the coupling interaction of the scalar field ϕ is proportional to the scalar curvature of the spacetime. The equation of motion has the form like non-linear wave equation. The next step is to prove local existence of solutions. We have show that both the k th linear energy and energy norm are bounded for the finite time with the initial data in H k+1 × H k. Finally, we prove the uniqueness and smoothness properties of the solution.

A scalar field inducing a non-metrical contribution to gravitational acceleration and a compatible add-on to light deflection

A scalar field model for explaining the anomalous acceleration and light deflection at galactic and cluster scales, without further dark matter, is presented. It is formulated in a scale covariant scalar tensor theory of gravity in the framework of integrable Weyl geometry and presupposes two different phases for the scalar field, like the superfluid approach of Berezhiani/Khoury. In low acceleration regimes of static gravitational fields (in the Einstein frame) with accordingly low values of the scalar field gradient, the scalar field Lagrangian combines a cubic kinetic term similar to the “a-quadratic” Lagrangian used in the first covariant generalization of MOND (RAQUAL) (Bekenstein and Milgrom in Astrophys J 286:7–14, 1984) and a second order derivative term introduced by Novello et al. in the context of a Weyl geometric approach to cosmology (Novello et al. in Int J Mod Phys D 1:641–677, 1993; de Oliveira et al. in Class Quantum Gravity 14(10):2833–2843, 1997). In varying with regard to phi the latter is variationally equivalent to a first order expression. The scalar field equation thus remains of order two. In the Einstein frame it assumes the form of a covariant generalization of the Milgrom equation known from the classical MOND approach in the deep MOND regime. It implies a corresponding “non-metrical” contribution to the acceleration of free fall trajectories. In contrast to pure RAQUAL, the second order derivative term of the Lagrangian leads to a non-negligible contribution to the energy momentum tensor and an add-on to the light deflection potential in beautiful agreement with the dynamics of low velocity trajectories. Although the model takes up important ingredients from the usual RAQUAL approach, it differs essentially from the latter.—In higher sectional curvature regions, respectively for higher accelerations in static fields, the scalar field Lagrangian consists of a Jordan–Brans–Dicke term with sufficiently high value of the JBD-constant to satisfy empirical constraints. Here the dynamics agrees effectively with the one of Einstein gravity.

Local existence of scalar wave equation on the Robertson-Walker universe as a background with k = 0

In this paper, we study about the wellposedness of scalar wave equation on Robertson-Walker universe as a background with zero spatial curvature, k = 0. We start from non-minimal Lagrangian for scalar field on curved background with potential turned on. Then we derive the equations of motion and tensor energy-momentum. After that we specify our case to k = 0. Finally, we prove the local existence and uniqueness of the solution of the equation of motion.

Notes for quantum gravitational field

We discuss the problems of dynamics of the gravitational field and try to solve them according to quantum field theory by suggesting canonical states for the gravitational field and its conjugate field. To solve the problem of quantization of gravitational field, we assume that the quantum gravitational field $e ^I$ changes the geometry of curved spacetime $x^\mu$, and relate this changing to quantization of the gravitational field. We introduce a field $\pi_I$ and consider it as a canonical momentum conjugates to a canonical gravitational field $\tilde e^I$. We use them in deriving the path integral of the gravitational field according to quantum field theory, we get Lagrangian with dependence only on the covariant derivative of the gravitational field $e^I$, similarly to Lagrangian of scalar field in curved spacetime. Then, we discuss the case of free gravitational field. We find that this case takes place only in background spacetime approximation of low matter density; weak gravity. Similarly, we study the Plebanski two form complex field $\Sigma ^{i}$ and derive its Lagrangian with dependence only on the covariant derivative of $\Sigma ^{i}$, which is represented in selfdual representation $\left| {\Sigma ^i } \right\rangle$. Then, We try to combine the gravitational and Plebanski fields into one field: $K_{\mu}^i$. Finally, we derive the static potential of exchanging gravitons between particles of scalar and spinor fields; the Newtonian gravitational potential.

Correspondence between modified gravity and general relativity with scalar fields

We describe a novel procedure to map the field equations of nonlinear Ricci-based metric-affine theories of gravity, coupled to scalar matter described by a given Lagrangian, into the field equations of General Relativity coupled to a different scalar field Lagrangian. Our analysis considers examples with a single and $N$ real scalar fields, described either by canonical Lagrangians or by generalized functions of the kinetic and potential terms. In particular, we consider several explicit examples involving $f(R)$ theories and the Eddington-inspired Born-Infeld gravity model, coupled to different scalar field Lagrangians. We show how the nonlinearities of the gravitational sector of these theories can be traded to nonlinearities in the matter fields, and how the procedure allows to find new solutions on both sides of the correspondence. The potential of this procedure for applications of scalar field models in astrophysical and cosmological scenarios is highlighted.

Thermodynamics of event horizon with modified Hawking temperature in scalar-tensor gravity

In recent past, Hawking temperature has been modified for the validity of thermodynamical laws at the event horizon in general relativity context. This lead to the introduction of modified Hawking temperature and it has been found that the modified Hawking temperature is more realistic on the event horizon. With this motivation, here we investigate the thermodynamical consistency of scalar-tensor gravity based models by examining the validity of the generalized second law of thermodynamics (GSLT) and thermodynamical equilibrium (TE) at the event horizon. In order to attain our goal, we consider a spatially flat Friedman–Robertson–Walker Universe filled with ordinary matter and the boundary of the Universe bounded by the event horizon that is in thermal equilibrium with modified Hawking temperature. Next, we calculate the general expressions for the GSLT and TE using modified Hawking temperature in the context of the more general action of scalar-tensor gravity where there is a non-minimally coupling between the scalar field and matter Lagrangian (as the chameleon field). From the general expression of GSLT, we find that the null energy condition must hold for a viable scalar-tensor model of the Universe dominated by a perfect fluid. Furthermore, in order to better understand these complicated general expressions of GSLT and TE, we explore the validity of the GSLT and TE for two viable models of scalar-tensor gravity namely Brans–Dicke gravity with a self-interacting potential and Chameleon gravity at the event horizon using special cosmological solutions. Finally, some graphical representation of the GSLT and TE have been presented. From the graphical analysis, we found that the power-law forms of the scale factor and scalar field is much favourable for the study of universal thermodynamics as compared to other choices of the scalar field and the analytic function.

Building analytical three-field cosmological models

A difficult task to deal with is the analytical treatment of models composed of three real scalar fields, as their equations of motion are in general coupled and hard to integrate. In order to overcome this problem we introduce a methodology to construct three-field models based on the so-called “extension method”. The fundamental idea of the procedure is to combine three one-field systems in a non-trivial way, to construct an effective three scalar field model. An interesting scenario where the method can be implemented is with inflationary models, where the Einstein–Hilbert Lagrangian is coupled with the scalar field Lagrangian. We exemplify how a new model constructed from our method can lead to non-trivial behaviors for cosmological parameters.

Heavy scalar boson in view of the unconfirmed 750 GeV LHC diphoton excess

We discuss the impact of the constraints from the measurements of the parameters of the observed 125 GeV Higgs boson and from the unconfirmed 750 GeV diphoton excess in the LHC experiments on the properties of a possible extra scalar boson predicted in various Standard Model extensions. We consider an SM extension based on a stabilized brane-world model, in which the effective low-energy Lagrangian for the scalar degrees of freedom turns out to be very general and, for different values of the model parameters, reproduces the scalar field Lagrangians of various SM extensions by a singlet scalar. It is shown that in the simplest variant of the model, where only the gravitational degrees of freedom propagate in the bulk, the 125 GeV scalar state can be consistently interpreted as a Higgs-dominated state for a rather wide range of the model parameters, whereas the production cross section of a heavier radion-dominated state with mass 750 GeV or more turns out to be too small in the allowed region of the model parameter space for producing the wouldbe diphoton excess.

Evolution of material surfaces in the temporal transition in channel flow

We report a Lagrangian study on the evolution of material surfaces in the Klebanoff-type temporal transitional channel flow. Based on the Eulerian velocity field from the direct numerical simulation, a backward-particle-tracking method is applied to solve the transport equation of the Lagrangian scalar field, and then the isosurfaces of the Lagrangian field can be extracted as material surfaces in the evolution. Three critical issues for Lagrangian investigations on the evolution of coherent structures using material surfaces are addressed. First, the initial scalar field is uniquely determined based on the proposed criteria, so that the initial material surfaces can be approximated as vortex surfaces, and remain invariant in the initial laminar state. Second, the evolution of typical material surfaces initially from different wall distances is presented, and then the influential material surface with the maximum deformation is identified. Large vorticity variations with the maximum curvature growth of vortex lines are also observed on this surface. Moreover, crucial events in the transition can be characterized in a Lagrangian approach by conditional statistics on the material surfaces. Finally, the influential material surface, which is initially a vortex surface, is demonstrated as a surrogate of the vortex surface before significant topological changes of vortical structures. Therefore, this material surface can be used to elucidate the continuous temporal evolution of vortical structures in transitional wall-bounded flows in a Lagrangian perspective. The evolution of the influential material surface is divided into three stages: the formation of a triangular bulge from an initially disturbed streamwise–spanwise sheet, rolling up of the vortex sheet near the bulge ridges with the vorticity intensification and the generation and evolution of signature hairpin-like structures with self-induced dynamics of vortex filaments.

Observable signatures of a classical transition

Eternal inflation arising from a potential landscape predicts that our universe is one realization of many possible cosmological histories. One way to access different cosmological histories is via the nucleation of bubble universes from a metastable false vacuum. Another way to sample different cosmological histories is via classical transitions, the creation of pocket universes through the collision between bubbles. Using relativistic numerical simulations, we examine the possibility of observationally determining if our observable universe resulted from a classical transition. We find that classical transitions produce spatially infinite, approximately open Friedman-Robertson-Walker universes. The leading set of observables in the aftermath of a classical transition are negative spatial curvature and a contribution to the Cosmic Microwave Background temperature quadrupole. The level of curvature and magnitude of the quadrupole are dependent on the position of the observer, and we determine the possible range of observables for two classes of single-scalar field models. For the first class, where the inflationary phase has a lower energy than the vacuum preceding the classical transition, the magnitude of the observed quadrupole generally falls to zero with distance from the collision while the spatial curvature grows to a constant. For the second class, where the inflationary phase has a higher energy than the vacuum preceding the classical transition, the magnitude of the observed quadrupole generically falls to zero with distance from the collision while the spatial curvature grows without bound. We find that the magnitude of the quadrupole and curvature grow with increasing centre of mass energy of the collision, and explore variations of the parameters in the scalar field lagrangian.

Evolutionary geometry of Lagrangian structures in a transitional boundary layer

We report a geometric study of Lagrangian structures in a weakly compressible, spatially evolving transitional boundary layer at the Mach number 0.7. The Lagrangian structures in the transition process are extracted from the Lagrangian scalar field by a sliding window filter at a sequence of reference times. The multi-scale and multi-directional geometric analysis is applied to characterize the geometry of spatially evolving Lagrangian structures, including the averaged inclination and sweep angles at different scales ranging from one half of the boundary layer thickness to several viscous length scales. Here, the inclination angle is on the plane of the streamwise and wall-normal directions, and the sweep angle is on the plane of the streamwise and spanwise directions. In general, the averaged inclination angle is increased and the sweep angle is decreased with the reference time. The variation of the angles for large-scale structures is smaller than that for small-scale structures. Before the transition, the averaged inclination and sweep angles are only slightly altered for all the scales. As the transition occurs, averaged inclination angles increase and sweep angles decrease rapidly for small-scale structures. In the late transitional stage, the averaged inclination angle of small-scale structures with 30 viscous length scales is approximately 42°, and the averaged sweep angle in the logarithm law region is approximately 30°. Additionally, the geometry of Lagrangian structures in transitional boundary layer flow is compared with that in the fully developed turbulent channel flow.

The big bang as a result of the first-order phase transition driven by a change of the scalar curvature in an expanding early Universe: The “hyperinflation” scenario

We suggest that the "Big Bang" may be a result of the first-order phase transition driven by changing scalar curvature of the 4D space-time in expanding cold Universe, filled with nonlinear scalar field $\phi $ and neutral matter with equation of state $p=\nu \varepsilon $ (where $p$ and $\varepsilon $ are pressure and energy density of matter). We consider a Lagrangian for scalar field in curved space-time with nonlinearity $\phi ^{4} $, which along with the quadratic term $-\xi R\left|\phi \right|^{2} $ (where $\xi $ is the interaction constant and $R$ is scalar curvature) contains a term $\sim \xi R\left(\phi +\phi ^{+} \right)$ linear in $\phi $. Due to this term the condition for the extrema of the potential energy of scalar field is given by a cubic equation. Provided $\nu > 1/3$ the scalar curvature $R=[\kappa (3\nu -1)\varepsilon -4\Lambda ]$ (where $\kappa $ and $\Lambda $ are Einstein's gravitational and cosmological constants) decreases along with decreasing $\varepsilon $ in the process of the Universe's expansion, and at some critical value $R_{c} < 0$ a first-order phase transition occurs, induced by an "external field" parameter proportional to $R$. Given certain conditions the critical radius of the early Universe at the point of the first-order phase transition may reach arbitrary large values, so this scenario of unrestricted "inflation" of the Universe may be called "hyperinflation". Beyond the point of phase transition the system is rolling down into the potential minimum with the release of the potential energy of scalar field, accompanied by oscillations of its amplitude $\phi $. The powerful heating of the Universe in the course of attenuation of these oscillations plays the role of "Big Bang".