Scalar Field Models Research Articles

Bianchi type-III THDE quintessence model with hybrid scale factor

The current research investigates the behavior of the Tsallis holographic dark energy (THDE) model with quintessence in a homogeneous and anisotropic Bianchi type-III space–time. We construct the model by using two conditions: ( i) expansion scalar ( θ) is proportionate to shear scalar ( σ) in the model and ( ii) hybrid scale factor a = t βe γt, where β > 0 and γ > 0 are constants. Our study is based on Type Ia supernovae data in combination with CMB and BAO observations (Giostri et al., JCAP 3, 27); the present values of Hubble constant and deceleration parameter are H0 = 73.8 and q0 = −0.54, respectively. Compiling our theoretical models with these data, we obtain [Formula: see text] for [Formula: see text], respectively. We completed an entirely novel form of cosmic model where the expansion occurs during the present accelerated phase for the constraints. We have discussed the conformity among the scalar field model of quintessence and THDE model. To understand the Universe, we have also established the relations for distance modulus, luminosity distance, and angular-diameter distance. Some geometric and physical aspects of the THDE model are also highlighted.

Cosmological solutions of chameleon scalar field model

We investigate cosmological solutions of the chameleon model with a non-minimal coupling between the matter and the scalar field through a conformal factor with gravitational strength. By considering the spatially flat FLRW metric and the matter density as a non-relativistic perfect fluid, we focus on the matter-dominated phase and the late-time accelerated-phase of the universe. In this regard, we manipulate and scrutinize the related field equations for the density parameters of the matter and the scalar fields with respect to the e-folding. Since the scalar field fluctuations depend on the background and the field equations become highly non-linear, we probe and derive the governing equations in the context of various cases of the relation between the kinetic and potential energies of the chameleon scalar field, or indeed, for some specific cases of the scalar field equation of state parameter. Thereupon, we schematically plot those density parameters for two different values of the chameleon non-minimal coupling parameter, and discuss the results. In the both considered phases, we specify that, when the kinetic energy of the chameleon scalar field is much less than its potential energy (i.e., when the scalar field equation of state parameter is ≃-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\simeq - 1 $$\\end{document}), the behavior of the chameleon model is similar to the ΛCDM\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda CDM$$\\end{document} model. Such compatibility suggests that the chameleon model is phenomenologically viable and can be tested with the observational data.

Alleviating cosmological tensions with a coupled scalar fields model

Alleviating cosmological tensions with a coupled scalar fields model

The interaction of neutrinos with phantom, quintessence, and quintum scalar fields and its effect on the formation of structures in the early universe

Despite the fact that the mass of the neutrinos is so small, they are produced in such vast numbers in the early Universe that their mass induces subtle effects on cosmological observables, primarily the growth of structure and the expansion history in the Universe. We consider the models where neutrino interacts with dark energy scalar field models; phantom, quintessence, and quintom. Also, we obtained the z_textrm{nr} (the redshift at which a mass of neutrino m_{nu } will become non-relativistic) and surveyed the effect of non-relativistic neutrinos on the structure formation. The data used in this paper are Pantheon + Analysis catalog, CMB, and BAO data. We obtained coupling constant beta for neutrino and three scalar fields and found that larger beta values will generally lead to larger neutrino mass in the Universe. For combination data, we found that the total mass of neutrino sum m_{nu }< 0.1197eV (95% confidence level (C.L.) for quintom model and sum m_{nu }< 0.121 eV (95% confidence level (C.L.) for phantom model and sum m_{nu }< 0.122eV (95% confidence level (C.L.) for quintessence model. These results are in broad agreement with the results of Planck 2018 where the total neutrino mass is sum m_{nu }<0.12eV (95% C.L., TT, TE, EE + lowE + lensing + BAO). Using the neutrino mass obtained from different models, we calculated z_textrm{nr} and co-moving wave number k_textrm{nr} and showed that neutrinos played a role on the structure formation in the early Universe.

Thermalization in quenched open quantum cosmology

In this article, we study the quantum field theoretic generalization of the Caldeira-Leggett model in general curved space-time considering interactions between two scalar fields in a classical gravitational background. The thermalization phenomena is then studied from the obtained de Sitter solution using quantum quench from one scalar field model obtained from path integrated effective action. We consider an instantaneous quench in the time-dependent mass protocol of the field of our interest. We find that the dynamics of the field post-quench can be described in terms of the state of the generalized Calabrese-Cardy (gCC) form and computed the different types of two-point correlation functions in this context. We explicitly found the conserved charges of W∞ algebra that represents the gCC state after a quench in de Sitter space and found it to be significantly different from the flat space-time results. We extend our study for the different two-point correlation functions not only considering the pre-quench state as the ground state, but also a squeezed state. We found that irrespective of the pre-quench state, the post quench state can be written in terms of the gCC state showing that the subsystem of our interest thermalizes in de Sitter space. Furthermore, we provide a general expression for the two-point correlators and explicitly show the thermalization process by considering a thermal Generalized Gibbs ensemble (GGE). Finally, from the equal time momentum dependent counterpart of the obtained results for the two-point correlators, we have studied the hidden features of the power spectra and studied its consequences for different choices of the quantum initial conditions.

On the equivalence between theories and Einstein gravity

In this brief note we present a somewhat trivial result. Namely, we show that perturbative off-shell f(R)-theory is equivalent to Einstein gravity, as well as to the Brans–Dicke theory and the Einstein scalar field model. We also discuss possible generalization of this result to higher-order gravitational field models.

Dynamical systems analysis of an interacting scalar field model in an anisotropic universe

In this paper, we investigate a non-canonical scalar field model in the background dynamics of anisotropic Locally Rotationally Symmetric (LRS) Bianchi type I universe where gravity is coupled minimally to scalar field which is taken as dark energy and pressureless dust as dark matter are the main matter content of the universe. We perform dynamical system analysis to characterize the cosmological evolution of the model with and without interaction in the dark sector separately. First, we convert the evolution equation into an autonomous system of ordinary differential equations by using a suitable choice of dimensionless variables, which are normalized over the Hubble scale. We choose scalar field coupling and potential in such a way that the autonomous system converted to a 2D system. Linear stability theory is employed to the extracted critical points to find the nature. From the analysis, we find some interesting cosmological scenarios, such as late-time scalar-field dominated solutions, which evolve in the quintessence era, cannot solve the coincidence problem. Accelerated scaling attractors are also obtained that correspond to the late phase evolution in agreement with present observational data, and these solutions also provide possible mechanisms to alleviate the coincidence problem. A complete cosmic evolution is obtained from early inflation to a late-time dark energy-dominated phase, connecting through a matter-dominated transient phase of the universe. Furthermore, we find that for different values of the interaction parameter α, the evolutionary trajectories of the Hubble parameter, and the distance modulus forecasted by the model are in quite well agreement with observational datasets.

Non-local tails in radiation in odd dimensions

Huygens principle violation in a spacetime of odd dimensions leads to the fact that the retarded massless fields of localised sources depend on their history of motion preceding the retarded time. This non-local character of retarded fields should result into the formation of tail signals in the radiation of localised sources. In particular, in gravity theories with odd number of extra spacetime dimensions the gravitational radiation of binary systems should contain the tail terms. In this work, we demonstrate the presence of tail signal in radiation within a simple model of scalar field interacting with the point charge moving on elliptical orbit in three dimensions. We find that the tail term results into the characteristic dependence of radiation power of the charge on time. In particular, its extremum points do not correspond to the moments when the charge passes the pericenter and apocenter of the orbit, in contrast with the four-dimensional theory. We obtain the formulae for the shifts of radiation power extremum points up to the contributions quadratic in the orbital eccentricity. We also compute the spectral distribution of radiation power of the charge. We find that in three dimensions the charge on elliptical orbit radiates into the lower harmonics of the spectrum, compared to the four-dimensional theory. We conjecture that in higher dimensions the character of spectral distributions is opposite — the charge mainly radiates into the higher harmonics of the spectrum.

Model for Origin and Modification of Mass and Coupling Constant

We build a model of the origin of physical constants, including masses and coupling constants. We consider the quantum correction of masses and coupling constants. Some exactly solved leading quantum corrections are given. In the model, the physical constant originates from a coupling between the matter field and a background field. We show that if such a background field as it should be in the real physical world is a quantum field, then the physical constant will have a space- and time-dependent quantum correction and will no longer be a constant. We build a scalar field model and a mechanics model. In these two models, we discuss the quantum correction of masses and coupling constants in the field framework and in the mechanics framework.

Background Constraints on Dark Energy Models

Due to the gravitational attraction of all the matter in the universe, the expansion rate of the cosmos has changed over time, decreasing (decelerating) in past, and more recently speeding up (accelerating). The hypothesis that the Universe is expanding quickly and is spatially nearing its limit now has a lot of cosmological evidence to back it up (assuming the density is at least somewhat time-independent). The majority of cosmologists believe that “dark energy” is to blame for the accelerated cosmological expansion that has been witnessed. The cosmological constant, an additional constant to the Einstein field equation, can be used to explain why the universe is expanding faster than before. The ΛCDM model is the simplest and most common model in use. Besides this, there are also dark energy models like the Barotropic fluid model, canonical scalar field model, and non-canonical scalar field model. We analyse the background constraints on dark energy models using current cosmological data available. We also present the comparison between dark energy models using Bayesian statistics.

Generalized non-local R2-like inflation

The R2 inflation which is an extension of general relativity (GR) by quadratic scalar curvature introduces a quasi-de Sitter expansion of the early Universe governed by Ricci scalar being an eigenmode of d’Alembertian operator. In this paper, we derive a most general theory of gravity admitting R2 inflationary solution which turned out to be higher curvature non-local extension of GR. We study in detail inflationary perturbations in this theory and analyse the structure of form-factors that leads to a massive scalar (scalaron) and massless tensor degrees of freedom. We argue that the theory contains only finite number of free parameters which can be fixed by cosmological observations. We derive predictions of our generalized non-local R2-like inflation and obtain the scalar spectral index ns ≈ 1 − frac{2}{N} and any value of the tensor-to-scalar ratio r < 0.036. In this theory, tensor spectral index can be either positive or negative nt ≶ 0 and the well-known consistency relation r = –8nt is violated in a non-trivial way. We also compute running of the tensor spectral index and discuss observational implications to distinguish this model from several classes of scalar field models of inflation. These predictions allow us to probe the nature of quantum gravity in the scope of future CMB and gravitational wave observations. Finally we comment on how the features of generalized non-local R2-like inflation cannot be captured by established notions of the so-called effective field theory of single field inflation and how we must redefine the way we pursue inflationary cosmology.

LRS Bianchi Type-II Cosmological Model with New Holographic Dark Energy in General Relativity with Quintessence

Abstract: In this paper, we investigate the LRS Bianchi Type-II universe filled with pressureless cold dark matter and non-interacting new holographic dark energy in the framework of general relativity. To obtain the deterministic solution of Einstein’s field equations, we assume the scalar of expansion to be proportional to the eigenvalue of the shear tensor. The expressions for some parameters of cosmological importance are obtained and physical and geometrical properties of the model are discussed. The correspondence between the new holographic dark energy and quintessence scalar field model is also established by comparing their equations of state and densities. Our results are consistent with the recent cosmological observations. Keywords: Bianchi type-II, Holographic principle, Dark energy, Quintessence.

Dynamical Compactification with Matter

In this work, we study cosmological solutions of the 8-dimensional Einstein Yang-Mills theory coupled to a perfect-fluid matter. A Yang-Mills instanton of extra dimensions causes a 4-dimensional expanding universe with dynamical compactification of the extra dimensions. To construct physically reliable situations, we impose the null energy condition on the matter. This energy condition is affected by the extra dimensions. Then, we consider cosmological constant to grasp the structure of the solution space. Even in this simple case, we find several interesting solutions, such as bouncing universes and oscillatory solutions, eventually arriving at a de Sitter universe with stabilized compact dimensions. In addition, we consider a class of matters whose energy density depends on the volume of the extra dimensions. This case shows another set of bouncing universes. Also, a real scalar with potential is taken into account. The scalar field model admits de Sitter solutions due to the choice of potential, and we demonstrate how potentials can be constructed using flow equations. Thus, what we discuss in this work is based on the 8-dimensional Einstein frame, which corresponds to the 4-dimensional Jordan frame by dimensional reduction. Consequently, the results are derived in the 4-dimensional Jordan frame, not in the 4-dimensional Einstein frame.

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.

Interacting DBI essence in viscous [formula omitted] gravity for different choices of scale factor and thermodynamics with power-law and logarithmic entropy corrections

From the hydrodynamic viewpoint, the inclusion of viscosity in the theory of cosmic fluid may appear as an abstraction. Using modern observational results for the Hubble parameter and standard Friedmann formalism, we may have a description of the universe up to the inflationary era, or we may be able to analyse the probable ultimate fate of the universe. Inspired by this bulk viscosity formalism reviewed in Brevik et al., (2017) in this work, we report a study of the DBI essence scalar field model of dark energy (DE) interacting with pressureless dark matter (DM) in the presence of bulk viscous pressure of the form ξ=ξ0+ξ1H+ξ2(Ḣ+H2). We choose the scale factor in three forms: emergent, logamediate, and intermediate. We choose the interaction term Q in the form Q=3HδρΛ, where ρΛ denotes the density of the scalar field model of DE. We present a detailed cosmology of the interacting DE and observe a quintom behaviour of the equation of state (EoS). We conduct a statefinder analysis to attain ΛCDM fixed point by the interacting DE. Subsequently, we report a reconstruction scheme for f(T) gravity. Finally, we conduct thermodynamic analysis where we consider entropy’s logarithmic and power-law corrections.

A parametric view of Hubble parameter for scalar field dark energy model

Abstract: In our present work, we have considered a simple parametric form of the Hubble parameter (H) for a canonical scalar field model described within a spatially flat FRW spacetime framework. Here we have considered a well-behaved parametrization scheme of the normalized Hubble parameter to explain the expansión history of the universe. Under this scenario, we have obtained the analytic solutions for various relevant cosmological parameters. We have also reconstructed the potential function V( φ) for the scalar field φ. It has been found that the deceleration parameter (q) shows exactly the nature which is well expected, i.e., an accelerated expansión for low z limit and deceleration for high z limit, which is essential for the structure formation of the Universe. Detailed data analysis has been carried out to check the viability of the proposed theoretical model by using combined dataset SNIa+H(z)+BAO/CMB and put constraints on the cosmological parameters, viz. the present value of the Hubble parameter H0.

A study of interacting scalar field model from the perspective of the dynamical systems theory

A study of interacting scalar field model from the perspective of the dynamical systems theory

Exact solutions in teleparallel dark energy model

One of the most important challenges facing modern cosmology is to explain the phenomenon of dark energy. Many models have been developed to describe the nature of dark energy in the literature. The scalar field model in the framework of teleparallel gravity is one of the most interesting ones. We investigate the teleparallel dark energy model via the anharmonic oscillator method. We obtain the exact cosmological solutions of the teleparallel dark energy model for the different potentials, such as the general power-law and Higgs potentials. Using Type Ia Supernovae (SNIa) and Pantheon data, we examine the parameter space of the model and determine the allowed regions for the proposed potentials. We study the power-law potential utilizing the χ2 method and Union2 data. Also, we analyze the Higgs potential by applying the MCMC method according to Pantheon data. Although both models are in agreement with the observational data, it can be realized that the Higgs potential can better support the data by comparing the AIC and BIC criteria.

Two Schwarzschild-like black holes balanced by their scalar hair

We show that, unlike vacuum General Relativity, Einstein-scalar theories allow balanced static, neutral, asymptotically flat, double-black hole solutions, for scalar field models minimally coupled to gravity, with appropriate self-interactions. These are scalar hairy versions of the double-Schwarzschild (or Bach-Weyl) solution, but regular on and outside the two (topologically spherical) horizons. The balancing repulsive force is provided by the scalar field. An explicit illustration is presented, using a Weyl-type construction adapted to numerical solutions, requiring no partial linearisation, or integrability structure, of the Einstein-scalar equations. Fixing the couplings of the model, the balanced configurationsform a one-parameter family of solutions, labelled by the proper distance between the black holes.

Constructing a family of conformally flat scalar field models

Using purely geometrical methods we present a mechanism to solve the scalar field equations of motion (non-minimally coupled with gravity) in a spherically symmetric background. We found that the full set of spacetimes, which are of Petrov type O (conformally flat) and admit a gradient conformal vector field, can be determined completely. It is shown that the full group of scalar field equations reduced to a single equation that depends only on the distance leaving the metric function (equivalently the functional form of the scalar field or the potential) freely chosen. Depending on the structure of the metric or the potential V (as a function of φ) a solution can be found either analytically or via numerical integration. We provide physically sound examples and prove that (Anti)-de Sitter fits this scheme. We also reconstruct a recently found solution (Strumia and Tetradis 2022 J. High Energy Phys. JHEP09(2022)203) representing an expanding scalar bubble with metric that has a singularity and corresponds to what is termed as Anti-de Sitter crunch.