K-essence Models Research Articles

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.

Asymptotically safe cosmology with non-canonical scalar field

We investigate the quantum modified cosmological dynamical equations in a Friedmann–Lemaître–Robertson–Walker universe filled with a barotropic fluid and a general non-canonical scalar field characterized by a Lagrangian similar to k-essence model but with a potential term. Quantum corrections are incorporated by considering the running of the gravitational and potential couplings, employing the functional renormalization group approach. Covariant conservation of the non-canonical scalar field and the background barotropic fluid is considered separately, imposing a constraint resulting from the Bianchi identity. This constraint determines the evolution of the cut-off scale with the scale factor and also reveals the cosmic fixed points, depending on whether the flow ceases or continues to evolve. We explore how the general non-canonical scalar field parameter affects the different types of cosmic fixed points and how it differs from the canonical case. Furthermore, we establish a bound on the ratio of the renormalization group parameters involving the non-canonical parameter for which the universe may exhibit accelerated expansion for mixed fixed points. This bound indicates the non-canonical scalar field includes larger sets of asymptotically safe renormalization group fixed point which may give rise to an accelerated universe.

Scaling solutions as Early Dark Energy resolutions to the Hubble tension

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

Generalized K-essence inflation in Jordan and Einstein frames

We here explore a generalized K-essence model which exhibits characteristics akin to ordinary matter. The inflationary framework proposed aims to unify old with chaotic inflation into a single scheme and it considers minimally and non-minimally coupled scenarios, adopting three classes of potentials, in both Jordan and Einstein frames. We show that, to obtain a suitable amount of particles obtained from vacuum energy conversion during inflation, mitigating the classical cosmological constant problem, large-field inflation and, particularly, the Starobinsky-like class of solutions appears the most suitable one.

Constraints on the speed of sound in the k-essence model of dark energy

We consider a k-essence scalar field model for the late-time cosmic acceleration in which the sound speed, parametrized as cs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$c_s$$\\end{document} is constant. We compute the relevant background and perturbation quantities corresponding to the observables like cosmic microwave background, type Ia supernova, cosmic chronometers, baryon acoustic oscillations, and the fσ8\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f\\sigma _8$$\\end{document}. We put constraints on the cs2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$c_s^2$$\\end{document} parameter from these observations along with other parameters. We find lower values of cs2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$c_s^2$$\\end{document} which are close to zero are tightly constrained. Particularly, we find mean value of log10(cs2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\log _\ extrm{10} (c_s^2)$$\\end{document} to be -0.61\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$-0.61$$\\end{document} and cs2≤10-3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$c_s^2 \\le 10^{-3}$$\\end{document} is more than 3σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma $$\\end{document} away from this mean value. This means these observations favor a homogeneous dark energy component compared to the clustering one.

Cosmological complexity in K-essence

We calculate the cosmological complexity under the framework of scalar curvature perturbations for a K-essence model with constant potential. In particular, the squeezed quantum states are defined by acting a two-mode squeezed operator which is characterized by squeezing parameters rk and ϕk on vacuum state. The evolution of these squeezing parameters are governed by the Schrödinger equation, in which the Hamiltonian operator is derived from the cosmological perturbative action. With aid of the solutions of rk and ϕk, one can calculate the quantum circuit complexity between unsqueezed vacuum state and squeezed quantum states via the wave-function approach. One advantage of K-essence is that it allows us to explore the effects of varied sound speeds on evolution of cosmological complexity. Besides, this model also provides a way for us to distinguish the different cosmological phases by extracting some basic information, like the scrambling time and Lyapunov exponent etc, from the evolution of cosmological complexity.

Inflation and late-time accelerated expansion driven by k -essence degenerate dynamics

We consider a k-essence model in which a single scalar field can be responsible for both primordial inflation and the present observed acceleration of the cosmological background geometry, while also admitting a nonsingular de Sitter beginning of the Universe (it arises from de Sitter and ends in de Sitter). The early one is driven by a slow-roll potential, and the late one is driven by a dynamical dimensional reduction process which freezes the scalar field in a degenerate surface, turning it into a cosmological constant. This is done by proposing a realizable stable cosmic time crystal, although giving a different interpretation to the “moving ground state”, in which there is no motion because the system loses degrees of freedom. Furthermore, the model is free of pathologies such as propagating superluminal perturbations, negative energies, and perturbation instabilities. Published by the American Physical Society 2024

Exploring new subclass of k-inflation: Tachyon inflation in [formula omitted] gravity model

It is explained that any scalar field in f(R,T) gravity model could present a new subclass of the k-essence model for inflation. While the case of the quintessence has been studied, there is an empty gap required to be filled by investigating more types of field models. Here, we are aiming to partially fill the gap and concentrate on the tachyon field. In this study, we explore the phenomenon of tachyon inflation in the context of the alternative gravity theory f(R,T)=R+ηT. By applying slow-roll approximations, we examine the model in detail for three different potentials: power-law, generalized T-mode, and inverse hyperbolic cosh. Using observational data and Python coding, we determine a range of values for the model’s free parameters that allow it to fit the data perfectly. In essence, this study provides a comprehensive analysis of tachyon inflation in the R+ηT gravity theory, offering new insights into this alternative framework and its potential to explain tachyon inflation.

Perturbations and stability conditions of k-essence and kinetic gravity braiding models in two-field measure theory

We study cosmological perturbations for k-essence and kinetic gravity braiding models in the context of the two-field measure theory (TMT). Considering scalar perturbations and the uniform field gauge, we obtain the sound speed of the fields and present a stability analysis by means of the kinetic matrix and the mass eigenvalues. For k-essence models, in the two-field measure theory, the speed of propagation of the field is modified completely due to the new measure field and it gives rise to crucial differences with respect to the case without new measure. The stability analysis gives a physical viable model for the Universe. For the kinetic gravity braiding models in the two-field measure theory we get that, in general, the speed of perturbations is equal to the speed of light which is a consequence of the properties of the new measure field. In the latter case, there is always a ghost field. Furthermore, we calculate general expressions for the mass eigenvalues and find, for an explicit example, the existence of tachyonic instabilities.

A generic instability in clustering dark energy?

In this paper, we study the effective field theory (EFT) of dark energy (DE) for the k-essence model beyond linear order. Using particle-mesh N-body simulations that consistently solve the DE evolution on a grid, we find that the next-to-leading order in the EFT expansion, which comprises the terms of the equations of motion that are quadratic in the field variables, gives rise to a generic instability in the regime of low speed of sound (high Mach number). We rule out the possibility of a numerical artefact by considering simplified cases in spherically and plane symmetric situations analytically. If the speed of sound vanishes exactly, the non-linear instability makes the evolution singular in finite time, signalling a breakdown of the EFT framework. The case of finite (but small) speed of sound is subtle, and the local singularity could be replaced by some other type of behaviour with strong non-linearities. While an ultraviolet completion may cure the problem in principle, there is no reason why this should be the case in general. As a result, for a large range of the effective speed of sound cs , a linear treatment is not adequate.

K-Essence Inflation Evading Swampland Conjectures and Inflationary Parameters

In this paper, we study the inflationary scenario in the realm of k-essence model and swampland conjectures. Taking into account three models of Chaplygin gas, such as generalized, modified, and generalized cosmic Chaplygin gas models, we discuss the equation of state (EoS) parameter ω, slow roll parameters (ϵ(ϕ),η(ϕ)), curvature perturbation (Ps), tensor to scalar ratio (r), and scalar spectral index (ns). As regards the k-essence model, the coupling function as a function of scalar field L(ϕ) is used. We investigate the swampland conjecture and then find the value of ζ(ϕ), i.e., bound of second conjecture for these three models by unifying swampland conjecture and k-essence. We plot the EoS parameter ω, inflationary parameters plane r−ns and bound of swampland conjecture ζ(ϕ)−ϕ, which determine that the values of ω<−1 for each model, r, are r<0.0094,r≤0.0065,r≤0.0067, and ranges for ns are [0.934,0.999],[0.9,0.999],[0.9,0.992] for generalized, modified, and generalized cosmic Chaplygin gas models, respectively, and compare their compatibility with the Planck data from 2018. Furthermore, we determine the bound for swampland conjecture as ζ(ϕ)≤0.992,ζ(ϕ)≤0.964,ζ(ϕ)≤0.964 for generalized, modified and generalized cosmic Chaplygin gas models, respectively.

The Phase Space Analysis of Interacting K-Essence Dark Energy Models in Loop Quantum Cosmology

The present work deals with two kinds of k-essence dark energy models within the framework of loop quantum cosmology (LQC). The two kinds of k-essence models originates from two forms of Lagrangians, i.e., L1=F(X)V(ϕ) and L2=F(X)−V(ϕ), where F(X) and V(ϕ) stand for the kinetic term and potential of the scalar field ϕ, respectively. Two models are based on different phase variables settings, and the general form of autonomous dynamical system is deduced for each Lagrangian. Then, the dynamical stabilities of the critical points in each model are analysed in different forms of F(X) and V(ϕ). Model I is a 3-dim system with four stable points, and Model II is a 4-dim system but reduced to a 3-dim system using the symmetry analysis, which has five stable points. Moreover, the corresponding cosmological quantities, such as Ωϕ, wϕ and q, are calculated at each critical point. To compare these with the case of the classical Einstein cosmology (EC), the dynamical evolutionary trajectories in the phase space and evolutionary curves of the cosmological quantities are drawn for both EC and LQC cases, which shows that the loop quantum gravity effects diminish in the late-time universe but are significant in the early time. Further, the effects of interaction Q=αHρm on the evolutions of the universe are discussed. With the loop quantum gravity effects, bouncing universe is achieved in both models for different initial values of ϕ0, ϕ˙0, H0, ρ0 and coupling parameter α, which helps to avoid singularities. However, the interaction has little effect on bounce, although it is important to the stability of some critical points.

Thawing k-essence dark energy in the PAge space

A broad class of dark energy models can be written in the form of k-essence, whose Lagrangian density is a two-variable function of a scalar field ϕ and its kinetic energy . In the thawing scenario, the scalar field becomes dynamic only when the Hubble friction drops below its mass scale in the late Universe. Thawing k-essence dark energy models can be randomly sampled by generating the Taylor expansion coefficients of its Lagrangian density from random matrices [Huang Z 2021 Phys. Rev. D 104 103533]. Reference [Huang Z 2021 Phys. Rev. D 104 103533] points out that the non-uniform distribution of the effective equation of state parameters (w 0, w a ) of the thawing k-essence model can be used to improve the statistics of model selection. The present work studies the statistics of thawing k-essence in a more general framework that is Parameterized by the Age of the Universe (PAge) [Huang Z 2020 Astrophys. J. Lett. 892 L28]. For fixed matter fraction Ω m , the random thawing k-essence models cluster in a narrow band in the PAge parameter space, providing a strong theoretical prior. We simulate cosmic shear power spectrum data for the Chinese Space Station Telescope optical survey, and compare the fisher forecast with and without the theoretical prior of thawing k-essence. For an optimal tomography binning scheme, the theoretical prior improves the figure of merit in PAge space by a factor of 3.3.

Slow-roll inflation in the k-essence model with a periodic scalar field function

In this paper, a periodic cosmological model is considered. Previously, it was assumed that the expansion of the universe slows down over time. Theorists proceeded from the assumption that the main part of the mass of the Universe is matter - both visible and invisible (dark matter). On the basis of new observations indicating the acceleration of expansion, it was found that in the Universe there is a previously unknown energy with negative pressure (equation of state). They called it "dark energy". In this paper, a scalar cosmological model is considered. The Lagrangian is derived and the system of equations of motion is obtained. To study the model, a scalar field in the form of a periodic function was chosen. The Hubble parameter, the scale factor, which has the meaning of the radius of the Universe, and in the case of a periodic function of the scalar field, which has an exponential dependence, the density of dark energy, the pressure and the potential of the scalar field are calculated, and their graphs are plotted in the time dependence section from 0 to 2p. To study the inflationary model, the potential is introduced in a power-law form. From it, the parameters of slow rolling through e-folding are derived and a plot of spectral indices for this model is plotted. The results obtained are consistent with the Planck observational data and confirm the correspondence of the model under study with the previously proposed ones.

Statistics of thawing k -essence dark energy models

K-essence is a minimally-coupled scalar field whose Lagrangian density $\mathcal{L}$ is a function of the field value $\phi$ and the kinetic energy $X=\frac{1}{2}\partial_\mu\phi\partial^\mu\phi$. In the thawing scenario, the scalar field is frozen by the large Hubble friction in the early universe, and therefore initial conditions are specified. We construct thawing k-essence models by generating Taylor expansion coefficients of $\mathcal{L}(\phi, X)$ from random matrices. From the ensemble of randomly generated thawing k-essence models, we select dark energy candidates by assuming negative pressure and non-growth of sub-horizon inhomogeneities. For each candidate model the dark energy equation of state function is fit to the Chevallier-Polarski-Linder parameterization $w(a) \approx w_0+w_a(1-a)$, where $a$ is the scale factor. The thawing k-essence dark models distribute very non-uniformly in the $(w_0, w_a)$ space. About 90\% models cluster in a narrow band in the proximity of a slow-roll line $w_a\approx -1.42 \left(\frac{\Omega_m}{0.3}\right)^{0.64}(1+w_0)$, where $\Omega_m$ is the present matter density fraction. This work is a proof of concept that for a certain class of models very non-uniform theoretical prior on $(w_0, w_a)$ can be obtained to improve the statistics of model selection.

Holographic complexity for black branes with momentum relaxation

We employ the "complexity equals action" conjecture to investigate the action growth rate for the charged and neutral AdS black branes of a holographic toy model consisting of Einstein-Maxwell theory in $d + 1$-dimensional bulk spacetime with $d - 1$ massless scalar fields which is called Einstein-Maxwell-Axion (EMA) theory. From the holographic point of view, the scalar fields source a spatially dependent field theory with momentum relaxation on the boundary, which is dual to the homogeneous and isotropic black branes. We find that the growth rate of the holographic complexity within the Wheeler-DeWitt (WDW) patch saturates the corresponding Lloyd's bound at the late time limit. Especially for the neutral AdS black branes, it will be shown that the complexity growth rate at late time vanishes for a particular value of relaxation parameter $\beta_{max}$ where the temperature of the black hole is minimal. Then, we investigate the transport properties of the holographic dual theory in the minimum temperature. A non-linear contribution of the axion field kinetic term in the context of k-essence model in the four-dimensional spacetime is considered as well. We also study the time evolution of the holographic complexity for the dyonic AdS black branes in this model.

Classical and quantum exact solutions for a FRW in chiral like cosmology

In this work, first, we study a flat Friedmann–Robertson–Walker Universe with two scalar fields but only one potential term, which can be thought as a simple quintessence plus a K-essence model. Employing the Hamiltonian formalism we are able to obtain the classical and quantum solutions. The second model studied, is also a flat Friedmann–Robertson–Walker Universe with two scalar fields, with the difference that the two potentials are considered as well as the standard kinetic energy and the mixed term (chiral field approach). Regarding this second model, it is shown that setting to zero the coefficient accompanying the mixed momenta term, two possible cases can be studied: a quintom like case () and a quintessence like case (). For both scenarios classical and quantum solutions are presented.

Partial UV completion of P(X) from a curved field space

The k-essence theory is a prototypical class of scalar-field models that already gives rich phenomenology and has been a target of extensive studies in cosmology. General forms of shift-symmetric k-essence are known to suffer from formation of caustics in a planar-symmetric configuration, with the only exceptions of canonical and DBI-/cuscuton-type kinetic terms. With this in mind, we seek for multi-field caustic-free completions of a general class of shift-symmetric k-essence models in this paper. The field space in UV theories is naturally curved, and we introduce the scale of the curvature as the parameter that controls the mass of the heavy field(s) that would be integrated out in the process of EFT reduction. By numerical methods, we demonstrate that the introduction of a heavy field indeed resolves the caustic problem by invoking its motion near the would-be caustic formation. We further study the cosmological application of the model. By expanding the equations with respect to the curvature scale of the field space, we prove that the EFT reduction is successfully done by taking the limit of infinite curvature, both for the background and perturbation, with gravity included. The next leading-order computation is consistently conducted and shows that the EFT reduction breaks down in the limit of vanishing sound speed of the perturbation.

Reconstructing k -essence: Unifying the attractor nS(N) and the swampland criteria

The reconstruction of a k-essence inflationary universe, considering the unification between the swampland criteria and the attractor given by the scalar spectral index $n_S(N)$ together with the slow roll parameter $\epsilon(N)$in terms of the number of $e$-folds $N$ is studied. In the context of a coupling of the form $L(\phi)\,X$ in the k-essence model, we find the effective potential $V$ and the coupling parameter $L$ in terms of the scalar spectral index and the slow roll parameter under a general formalism. To apply the unification in our model, we consider some examples in order to rebuild the effective potential $V(\phi)$ and the coupling parameter $L(\phi)$ as a function of the inflaton field $\phi$. Here, we find that the reconstruction gives rise to an exponential potential and also to natural and hyperbolic inflation, respectively. Thus, in this article we show that it is possible to unify the theoretical foundations from the swampland criteria and the observational parameters corroborated by observations, in the reconstruction of an inflationary universe.

Cosmology of Tsallis holographic scalar field models in Chern–Simons modified gravity and optimization of model parameters through χ 2 minimization

Abstract The present study reports reconstruction schemes for tachyon, k-essence and dilaton scalar field model of Dark Energy (DE) through Tsallis holographic dark fluid under the framework of Chern–Simons modified gravity. Reproducing the conservation equation for a coupled model with interaction term Q = 3 H b 2 ρ m $Q=3H{b}^{2}{\rho }_{m}$ we have reconstructed the different scalar fields and the corresponding potentials. In the case of tachyon, ΛCDM fixed point is attained under this cosmological settings. Considering k-essence in this interacting situation, we have derived some constraints on the interaction term as well as Tsallis holographic dark energy parameter. Reconstructing dilaton scalar field, we have studied the behavior of scalar field and potential. In all those cases, the reconstructed Equation of State (EoS) parameters have been plotted and when computed for current universe z = 0 are found to be consistent with various observational data including Planck + WP + BAO. The only exception is a particular case of reconstructed k-essence model where phantom behavior is apparent, but its numerical value is deviated from the bounce set by the observations. Expressions for different constraints have been obtained and evolutionary behavior of reconstructed scalar fields and potentials for the various cases have been pictorially presented. Finally, we have developed a functional relationship between Hubble parameter and redshift and optimized the parameter values through χ 2 minimization using the observed Hubble parameter values from Hai Yu et al. 2018 ApJ 856 3.