We study an early dark energy (EDE) model as a K-essence scalar field in the framework of FLRW universe using an effective parametrization of the state equation as a function of the redshift $z$ with the tracker condition during radiation domination, but also demanding an accelerated expansion of the universe at late times emulating cosmological constant. We found all the dynamical variables of the EDE system. We use the luminosity distances of the SNIA to get the best estimations for the free parameters of the model and also, we constrain the model using primordial abundances of light nuclei in BBN theory. We summarize the necessary conditions to achieve BBN predictions and the accelerated expansion of the universe at late times.
We investigated the scenario of time-dependent diffusive interaction between dark matter and dark energy and showed that such a model can be accommodated within the observations of luminosity distance - redshift data in Supernova Ia (SNe Ia) observations. We obtain constrains on different relevant parameters of this model from the observational data. We consider a homogeneous scalar field $ϕ(t)$ driven by a $k-$essence Lagrangian of the from $L = V(ϕ)F(X)$ with constant potential $V(ϕ) = V$, to describe the dynamics of dark energy in this model. Using the temporal behaviour of the FRW scale fa…
It has been shown by \textit{Scherrer and Putter et.al} that, when dynamics of dark energy is driven by a homogeneous $k-$essence scalar field $ϕ$, with a Lagrangian of the form $L = V_0F(X)$ with a constant potential $V_0$ and $X = \frac{1}{2}\nabla^μϕ\nabla_μϕ= \frac{1}{2}\dotϕ^2$, one obtains a scaling relation $X(dF/dX)^2 = Ca^{-6}$ , where $C$ is a constant and $a$ is the FRW scale factor of the universe. The separate energy conservation in the dark energy sector and the constancy of $k-$essence potential are instrumental in obtaining such a scaling. In this paper, we have shown that even…
From Dark Radiation to Dark Energy: Unified Cosmological Evolution in K-essence Models
Universidad de Guanajuato（瓜纳华托大学）；Centro de Investigación y de Estudios Avanzados del I.P.N.（墨西哥国立自治研究所高级研究中心）；Secretaría de Ciencia, Humanidades, Tecnología e Innovación（科学、人文、技术与创新秘书处）
Hubble tension in k-essence: Evidence for robust tension alleviation
Botswana International University of Science and Technology（博茨瓦纳国际科学与技术大学）；University of Cape Town（开普敦大学）；North-West University（西北大学）；Omdurman Islamic University（恩图曼伊斯兰大学）
We reexamine $k$-essence dark energy models with a scalar field $ϕ$ and a factorized Lagrangian, $\mathcal L = V(ϕ)F(X)$, with $X = \frac{1}{2} \nabla_μϕ\nabla^μϕ.$ A value of the equation of state parameter, $w$, near $-1$ requires either $X \approx 0$ or $dF/dX \approx 0$. Previous work showed that thawing models with $X \approx 0$ evolve along a set of unique trajectories for $w(a)$, while those with $dF/dX \approx 0$ can result in a variety of different forms for $w(a)$. We show that if $dV/dϕ$ is small and $(1/V)(dV/dϕ)$ is roughly constant, then the latter models also converge toward a s…
In this paper the Lagrangian density of a purely kinetic k--essence that models the behavior of dark energy described by four parameterized equations of state proposed by Cooray \& Huterer (Astrophys. J. {\bf 513} L95, 1999), Zhang \& Wu (Mod. Phys. Lett. A {\bf 27} 1250030, 2012), Linder (Phys. Rev. Lett. {\bf 90} 091301, 2003), Efstathiou (Mon. Not. Roy. Astron. Soc. {\bf 310} 842, 2000), and Feng \& Lu (J. Cosmol. Astropart. Phys. {\bf 1111} 034, 2011) has been reconstructed. This reconstruction is performed using the method outlined by de Putter \& Linder (Astropart.\ Phys.\ {\bf 28} 263, …
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 $X\equiv \frac{1}{2}\partial^μϕ\partial_μϕ$. 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 \cite{thaws}. Ref. \cite{thaws} points out that the non-uniform distribution of effectiv…
We consider scalar dark matter models where the theory has a shift symmetry only broken by the scalar mass term. We restrict ourselves to K-essence kinetic terms where the shift symmetric part of the Lagrangian is a function of the first derivatives of the scalar field only. In the low-amplitude and nonrelativistic regime, which applies on large galactic scales, scalar clouds form solitons with a finite core. Close to the center of galaxies, where a supermassive Black Hole (BH) resides, we analyze the scalar field distribution and the fate of the dark matter soliton when subject to the BH grav…
Early dark energy (EDE) that becomes subdominant around the epoch of matter-radiation equality can be used to ease the Hubble tension. However, there is a theoretical problem that why the energy scale of EDE is in coincidence with that of matter-radiation equality when their physics are completely unrelated. Sakstein and Trodden [Phys. Rev. Lett. 124, 161301 (2020)] proposed a mechanism to solve this coincidence problem with $\mathcal{O}({\rm eV})$-mass neutrino. In this paper, in order to solve the coincidence problem, we propose a new scenario for EDE, in which the onset and ending of EDE ar…
K-essence is a minimally-coupled scalar field whose Lagrangian density $\mathcal{L}$ is a function of the field value $ϕ$ and the kinetic energy $X=\frac{1}{2}\partial_μϕ\partial^μϕ$. 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 $\mathcal{L}(ϕ, X)$ from random matrices. From the ensemble of randomly generated thawing k-essence models, we select dark energy candidates by assuming negative pressure and non-…
Purely kinetic k-essence models have been shown in the literature to be a field theory equivalent of barotropic fluid models of dark energy or dark matter-dark energy unification. In the modeling framework where the speed of sound squared of a barotropic fluid is modeled as a function of its Equation of State parameter, a systematic procedure of obtaining the Lagrangian density of an equivalent purely kinetic k-essence model is presented. As this modeling approach starts from the speed of sound, purely kinetic k-essence models can be constructed for which the speed of sound is in agreement wit…
In this article we try to find out the conditions when a ghost field in conjunction with a barotropic fluid produces a stable accelerating expansion phase of the universe. It is seen that in many cases the ghost field produces a condensate and drives the fluid energy density to zero in the final accelerating phase, but there can be other possibilities. We have shown that a pure kinetic $k$-essence field (which is not a ghost field) interacting with a fluid can also form an interaction induced condensate and produce a stable accelerating phase of the universe. In the latter case the fluid energ…
We propose a new non-trivial way to combine mimetic dark matter with the mimetic formulation of unimodular gravity. This yields a Weyl-invariant higher-derivative scalar-vector-tensor theory. We demonstrate that on-shell its behavior mimics GR with an additional k-essence scalar. The overall scale of the k-essence arises as an integration constant -- a global degree of freedom. Interestingly, we find that the resulting fluid cannot make transition through ultra-relativistic equation of state. We develop a method to find a mimetic theory corresponding to any eligible k-essence and identify, whi…
In the present work we investigate the stability of the k-essence models allowing upto quadratic terms of the kinetic energy. The system of field equations is written as an autonomous system in terms of dimensionless variables and the stability criteria of the equilibria have been extensively investigated. The results strongly indicate that cosmologically consistent models dynamically evolve towards the quintessence model, a stable solution with a canonical form of the dark energy.
Is Phantom Divide Crossing in General Relativity Completely Impossible? Shortcomings in canonical and minimally coupled scalar field and Possible Solutions in $k$-essence Models
High Energy Accelerator Research Organization (KEK)（高能加速器研究机构）；Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University（名古屋大学小林-益川粒子宇宙起源研究所）；ICREA（加泰罗尼亚高级研究中心）；Institute of Space Sciences (IEEC-CSIC)（空间科学研究所）；Institut d’Estudis Espacials de Catalunya (IEEC)（加泰罗尼亚空间研究学院）；Aristotle University of Thessaloniki（塞萨洛尼基亚里士多德大学）；Khazar University（哈扎尔大学）
We study the vacuum Cauchy problem for K-essence, i.e. cosmologically relevant scalar-tensor theories that involve first-order derivative self-interactions, and which pass all existing gravitational wave bounds. We restrict to spherical symmetry and show that there exists a large class of theories for which no breakdown of the Cauchy problem occurs outside apparent black hole horizons, even in the presence of scalar shocks/caustics, except for a small set of initial data sufficiently close to critical black hole collapse. We characterise these problematic initial data, and show that they lead …
Botswana International University of Science and Technology（博茨瓦纳国际科技大学）；University of Cape Town（开普敦大学）；North-West University（西北大学）；Omdurman Islamic University（恩图曼伊斯兰大学）
In this work we shall study the late-time behavior of $k$-Essence $f(R)$ gravity without scalar potential, in the presence of matter and radiation perfect fluids. We quantify the late-time study by using the statefinder function $Y_H(z)=\frac{ρ_{DE}}{ρ_m^{(0)}}$, which is a function of the redshift and of the Hubble rate. By appropriately rewriting the Friedmann equation in terms of the redshift and of the function $Y_H(z)$, we numerically solve it using appropriate initial conditions, and we critically examine the effects of the $k$-Essence higher order kinetic terms. As we demonstrate, the e…
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 $ε(N)$in terms of the number of $e$-folds $N$ is studied. In the context of a coupling of the form $L(ϕ)\,X$ 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 ef…
In this work we study a modified version of $f(R)$ gravity in which higher order kinetic terms of a scalar field are added in the action of vacuum $f(R)$ gravity. This type of theory is a type of $k$-essence $f(R)$ gravity, and it belongs to the general class of $f(R,ϕ,X)$ theories of gravity, where $ϕ$ is a scalar field and $X=\frac{1}{2}\partial^μϕ\partial_μϕ$. We focus on the inflationary phenomenology of the model, in the slow-roll approximation, and we investigate whether viable inflationary evolutions can be realized in the context of this theory. We use two approaches, firstly by imposi…
Dynamical System of Scalar Field from 2-Dimension to 3-D and its Cosmological Implication
我们对大多数流行的标量场暗能量模型，包括（幻影）quintessence，（幻影）tachyon，k-essence和一般的非正则标量场模型，给出了三维动力学自治系统，将动力学变量从变量$(x, y, λ)$变为可观测的相关变量$(w_ϕ, Ω_ϕ, λ)$，并展示了k-本质三维系统可还原为（幻影）快子的那些标量场之间的密切关系，一般的非正则标量场可以归约为（幻影）quintessence，k-本质在某些特殊情况下也可以归约为（幻影）quintessence。对于三维动力系统的应用，我们研究了几种特殊情况，并给出了详细的精确动力学解。本文最后指出，用$(w_ϕ, Ω_ϕ, λ)$代替变量$(x, y, λ)$来表示动力系统的微分方程，用三维来研究动力系统比用二维来研究动力系统更方便，也更有物理意义。我们还提出了一个问题，在空间平坦的单标量场FRW宇宙模型中的混沌行为的可能性在普通物质的存在。
We study gravitational collapse in K-essence model with shift symmetry. For these models, we have the formation of two types of horizons, event and sonic. For the particular case $K(X)=X+βX^2$ we found three different regimes. In the weak field regime the scalar field disperses to infinity, in the very strong regime both horizons form at the same time and finally for the intermediate regime, the sonic horizon could form first or both horizons form at the same time. The threshold of formation of black hole is found in the regime where the sonic horizon forms first. We observe a universal behavi…
We consider k-essence, a scalar-tensor theory with first-order derivative self-interactions that can screen local scales from scalar fifth forces, while allowing for sizeable deviations from General Relativity on cosmological scales. We construct fully nonlinear static stellar solutions that show the presence of this screening mechanism, and we use them as initial data for simulations of stellar oscillations and gravitational collapse in spherical symmetry. We find that for k-essence theories of relevance for cosmology, the screening mechanism works in the case of stellar oscillation and suppr…
