Narrow Results

We study spatially flat isotropic universes driven by k-essence. It is shown that Friedmann and k-field equations may be analytically integrated for arbitrary k-field potentials during evolution with a constant baryotropic index. It follows that there is an infinite number of dynamically different k-theories with equivalent kinematics of the gravitational field. We show that there is a large "window" of stable solutions, and that the dust-like behavior separates stable from unstable expansion. Restricting to the family of power law solutions, it is argued that the linear scalar field model, with constant function F, is isomorphic to a model with divergent speed of sound and this makes them less suitable for cosmological modeling than the nonlinear k-field solutions we find in this paper.

We implement the transition from dark matter to dark energy in k-essence cosmologies for a very large set of kinetic functions F, in a way alternative to recent proposals which use generalized Chaplygin gas and transient models. Here we require that the pressure admits a power-law expansion around some value of the kinetic energy where the pressure vanishes. In addition, for suitable values of the parameters of the model, the speed of sound of the dark matter will be low. We first present the discussion in fairly general terms, and later consider for illustration two examples.

We construct the non-canonical kinetic term of a k-essence field directly from the effective equation of state function w_k(z), which describes the properties of the dark energy. Adopting the usual parametrizations of equation of state, we numerically reproduce the shape of the non-canonical kinetic term and discuss some features of the constructed form of k-essence.

We study a flat three-brane in the presence of a linear k field with nonzero cosmological constant Λ₄. In this model the crossing of the phantom divide (PD) occurs when the k-essence energy density becomes negative. We show that in the high energy regime the effective equation of state has a resemblance of a modified Chaplygin gas while in the low energy regime it becomes linear. We find a scale factor that begins from a singularity and evolves to a de Sitter stable stage while other solutions have a super-accelerated regime and end with a big rip. We use the energy conditions to show when the effective equation of state of the brane-universe crosses the PD.

In this paper, we have researched tachyon field, k-essence and quintessence dark energy (DE) models for Friedmann–Robertson–Walker (FRW) universe with varying G and $\mathrm{\Lambda }$ in f(R, T) gravitation theory. The theory of f(R, T) is proposed by Harko et al. [Phys. Rev. D84, 024020, 2011]. In this theory, R is the Ricci scalar and T is the trace of energy–momentum tensor. For the solutions of field equations, we have used linearly varying deceleration parameter (LVDP), the equation of state (EoS) and the ratio between $\mathrm{\Lambda }$ and Hubble parameter. Also, we have discussed some physical behavior of the models with various graphics.

In this paper, we exploit dynamics of a $k$-essence scalar field to realize interactions between dark components of universe resulting in an evolution consistent with observed features of late-time phase of cosmic evolution. Stress–energy tensor corresponding to a $k$-essence Lagrangian $L=V(\varphi )F(X)$ (where $X=\frac{1}{2}{g}^{\mu \nu }{\nabla }_{\mu }\varphi {\nabla }_{\nu }\varphi$) is shown to be equivalent to an ideal fluid with two components having same equation of state. Stress–energy tensor of one of the components may be generated from a constant potential $k$-essence Lagrangian of form $L_1=V_{0}F(X)$ ($V_0$ constant) and that of other from another Lagrangian of form $L_2=V_1(\varphi )F(X)$ with $V=V_0+V_1(\varphi )$. We have shown that the unified dynamics of dark matter and dark energy described by a single scalar field $\varphi$ driven by a $k$-essence Lagrangian $L=V(\varphi )F(X)$ may be viewed in terms of diffusive interactions between the two hypothetical fluid components “1” and “2” with stress–energy tensors equivalent to that of Lagrangians $L_1$ and $L_2$, respectively. The energy transfer between the fluid components is determined by functions $V(\varphi )$, $F(X)$ and their derivatives. Such a realization is shown to be consistent with the Supernova Ia data with certain constraints on the temporal behavior of $k$-essence potential $V(\varphi )$. We have described a methodology to obtain such constraints.

In this research, we have investigated tachyon and $k$-essence dark energy (DE) candidates with varying $G$ and $\mathrm{\Lambda }$ for Marder universe in $f(R,T)$ gravitation theory [Harko et al., Phys. Rev. D84, 024020 (2011)]. Here, $f(R,T)$ is the arbitrary function of Ricci scalar ($R$) and the trace of $T_{ik}$. To solve $f(R,T)$ gravity field equations, three different approximations have been used such as cosmological term, equation of state (EoS) parameter and the anisotropy feature of Marder universe. Also, we have discussed some physical results with various graphics.

In this paper, we investigate the Sharma–Mittal holographic dark energy (SMHDE) model in the context of a spatially homogeneous and isotropic flat Friedmann–Robertson–Walker (FRW) Universe by taking various values of model parameters $R$ and $\delta$ and the Hubble horizon is taken as the infrared cut-off. We have analyzed the deceleration parameter $(q)$ and the EoS parameter. According to the deceleration parameter, the Universe is in an accelerating and expanding phase, which is compatible with the observational data. The EoS parameter depicts that presently the Universe is lying in the quintessence region and at a late time it will show $\mathrm{\Lambda }$CDM behavior. It is also concluded by the stability analysis that SMHDE model is classically stable at present and future. To understand the dynamics of our Universe, we have established a correspondence among SMHDE and the quintessence, tachyon and K-essence scalar-field models. Our results show that the Universe is in an accelerating expansion mode described by quintessence like behavior. We go further and estimate the model parameters by using the distance modulus measurement of the recent Union 2.1 dataset of supernovae.

In order to solve the mystery of the accelerating and expanding universe model first, various dark energy candidates, such as Quintessence, Tachyon, k-essence, Phantom and DBI-essence, were investigated in detail in the $f(Q)$ modified symmetric teleparallel gravitation theory for homogeneous and isotropic FRLW universe model. The $f(Q)=a{Q}^n+b$ model is used to obtain solutions in $f(Q)$ theory. Also, the physical behaviors of some cosmological parameters such as pressure and density were studied. Dark energy candidates were analyzed for different values of n with various graphs.

An alternative scenario about the phenomenology of primordial universe is $k$-inflation. According to this concept, inflation can be achieved by nonstandard kinetic term of scalar field, namely, the inflaton. In this paper, we focus on $k$-essence models in the presence of a higher order and a linear kinetic term. Furthermore, the inflationary phenomenology with a Dirac–Born–Infeld scalar field is briefly examined, which arises from quantum theories of gravity such as superstring theory. Our approach about the inflationary era is that it can be described in the context of Einstein’s gravity involving quantum corrections such as the Chern–Simons string inspired parity violating gravitational term. The equations of motion namely, the Friedmann equation, the Raychadhuri equation and the Klein–Gordon equation for an expanding background are extracted from the gravitational action utilizing the variational principle. The consequential system of differential equations with respect to Hubble’s parameter and the inflaton field was quite perplexed in order to be solved with an analytic way. Therefore, the slow-roll conditions during inflationary era were imposed and terms with minor numerically contribution were neglected. From the overall phenomenological analysis, it is proved that models with exotic kinetic terms can generate viable results in consistency with the latest Planck data. Finally, the presence of Chern–Simons quantum corrections shifts the primordial spectral tensor index to blue. Even though blue gravitational waves are yet to be observed, if detected, compatibility with the aforementioned theory can be achieved.

We study the structural stability of a cosmic acceleration (inflation) in a class of k-essence cosmologies against changes in the shape of the potential. Those models may be viewed as generalized tachyon cosmologies and this analysis extends previous results on the structural stability of cosmic acceleration in tachyon cosmologies. The study considers both phantom and non-phantom cases. The concepts of rigidity and fragility are defined through a condition on the functional form of the Hubble factor. Given the known result of the existence of inflationary (non-phantom) and super-inflationary (phantom) attractors we formulate the question of their structural stability. We find that those attractors are rigid in the sense that they never change as long as the conditions for inflation or super-inflation are met.

We investigate a k-essence field localized on the brane evolving linearly with the cosmological time for some kinetic functions and consider the atypical k-essence model for linear and nonlinear k-fields in Friedmann–Robertson–Walker (FRW) cosmology. In the former case the k-field is driven by an inverse quadratic polynomial potential and the solutions exhibit several different behaviors which include expanding, contracting and bouncing universes as well as a model with a finite time span, some of them ending in a big crunch or a big rip. In the latter case we find the potential and show that the atypical k-essence model is dynamically incomplete. Particularly, by selecting the extended tachyonic kinetic functions we analyze the high and low energy limits of our model, obtaining the nearly power-law solution. We introduce a tachyon field with negative energy density and show that the universe evolves between two singularities.

We review some properties of black hole structures appearing in gravity with a massless scalar field, with both minimal and nonminimal coupling. The main properties of the resulting cold black holes are described. The study of black holes in scalar-gravity systems is extended to $k$-essence theories, and some examples are explicitly worked out. In these cases, even while the existence of horizons is possible, the metric regularity requirement on the horizon implies either a cold black type structure or a singular behavior of the scalar field.

Dark energy models and modified gravity theories have been actively studied and the behaviors in the solar system have been also carefully investigated in a part of the models. However, the isotropic solutions of the field equations in the simple models of dark energy, e.g. quintessence model without matter coupling, have not been well investigated. One of the reason would be the nonlinearity of the field equations. In this paper, a method to evaluate the solution of the field equations is constructed, and it is shown that there is a model that can easily pass the solar system tests, whereas, there is also a model that is constrained from the solar system tests.

We study the stability properties of static, spherically symmetric configurations in $k$-essence theories with the Lagrangians of the form $F(X)$, $X\equiv {\varphi }_{,\alpha }{\varphi }^{,\alpha }$. The instability under spherically symmetric perturbations is proved for the two recently obtained exact solutions for $F(X)=F_0{X}^{1/3}$ and for $F(X)=F_0{X}^{1/2}-2\mathrm{\Lambda }$, where $F_0$ and $\mathrm{\Lambda }$ are constants. The first solution describes a black hole in an asymptotically singular spacetime, the second one contains two horizons of infinite area connected by a wormhole. It is argued that spherically symmetric $k$-essence configurations with $n<1/2$ are generically unstable because the perturbation equation is not of hyperbolic type.

In this paper, $k$-inflation is analyzed in warm braneworld scenario. A general class of $k$-essence models with power-law kinetic term is investigated and weak and strong dissipation regimes are studied. Scalar perturbations and spectral index are derived. The results are discussed and applied to specific examples.

In this paper, we investigate Barrow holographic dark energy (BHDE) using Hubble horizon as infrared cut-off in the framework of Bianchi-I, anisotropic model by considering hybrid expansion law (HEL). We have examined different cosmological parameters like energy density parameters, EoS parameter of BHDE model, which support the present accelerated expansion of the Universe. We have also reconciled BHDE by reconstructing the evolution of scalar field potential. The K-essence has been taken for the study of this reconstruction, which also exhibits the accelerated expansion at present.

The cosmology has made enormous progress after the construction of General Relativity (GR) in 1915. The theoretical predictions of GR — such as the existence of black holes and gravitational waves — have been directly/indirectly confirmed by observations. Now, we know that GR is sufficiently dependable to describe the gravitational law in the solar system.