Search

We introduce a holographic dark energy model that incorporates the first-order approximate Kaniadaski entropy, utilizing the Hubble horizon, $1/H$, as the infrared cutoff. We investigate the cosmological evolution within this framework. The model introduces an extra parameter relative to the $\Lambda$CDM model. It posits a Universe that is initially dominated by dark matter, which then evolves to a phase where dark energy becomes the predominant component, with this transition occurring at a redshift of approximately $z \sim 0.419$. The energy density of dark energy is ultimately expected to become constant, thereby circumventing the potential issue of a "big rip". Employing the most recent Type Ia supernova and Hubble parameter data, we constrain the model's parameters and find a Hubble constant of $H_0=72.8$ km/s/Mpc, thereby resolving the Hubble tension issue. The estimated age of the Universe, based on the best-fit parameter values, is $14.2$ Gyr. Furthermore, we predict the number of strong gravitational lenses and conduct statefinder and $Om$ diagnostic analyses to validate and characterize the model., Comment: 9 pages, 5 figures

We investigate the cosmological evolution of the power law K-essence dark energy (DE) model $F(X)= -\sqrt{X} + X$ with a new interaction $Q = \alpha\rho _m\rho _{\phi }H^{-1}$ in FRWL spacetime. The evolution behavior of dark energy under this interaction is analyzed by using dynamical systems method, and ten critical points are obtained. Among those critical points, a new stable point, which we called Scaling-like dark energy(DE) solution, is very important and interesting. The cosmological meaning of this attractor is different from the Scaling solution and dark energy dominated solution. For some value of model parameters, the universe will evolve to the attractor solution with the dark energy density parameter $\Omega_{\phi}=0.682946$ and the the equation of state $w_{\phi}=-0.99$, which can be in good agreement with the observed data, and alleviate the Coincidence Problem.

$f(R)$ gravity is one of the simplest theories of modified gravity to explain the accelerated cosmic expansion. Although it is usually assumed that the quasi-Newtonian approach (a combination of the quasi-static approximation and sub-Hubble limit) for cosmic perturbations is good enough to describe the evolution of large scale structure in $f(R)$ models, some studies have suggested that this method is not valid for all $f(R)$ models. Here, we show that in the matter-dominated era, the pressure and shear equations alone, which can be recast into four first-order equations to solve for cosmological perturbations exactly, are sufficient to solve for the Newtonian potential, $\Psi$, and the curvature potential, $\Phi$. Based on these two equations, we are able to clarify how the exact linear perturbations fit into different limits. We find that the Compton length controls the quasi-static behaviours in $f(R)$ gravity. In addition, regardless the validity of quasi-static approximation, a strong version of the sub-Hubble limit alone is sufficient to reduce the exact linear perturbations in any viable $f(R)$ gravity to second order. Our findings disagree with some previous studies where we find little difference between our exact and quasi-Newtonian solutions even up to $k=10 c^{-1} \mathcal{H}_0$.

We give a full investigation on the dynamics of power-law kinetic quintessence $L(X, \phi)=V(\phi)(-X+X^2)$ by considering the potential related parameter $\Gamma$($=\frac{V V''}{V'^2}$) as a function of another potential parameter $\lambda$($=\frac{V'}{\kappa V^{3/2}}$), which correspondingly extends the analysis of the dynamical system of our universe from two-dimension to three-dimension. Beside the critical points found in previous papers, we find a new de-Sitter-like dominant attractor(\textit{cp$6$}) and give its stable condition using the center manifold theorem. For the dark energy dominant solution(\textit{cp$6$} and \textit{cp$7$}), it could be distinguished from canonical quintessence and tachyon models since the sound speed $c_s^2=0$ or $c_s^2\ll 1$. For the scaling solution (\textit{cp$8$}), it is very interesting that the sound speed $c_s^2=1/5$ while it behaves as ordinary matter. We therefore point out that the power-law kinetic quintessence should have different signatures on cold dark matter power spectrum and cosmic microwave background both at early time when this scalar field is an early dark energy with $\Omega_\phi$ being non-negligible at high redshift and at late time when it drives the accelerating expansion. We even do not know whether there are any degeneracies of the impacts between these two epoches. They are expected to be investigated in future., Comment: 17 pages, 4 figures, accepted by Physical Review D, in press

We give the three-dimensional dynamical autonomous systems for most of the popular scalar field dark energy models including (phantom) quintessence, (phantom) tachyon, k-essence and general non-canonical scalar field models, change the dynamical variables from variables $(x, y, \lambda)$ to observable related variables $(w_{\phi}, \Omega_{\phi}, \lambda)$, and show the intimate relationships between those scalar fields that the three-dimensional system of k-essence can reduce to (phantom) tachyon, general non-canonical scalar field can reduce to (phantom) quintessence and k-essence can also reduce to (phantom) quintessence for some special cases. For the applications of the three-dimensional dynamical systems, we investigate several special cases and give the exactly dynamical solutions in detail. In the end of this paper, we argue that, it is more convenient and also has more physical meaning to express the differential equations of dynamical systems in $(w_{\phi}, \Omega_{\phi}, \lambda)$ instead of variables $(x, y, \lambda)$ and to investigate the dynamical system in 3-Dimension instead of 2-Dimension. We also raise a question about the possibility of the chaotic behavior in the spatially flat single scalar field FRW cosmological models in the presence of ordinary matter., Comment: 20 pages, 8 figures,some references added. Minor changes according to the suggestions from referees