Abstract:In this paper, we examine the interacting dark energy model in (T ) cosmology. We assume dark energy as a perfect fluid and choose a specific cosmologically viable form (T ) = β √ T . We show that there is one attractor solution to the dynamical equation of (T ) Friedmann equations. Further we investigate the stability in phase space for a general (T ) model with two interacting fluids. By studying the local stability near the critical points, we show that the critical points lie on the sheet * = ( − 1) * in the phase space, spanned by coordinates ( Ω T ). From this critical sheet, we conclude that the coupling between the dark energy and matter ∈ (−2 0). PACS (2008):

We construct a holographic dark energy scenario based on Kaniadakis entropy, which is a generalization of Boltzmann-Gibbs entropy that arises from relativistic statistical theory and is characterized by a single parameter K which quantifies the deviations from standard expressions, and we use the future event horizon as the Infrared cutoff. We extract the differential equation that determines the evolution of the effective dark energy density parameter, and we provide analytical expressions for the corresponding equation-of-state and deceleration parameters. We show that the universe exhibits the standard thermal history, with the sequence of matter and dark-energy eras, while the transition to acceleration takes place at $$z\approx 0.6$$ z ≈ 0.6 . Concerning the dark-energy equation-of-state parameter we show that it can have a rich behavior, being quintessence-like, phantom-like, or experience the phantom-divide crossing in the past or in the future. Finally, in the far future dark energy dominates completely, and the asymptotic value of its equation of state depends on the values of the two model parameters.

No abstract

The present work addresses the study and characterization of the integrability of some generalized Heisenberg ferromagnet equations (GHFE) in 1+1 dimensions. Lax representations for these GHFE are successfully obtained. The gauge equivalent counterparts of these integrable GHFE are presented.

We investigate Kaniadakis-holographic dark energy by confronting it with observations. We perform a Markov Chain Monte Carlo analysis using cosmic chronometers, supernovae type Ia, and Baryon Acoustic Oscillations data. Concerning the Kaniadakis parameter, we find that it is constrained around zero, namely around the value in which Kaniadakis entropy recovers standard Bekenstein-Hawking one. Additionally, for the present matter density parameter $\Omega _m^{(0)}$, we obtain a value slightly smaller compared to ΛCDM scenario. Furthermore, we reconstruct the evolution of the Hubble, deceleration and jerk parameters extracting the deceleration-acceleration transition redshift as $z_T = 0.86^{+0.21}_{-0.14}$. Finally, performing a detailed local and global dynamical system analysis, we find that the past attractor of the Universe is the matter-dominated solution, while the late-time stable solution is the dark-energy-dominated one.

Motion of curves and surfaces in R 3 lead to nonlinear evolution equations which are often integrable. They are also intimately connected to the dynamics of spin chains in the continuum limit and integrable soliton systems through geometric and gauge symmetric connections/equivalence. Here we point out the fact that a more general situation in which the curves evolve in the presence of additional self consistent vector potentials can lead to interesting generalized spin systems with self consistent potentials or soliton equations with self consistent potentials. We obtain the general form of the evolution equations of underlying curves and report specific examples of generalized spin chains and soliton equations. These include principal chiral model and various Myrzakulov spin equations in (1+1) dimensions and their geometrically equivalent generalized nonlinear Schrödinger (NLS) family of equations, including Hirota-Maxwell-Bloch equations, all in the presence of self consistent potential fields. The associated gauge equivalent Lax pairs are also presented to confirm their integrability.

We demonstrate two periodic or quasi-periodic generalizations of the Chaplygin gas (CG) type models to explain the origins of dark energy as well as dark matter by using the Weierstrass ℘(t), σ(t) and ζ(t) functions with two periods being infinite. If the universe can evolve periodically, a non-singular universe can be realized. Furthermore, we examine the cosmological evolution and nature of the equation of state (EoS) of dark energy in the Friedmann-Lemaître-Robertson-Walker cosmology. It is explicitly illustrated that there exist three type models in which the universe always stays in the non-phantom (quintessence) phase, whereas it always evolves in the phantom phase, or the crossing of the phantom divide can be realized. The scalar fields and the corresponding potentials are also analyzed for different types of models.

No abstract