We study the scenario of Kaniadakis horizon-entropy cosmology, which arises from the application of the gravity-thermodynamics conjecture using the Kaniadakis modified entropy. The resulting modified Friedmann equations contain extra terms that constitute an effective dark energy sector. We use data from cosmic chronometers, Type Ia supernova, H ii galaxies, strong lensing systems, and baryon acoustic oscillation observations, and we apply a Bayesian Markov chain Monte Carlo analysis to construct the likelihood contours for the model parameters. We find that the Kaniadakis parameter is constrained around 0, namely around the value where the standard Bekenstein–Hawking is recovered. Concerning the normalized Hubble parameter, we find |$h=0.708^{+0.012}_{-0.011}$|⁠, a result that is independently verified by applying the |$\mathbf {\mathbb {H}}0(z)$| diagnostic and, thus, we conclude that the scenario at hand can alleviate the H₀ tension problem. Regarding the transition redshift, the reconstruction of the cosmographic parameters gives |$z_{\rm T}=0.715^{+0.042}_{-0.041}$|⁠. Furthermore, we apply the Akaike, Bayesian, and deviance information criteria, and we find that in most data sets the scenario is statistical equivalent to Λ cold dark matter one. Moreover, we examine the big bang nucleosynthesis, and we show that the scenario satisfies the corresponding requirements. Additionally, we perform a phase-space analysis, and we show that the Universe past attractor is the matter-dominated epoch, while at late times the Universe results in the dark-energy-dominated solution. Finally, we show that Kaniadakis horizon-entropy cosmology accepts heteroclinic sequences, but it cannot exhibit bounce and turnaround solutions.

In this paper, we examine the interacting dark energy model in f(T) cosmology. We assume dark energy as a perfect fluid and choose a specific cosmologically viable form f(T) = β√T. We show that there is one attractor solution to the dynamical equation of f(T) Friedmann equations. Further we investigate the stability in phase space for a general f(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 u* = (c − 1)v* in the phase space, spanned by coordinates (u, v, Ω, T). From this critical sheet, we conclude that the coupling between the dark energy and matter c ∈ (−2, 0).

We confront $f(T,T_G)$ gravity, with big bang nucleosynthesis (BBN) requirements. The former is obtained using both the torsion scalar, as well as the teleparallel equivalent of the Gauss–Bonnet term, in the Lagrangian, resulting to modified Friedmann equations in which the extra torsional terms constitute an effective dark energy sector. We calculate the deviations of the freeze-out temperature $T_f$, caused by the extra torsion terms in comparison to $\Lambda$CDM paradigm. Then, we impose five specific $f(T,T_G)$ models and extract the constraints on the model parameters in order for the ratio $|\Delta T_f/T_f|$ to satisfy the observational BBN bound. As we find, in most of the models the involved parameters are bounded in a narrow window around their general relativity values as expected, asin the power-law model, where the exponent n needs to be $n\lesssim 0.5$. Nevertheless, the logarithmic model can easily satisfy the BBN constraints for large regions of the model parameters. This feature should be taken into account in future model building.

In this paper, we consider the (2+1)-dimensional complex modified Korteweg-de Vries equations (CMKdVE). Using the Lax pair, we construct a Darboux transformation and namely one-fold and n-fold transformations. The soliton solutions are obtained from the different "seeds" by using this Darboux transformation.