We apply Gaussian processes and Hubble function data in f(T) cosmology to reconstruct for the first time the f(T) form in a model-independent way. In particular, using H(z) data sets coming from cosmic chronometers as well as from the method of radial baryon acoustic oscillations, alongside the latest released local value of H ₀ = 73.52 ± 1.62 km s⁻¹ Mpc⁻¹, we reconstruct H(z) and its derivatives, resulting eventually in a reconstructed region for f(T), without any assumption. Although the cosmological constant lies in the central part of the reconstructed region, the obtained mean curve follows a quadratic function. Inspired by this we propose a new f(T) parameterization, i.e., f(T) = −2Λ + ξT ², with ξ the sole free parameter that quantifies the deviation from ΛCDM cosmology. Additionally, we confront three viable one-parameter f(T) models from the literature, which are the power-law, the square-root exponential, and the exponential models, with the reconstructed f(T) region, and then we extract significantly improved constraints for their model parameters, comparing to the constraints that arise from the usual observational analysis. Finally, we argue that since we are using the direct Hubble measurements and the local value for H ₀ in our analysis, the H ₀ tension can be efficiently alleviated with the above reconstruction of f(T).

In this paper, the formation of specific static wormhole models is discussed, by assuming an $f(R,T)=R+2\lambda T$ extended theory of gravity, $T=-\rho +P_r+2P_l$ being the trace of the energy momentum tensor. In the first part, wormhole solutions are constructed imposing that the radial pressure admits an equation of state corresponding to a varying Chaplygin gas. Two forms for the varying Chaplygin gas are considered, namely $P_r=-Bb(r{)}^u/{\rho }^{\alpha }$ and $P_r=-\mathit{BR}(r{)}^m/{\rho }^{\alpha }$, respectively. In the second part, the wormhole models are constructed assuming that the radial pressure can be described by a varying barotropic fluid. In particular, $P_r=\omega b(r{)}^v\rho$ and $P_r=\widehat{\omega }{r}^{k}R(r{)}^{\eta }\rho$ are considered, respectively, leading to two additional, traversable wormhole models. In all cases, $b(r)$ is the shape function, and $R(r)$ the Ricci scalar obtained from the wormhole metric for a redshift function equal to 1. With the help of specific examples, it is demonstrated that the shape functions of the exact wormhole models previously constructed do obey the necessary metric conditions. The same energy conditions help reveal the physical properties of these models. A general feature is the violation of the null energy condition (NEC) ($\rho +P_i\ge 0$) in terms of the radial pressure $P_r$ at the throat of the wormhole. For some of the models, one can satisfy the NEC at the throat while a violation of the dominant energy condition (DEC) ($\rho -P_i\ge 0$) occurs. To summarize, exact wormhole models can be constructed with a possible violation of the NEC and DEC at the throat of the wormhole, while being $\rho \ge 0$. Thus, the interesting feature appears that one has a violation of the weak energy condition ($\rho \ge 0$ and $\rho +P_i\ge 0$) not related to the energy density behavior (the index $i$, being $r$ respectively $l$, indicates radial respectively lateral pressure).

In this paper, we study two different models of dark energy based on the Chaplygin gas equation of state. The first model is the variable modified Chaplygin gas, while the second one is the extended Chaplygin gas. Both models are considered in the framework of higher order \(f(R)\) modified gravity. We also consider the case of time-varying gravitational constant \(G\) and \(\Lambda \) for both models. We investigate some cosmological parameters such as the Hubble, the deceleration, and the equation of state parameters. Then we show that the model that we consider, the extended Chaplygin gas with time-dependent \(G\) and \(\Lambda \) , is consistent with the observational data. Finally we conclude with the discussion of cosmological perturbations of our model.

In this paper, after reconstructing the redshift evolution of the Hubble function by adopting Gaussian process techniques, we estimate the best-fit parameters for some flat Friedmann cosmological models based on a modified Chaplygin gas interacting with dark matter. In fact, the expansion history of the Universe will be investigated because passively evolving galaxies constitute cosmic chronometers. An estimate for the present-day values of the deceleration parameter, adiabatic speed of sound within the dark energy fluid, effective dark energy, and dark matter equation of state parameters is provided. By this, we mean that the interaction term between the two dark fluids, which breaks the Bianchi symmetries, will be interpreted as an effective contribution to the dark matter pressure similarly to the framework of the “Generalized Dark Matter”. We investigate whether the estimates of the Hubble constant and of the present-day abundance of dark matter are sensitive to the dark matter–dark energy coupling. We will also show that the cosmic chronometers data favor a cold dark matter, and that our findings are in agreement with the Le Châtelier–Braun principle according to which dark energy should decay into dark matter.