In this paper, applying the Hartman-Grobman theorem we carry out a qualitative late-time analysis of some unified dark energy-matter Friedmann cosmological models, where the two interact through linear energy exchanges, and the dark energy fluid obeys to the dynamical equation of state of Redlich-Kwong, Modified Berthelot, and Dieterici respectively. The identification of appropriate late-time attractors allows to restrict the range of validity of the free parameters of the models under investigation. We show that the strength of deviation from an ideal fluid for the dark energy does not influence the stability of the late-time attractors, as well as the values of all the cosmological parameters at equilibrium, but for the Hubble function (which represents the age of the universe). Our analysis also shows that a singularity in the effective equation of state parameter for the dark energy fluid is not possible within this class of models.

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.

In this paper, we investigate the potential-driven inflation models with a disformal coupling to Einstein gravity, to find out the effects of such a coupling on these models. We consider a simple coupling form which introduces only one parameter, and three inflation models, namely the chaotic inflation, the Higgs inflation, and the monodromy inflation. We find that the disformal coupling can have some modifications to the observational variables of these models such as the power spectrum, the spectral index as well as the tensor/scalar ratio, although not too large due to the constraints on the disformal coupling parameter. With these modifications, one has the opportunity of improving models that lie on the edge of the favorable regions of Planck observational data, such as monodromy inflation. Moreover, the nontrivial sound speed of tensor perturbations (gravitational waves) may come out, due to the coupling of gravity and kinetic terms of the field.

Bayesian Machine Learning (BML) and strong lensing time delay (SLTD) techniques are used in order to tackle the $$H_{0}$$ H 0 tension in f(T) gravity. The power of BML relies on employing a model-based generative process which already plays an important role in different domains of cosmology and astrophysics, being the present work a further proof of this. Three viable f(T) models are considered: a power law, an exponential, and a squared exponential model. The learned constraints and respective results indicate that the exponential model, $$f(T)=\alpha T_{0}\left( 1-e^{-p T / T_{0}}\right) $$ f ( T ) = α T 0 1 - e - p T / T 0 , has the capability to solve the $$H_{0}$$ H 0 tension quite efficiently. The forecasting power and robustness of the method are shown by considering different redshift ranges and parameters for the lenses and sources involved. The lesson learned is that these values can strongly affect our understanding of the $$H_{0}$$ H 0 tension, as it does happen in the case of the model considered. The resulting constraints of the learning method are eventually validated by using the observational Hubble data (OHD).