We consider a cosmology in which dark matter and a quintessence scalar field responsible for the acceleration of the Universe are allowed to interact. Allowing for both conformal and disformal couplings, we perform a global analysis of the constraints on our model using Hubble parameter measurements, baryon acoustic oscillation distance measurements, and a Supernovae Type Ia data set. We find that the additional disformal coupling relaxes the conformal coupling constraints. Moreover, we show that, at the background level, a disformal interaction within the dark sector is preferred to both $\mathrm{\Lambda }\mathrm{CDM}$ and uncoupled quintessence, hence favoring interacting dark energy.

We consider several cosmological models which allow for nongravitational direct couplings between dark matter and dark energy. The distinguishing cosmological features of these couplings can be probed by current cosmological observations, thus enabling us to place constraints on these specific interactions which are composed of the conformal and disformal coupling functions. We perform a global analysis in order to independently constrain the conformal, disformal, and mixed interactions between dark matter and dark energy by combining current data from: Planck observations of the cosmic microwave background radiation anisotropies, a combination of measurements of baryon acoustic oscillations, a supernova type Ia sample, a compilation of Hubble parameter measurements estimated from the cosmic chronometers approach, direct measurements of the expansion rate of the Universe today, and a compilation of growth of structure measurements. We find that in these coupled dark-energy models, the influence of the local value of the Hubble constant does not significantly alter the inferred constraints when we consider joint analyses that include all cosmological probes. Moreover, the parameter constraints are remarkably improved with the inclusion of the growth of structure data set measurements. We find no compelling evidence for an interaction within the dark sector of the Universe.

In this work, we use a combined approach of Hubble parameter data together with redshift-space-distortion (fσ₈) data, which together are used to reconstruct the teleparallel gravity (TG) Lagrangian via Gaussian processes (GP). The adopted Hubble data mainly comes from cosmic chronometers, while for the Type Ia supernovae data we use the latest jointly calibrated Pantheon compilation. Moreover, we consider two main GP covariance functions, namely the squared-exponential and Cauchy kernels in order to show consistency (to within 1σ uncertainties). The core results of this work are the numerical reconstructions of the TG Lagrangian from GP reconstructed Hubble and growth data. We take different possible combinations of the datasets and kernels to illustrate any potential differences in this regard. We show that nontrivial cosmology beyond ΛCDM falls within the uncertainties of the reconstructions from growth data, which therefore indicates no significant departure from the concordance cosmological model.

In the context of a Hubble tension problem that is growing in its statistical significance, we reconsider the effectiveness of non-parametric reconstruction techniques which are independent of prescriptive cosmological models. By taking cosmic chronometers, Type Ia Supernovae and baryonic acoustic oscillation data, we compare and contrast two important reconstruction approaches, namely Gaussian processes (GP) and the Locally weighted Scatterplot Smoothing together with Simulation and extrapolation method (LOESS-Simex or LS). In the context of these methods, besides not requiring a cosmological model, they also do not require physical parameters in their approach to their reconstruction of data (but they do depend on statistical hyperparameters). We firstly show how both GP and LOESS-Simex can be used to successively reconstruct various data sets to a high level of precision. We then directly compare both approaches in a quantitative manner by considering several factors, such as how well the reconstructions approximate the data sets themselves to how their respective uncertainties evolve. In light of the puzzling Hubble tension, it is important to consider how the uncertain regions evolve over redshift and the methods compare for estimating cosmological parameters at current times. For cosmic chronometers and baryonic acoustic oscillation compiled data sets, we find that GP generically produce smaller variances for the reconstructed data with a minimum value of σ_GP-min = 1.1, while the situation for LS is totally different with a minimum of σ_LS-min = 50.8. Moreover, some of these characteristics can be alleviate at low z, where LS presents less underestimation in comparison to GP.