The understanding of the accelerated expansion of the Universe poses one of the most fundamental questions in physics and cosmology today. Whether or not the acceleration is driven by some form of dark energy, and in the absence of a well-based theory to interpret the observations, many models have been proposed to solve this problem, both in the context of General Relativity and alternative theories of gravity. Actually, a further possibility to investigate the nature of dark energy lies in measuring the dark energy equation of state (EOS) , w, and its time (or redshift) dependence at high accuracy. However, since w(z) is not directly accessible to measurement, reconstruction methods are needed to extract it reliably from observations. Here we investigate different models of dark energy, described through several parametrizations of the EOS. Our high-redshift analysis is based on the Union2 Type Ia Supernovae (SNIa) data set, the Hubble diagram constructed from some Gamma Ray Bursts (GRBs) luminosity distance indicators, and Gaussian priors on the distance from the Baryon Acoustic Oscillations (BAO), and the Hubble constant h (these priors have been included in order to help break the degeneracies among model parameters). To perform our statistical analysis and to explore the probability distributions of the EOS parameters we use the Markov Chain Monte Carlo Method (MCMC). It turns out that the dark energy equation of state is evolving for all the parametrizations that we considered. We finally compare our results with the ones obtained by previous cosmographic analysis performed on the same astronomical datasets, showing that the latter ones are sufficient to test and compare the new parametrizations.

In the last dozen years a wide and variegated mass of observational data revealed that the universe is now expanding at an accelerated rate. In the absence of a well-based theory to interpret the observations, cosmography provides information about the evolution of the Universe from measured distances, only assuming that the geometry of the can be described by the Friedmann-Lemaitre-Robertson -Walker metric. We perform a high-redshift analysis allows us to put constraints on the cosmographic parameters up to the fifth order, thus inducing indirect constraints on any gravity theory. Here we are interested in the so called teleparallel gravity theory, f (T ). Actually we use the analytical expressions of the present day values of f (T ) and its derivatives as functions of the cosmographic parameters to map the cosmography region of confidences into confidence ranges for f (T ) and its derivative. Moreover, we show how these can be used to test some teleparallel gravity models without solving the dynamical equations. Our analysis is based on the Union2 Type Ia Supernovae (SNIa) data set, a set of 28 measurements of the Hubble parameter, the Hubble diagram constructed from some Gamma Ray Bursts (GRB) luminosity distance indicators, and gaussian priors on the distance from the Baryon Acoustic Oscillations (BAO), and the Hubble constant h. To perform our statistical analysis and to explore the probability distributions of the cosmographic parameters we use the Markov Chain Monte Carlo Method (MCMC).