In this paper, we consider the recently proposed hybrid metric-Palatini gravitational theory, which consists of adding to the Einstein-Hilbert Lagrangian an f (R) term constructedà la Palatini. Using the respective dynamically equivalent scalar-tensor representation, we explore the cosmological evolution of a specific model, given by f (R) ∝ R 2 , and obtain constraints on the free parameters by using different sources of cosmological data. The viability of the model is analysed by combining the conditions imposed by the Supernovae Ia and Baryonic Acoustic Oscillations data and the results are compared with the local constraints.PACS numbers: 04.50. Kd, 95.36.+x

The reconstruction of a (non)canonical scalar field Lagrangian from the dark energy Equation of State (EoS) parameter is studied, where it is shown that any EoS parametrization can be well reconstructed in terms of scalar fields. Several examples of EoS parameters are studied and the particular scalar field Lagrangian is reconstructed. Then, we propose some new parametrizations that may present a (fast) transition to a phantom dark energy EoS (where wDE < −1) and the scalar field Lagrangian is also reconstructed numerically. Furthermore, the properties of these parametrizations of the dark energy EoS are studied by using supernovae Ia data (HST Cluster Supernova Survey) combined with Standard Ruler datasets [Cosmic Microwave Background (CMB) and Baryon Acoustic Oscillations (BAO)] and its comparison with the ΛCDM model is analyzed. Then, the best fit of the models is obtained, which provides some information about whether a phantom transition may be supported by the observations. In this regard, the crossing of the phantom barrier is allowed statistically but the occurrence of a future singularity seems unlikely.PACS numbers: 98.80 -k, 98.80.Es

We explore the observational adequacy of a class of Unified Dark Energy/Matter (UDE/M) models with a fast transition. Our constraints are set using a combination of geometric probes, some low redshift ones, and some high redshift ones (CMB related included). The transition is phenomenologically modeled by two different transition functions corresponding to a fast and to an ultra-fast transition respectively. We find that the key parameters governing the transition can be well constrained, and from the statistical point of view it follows that the models cannot be discarded when compared to LCDM. We find the intriguing result that standard/input parameters such as Ωm and Ω b are far better constrained than in LCDM, and this is the case for the derived/output parameter measuring the deceleration value at present, q0.

We test the viability of a single fluid cosmological model containing a transition from a darkmatter-like regime to a dark-energy-like regime. The fluid is a k-essence scalar field with a welldefined Lagrangian. We constrain its model parameters with a combination of geometric probes and conclude that the evidence for this model is similar to the evidence for ΛCDM. In addition, we find a lower bound for the rapidity of the transition, implying that fast transitions are favored with respect to slow ones even at background level.

The cosmological redshift drift could lead to the next step in high-precision cosmic geometric observations, becoming a direct and irrefutable test for cosmic acceleration. In order to test the viability and possible properties of this effect, also called Sandage–Loeb (SL) test, we generate a model-independent mock data set in order to compare its constraining power with that of the future mock data sets of Type Ia Supernovae (SNe) and Baryon Acoustic Oscillations (BAO). The performance of those data sets is analyzed by testing several cosmological models with the Markov chain Monte Carlo (MCMC) method, both independently as well as combining all data sets. Final results show that, in general, SL data sets allow for remarkable constraints on the matter density parameter today on every tested model, showing also a great complementarity with SNe and BAO data regarding dark energy parameters.