f(R) gravity modifications: from the action to the data.

It is a very well established matter nowadays that many modified gravity models can offer a sound alternative to General Relativity for the description of the accelerated expansion of the universe. But it is also equally well known that no clear and sharp discrimination between any alternative theory and the classical one has been found so far. In this work, we attempt at formulating a different approach starting from the general class of f(R) theories as test probes: we try to reformulate f(R) Lagrangian terms as explicit functions of the redshift, i.e., as f(z). In this context, the f(R) setting to the consensus cosmological model, the [Formula: see text]CDM model, can be written as a polynomial including just a constant and a third-order term. Starting from this result, we propose various different polynomial parameterizations f(z), including new terms which would allow for deviations from [Formula: see text]CDM, and we thoroughly compare them with observational data. While on the one hand we have found no statistically preference for our proposals (even if some of them are as good as [Formula: see text]CDM by using Bayesian Evidence comparison), we think that our novel approach could provide a different perspective for the development of new and observationally reliable alternative models of gravity.

Forecast and analysis of the cosmological redshift drift.

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 [Formula: see text] on every tested model, showing also a great complementarity with SNe and BAO data regarding dark energy parameters.

Measuring the speed of light with baryon acoustic oscillations.

In this Letter, we describe a new method to use baryon acoustic oscillations (BAO) to derive a constraint on the possible variation of the speed of light. The method relies on the fact that there is a simple relation between the angular diameter distance (D(A)) maximum and the Hubble function (H) evaluated at the same maximum-condition redshift, which includes speed of light c. We note the close analogy of the BAO probe with a laboratory experiment: here we have D(A) which plays the role of a standard (cosmological) ruler, and H^{-1}, with the dimension of time, as a (cosmological) clock. We evaluate if current or future missions such as Euclid can be sensitive enough to detect any variation of c.