Oscillations in the dark energy EoS: new MCMC lessons

We study the possibility of detecting oscillating patterns in the equation of state (EoS) of the dark energy using different cosmological datasets. We follow a phenomenological approach and study three different oscillating models for the EoS, one of them periodic and the other two damped (proposed here for the first time). All the models are characterised by the amplitude value, the centre and the frequency of oscillations. In contrast to previous works in the literature, we do not fix the value of the frequency to a fiducial value related to the time extension of chosen datasets, but consider a discrete set of values, so to avoid arbitrariness and try and detect any possible time period in the EoS. We test the models using a recent collection of SNeIa, direct Hubble data and Gamma Ray Bursts data. Main results are: I. even if constraints on the amplitude are not too strong, we detect a trend of it versus the frequency, i.e. decreasing (and even negatives) amplitudes for higher frequencies; II. the centre of oscillation (which corresponds to the present value of the EoS parameter) is very well constrained, phantom behaviour is excluded at $1\sigma$ level and trend which is in agreement with the one for the amplitude appears; III. the frequency is hard to constrain, showing similar statistical validity for all the values of the discrete set chosen, but the best fit of all the scenarios considered is associated with a period which is in the redshift range depicted by our cosmological data. The "best" oscillating models are compared with $\Lambda$CDM using dimensionally consistent a Bayesian approach based information criterion and the conclusion reached is the non existence of significant evidence against dark energy oscillations.