The currently most precise measurement of the local expansion rate H_0 by Riess et. al (2016) differs by ~3.4 standard deviations from the value reported by the Planck Collaboration (2015) assuming the standard cosmological model. Since the two approaches, namely using the geometric distance calibrations of Cepheids and the cosmic microwave background data, sample different epochs in cosmic evolution, and one of them uses the standard cosmological model as the fiducial cosmology, this tension in the value of H_0 has given rise to speculations. It has been argued that either new physics beyond the standard cosmology or the influence of local structures must be taken into account in order to reconcile these H_0 estimates. In this talk I introduce this H_0 tension and I present the results of our recent paper, where the effect of this discrepancy has been explored through a Bayesian analysis with the current Planck 2015 and Riess 2016 data. I present a way to alleviate such a tension studying the observational viability of the scale invariant spectrum and two of its extensions, i.e., assuming as free parameter the primordial helium mass fraction and the effective number of relativistic degrees of freedom (Neff). Also, I present analysis using Baryon Acoustic Oscillations measurements and Cluster Number counts and Weak Lensing data in order to take into account the tension on fluctuation amplitude parameter, σ8, value which so far has always brought standard model with Neff extension to be discarded.