From agnostic to believer: model independent reconstruction of non standard cosmological models and the role of theoretical priors.

Upcoming Large Scale Structure surveys will provide information on the distribution of matter in the Universe which, united with Cosmic Microwave Background data from Planck, has the potential to significantly constrain our alternatives to the LCDM model and to General Relativity. In this talk I will review the recent results obtained by Planck, discussing the parametrized approach used to test for departures from LCDM. I will the discuss what kind of prior expectation on these departures can be obtained by theoretical considerations and how this prior can be used to reduce the parameter space available for these parameterizations. Furthermore, I will include these theoretical priors in a non parametric reconstruction of deviations from GR, highlighting how these can establish a link between viable physical theories and the phenomenological departures from the standard cosmological model.