  We present and discuss a new approach increasing by orders of magnitude the speed of performing Bayesian inference and parameter estimation within the framework of slow-roll inflation. The method relies on the determination of an effective likelihood for inflation which is a function of the primordial amplitude of the scalar perturbations complemented with the necessary number of the so-called Hubble flow functions to reach the desired accuracy. Starting from any cosmological data set, the effective likelihood is obtained by marginalisation over the standard cosmological parameters, here viewed as "nuisance" from the early Universe point of view. As being low-dimensional, basic machine-learning algorithms can be trained to accurately reproduce its multidimensional shape and then be used as a proxy to perform fast Bayesian inference on the inflationary models. The robustness and accuracy of the method are illustrated using the Planck Cosmic Microwave Background (CMB) data to perform primordial parameter estimation for the large field models of inflation. In particular, marginalised over all possible reheating history, we find the power index of the potential to verify p < 2.3 at 95% of confidence. 
Fast Bayesian inference for slow-roll inflation