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 .