Cosmic Inflation, the currently favoured physical mechanism at the origin of structures in our universe, can be realised in many ways, ranging from modified gravity to string-theoretical constructions. However, up to now, its simplest incarnations, made of a scalar field slow-rolling a plateau-like potential, have passed all the observational tests. Will these models be confirmed by the upcoming Euclid and other large-scale structure surveys?
In this talk, we will present how to quantitatively answer this question using Bayesian statistics and explicit constructions of hundreds of single-field slow-roll models. Not only allowing for model comparison, these techniques can be used to extract global statistics, in model space, and their associated predictions end up being accurate and testable.