Loop Blow-Up Inflation: a novel way to inflate with the K\"ahler moduli

The topic of this talk is a new inflationary model in the context of Type IIB string compactifications called Loop Blow-Up Inflation, presented in arXiv:2403.04831. The original Blow-Up Inflation model, whose potential was purely non-perturbative, suffers from the $\eta$-problem, being sensitive to string-loop corrections. If these corrections are introduced in the nflationary potential, they become dominant over the non-perturbative contributions as soon as the inflaton is displaced from its minimum. Therefore, the inflationary potential takes a new inverse-power law behavior. We show that slow-roll inflation is not ultimately spoiled and focus on the post-inflationary history in different scenarios of microscopic Standard Model (SM) realization. Each of them gives precise predictions for the spectral index and the tensor-to-scalar ratio in agreement with CMB data .The model also predicts an amount of dark radiation potentially observable by next-generation CMB experiments. This article is a contribution to the proceedings of the Second General Meeting of the COST Action CA21106 Cosmic WISPers.