Gauge subtleties and the finiteness of loop corrections beyond slow roll

The early universe undergoes a phase of exponential expansion called inflation, under which quantum fluctuations are amplified and later seed cosmological structures. A long-standing question is whether interactions of these quantum fields may significantly affect the n-point statistics of cosmological observables. These corrections are known as loop corrections. Recently, Kristiano and Yokoyama claimed that, in scenarios beyond slow-roll inflation, the one-loop correction of super-Hubble fluctuations could become non-negligible and violate cosmological-perturbation theory. This result is highly debated, and in this talk we will use a non-linear approach known as delta N formalism to evaluate these loop corrections. We find the existence of loop corrections for modes close to the Hubble scale, however, these corrections are quickly suppressed for long-wavelength modes. We also show how the result of Kristiano and Yokoyama may arise when truncating the perturbative expansion, and how this result depends on the chosen gauge.