Fat Inflatons, Large Turns and the $\eta$-problem

It is commonly believed that a successful period of inflation driven by a single or several scalar fields requires a specific hierarchy of masses given by $M_{inf}\ll H \ll M_{heavy}$, where $M_{inf}$ can correspond to several or a single light field and $M_{heavy}\,\,\,$ corresponds to any heavy field that might be integrated out if it satisfies suitable conditions. This is at the heart of the so called $\eta$-problem in inflation, since large contributions to the masses of the inflatons might spoil the slow-roll conditions required for inflation. We show that, while this is an unavoidable conclusion in single field inflation, in multifield inflation, heavy fields as defined above, may be fully responsible for a successful period of what we call fat slow-roll inflation. Moreover we show that in this scenario, the turning rate of the inflationary trajectory, $\Omega/H$, is larger than one. Thus, the $\eta$-problem is evaded with large turns in fat inflation. Depending on the perturbations' mass spectra, cosmological predictions will differ either slightly or largely with respect to those of the single field case. We illustrate this scenario in a concrete example in Type IIB string flux compactifications, where a probe D5-brane moving along the angular and radial directions in a warped throat drives fat D5-brane natural inflation. An instantaneous superplanckian decay constant can be defined, consistent with our low energy approximations, thanks to the strong warping of the geometry. We compute the cosmological observables, which differ from the single field case. We also discuss fat inflation in the context of recently proposed swampland de Sitter conjectures.