We explore different corners of the parameter space of inflation with multiple fields. In all cases we find quite counterintuitive phenomenology. First, we will see how additional heavy fields might reveal themselves in the data. Second, multi-field models with coupled ultra-light fields turn out to look a lot like single field. Therefore, in contrast with naive expectation, they are consistent with the current Planck data. We find an exact (toy) model with a hyperbolic field space and show that a scaling symmetry can explain this surprising behavior. Finally, we study the multi-field generalization of the recently developed $\alpha$-attractors. The hyperbolic geometry of field space completely dictates the dynamics of the fields. We find that the predictions are insensitive to significant modifications of the potential, they are universal.

Consistency with quantum gravity can have significant consequences on low energy physics. For instance, using the Weak Gravity Conjecture, it has been recently argued by Ooguri and Vafa that non supersymmetric stable AdS vacua are incompatible with quantum gravity. However, it is known that AdS vacua can appear from compactifying the Standard Model to 2 or 3 dimensions. By requiring the absence of these vacua we can put constraints on the SM and BSM spectra, obtaining a lower bound for the cosmological constant in terms of the neutrino masses. This can also be translated into an upper bound for the EW scale around the TeV range, bringing a new perspective into the issue of the EW hierarchy.