Inflation and topology from the no-boundary state

The no-boundary wavefunction for slow-roll inflation on the 3-sphere exponentially favors a small universe, in sharp disagreement with observations. We show that this problem is resolved by changing the spatial topology to the 3-torus. The sum over the $\mathrm{S}\mathrm{L}(3,\mathbb{Z})$ family of geometries, computed using the theory of automorphic forms for $\mathrm{G}\mathrm{L}(3)$, produces a wavefunction favoring a large inflating universe with $\mathcal{N}\gtrsim 250$ e-folds. We also compute corrections to the CMB power spectrum induced by torus moduli fluctuations.