Cosmic Acceleration from Nothing

We demonstrate that if the universe started as a vacuum fluctuation rather than from a singular Big Bang state, the universe must have a late-time cosmic acceleration. This is required by a ``cosmological sum rule'' derived using the Schwarzian form of the Friedmann equations. We discuss possible connections to conformal and M\"obius transformations, and also compute that the best fit present cosmic data is consistent with the necessary crossing of the Schwarzian through zero having occurred (while it would not yet have happened in a $\Lambda$CDM cosmology).