  Motivated by string dualities we propose topological gravity as the early
phase of our universe. The topological nature of this phase naturally leads to
the explanation of many of the puzzles of early universe cosmology. A concrete
realization of this scenario using Witten's four dimensional topological
gravity is considered. This model leads to the power spectrum of CMB
fluctuations which is controlled by the conformal anomaly coefficients $a,c$.
In particular the strength of the fluctuation is controlled by $1/a$ and its
tilt by $c g^2$ where $g$ is the coupling constant of topological gravity. The
positivity of $c$, a consequence of unitarity, leads automatically to an IR
tilt for the power spectrum. In contrast with standard inflationary models,
this scenario predicts $\mathcal{O}(1)$ non-Gaussianities for four- and
higher-point correlators and the absence of tensor modes in the CMB
fluctuations.
