Holography and the scale invariance of density fluctuations

We study a scenario for the very early universe in which there is a fast phase transition from a non-geometric, high temperature phase to a low temperature, geometric phase described by a classical solution to the Einstein equations. In spite of the absence of a classical metric, the thermodynamics of the high temperature phase may be described by making use of the holographic principle. The thermal spectrum of fluctuations in the high temperature phase manifests itself after the phase transition as a scale-invariant spectrum of fluctuations. A simple model of the phase transition confirms that the near scale invariance of the fluctuations is natural, but the model also withstands a detailed comparison with the data.