Early Universe Cosmology in Internal Relativity

We present a new approach to early universe cosmology. Inflation is replaced by a phase transition in which both matter and geometry are created simultaneously. We calculate the spectrum of metric perturbations and show that it is flat. We then argue that as a consequence of the dynamic nature of the phase transition the spectrum is likely not completely flat but tilted. We argue that the tilt is related to $\eta$, one of the critical exponents characterizing the phase transition. This exponent generically lies between 0.03 and 0.06. It thus coincides with the observed tilt of the perturbation spectrum. Because the critical exponent is related to the presence of an additional small length scale we argue that the deviation of the observed spectrum from flatness might be an experimental indication that our world is in fact discrete.