Large Scale White Noise and Cosmology

The generation of large scales white noise is a generic property of the dynamics of physical systems described by local non-linear partial differential equations. Non-linearities prevent the small scale dynamics to be erased by smoothing. Unresolved small scale dynamics act as an uncorrelated (white or Poissonian) noise (seemingly stochastic but actually deterministic) contribution to large scale dynamics. Such is the case for cosmic inhomogeneities. In the standard model of cosmology the primordial density power spectrum is taken to be sub-Poissonian and subsequent non-linear evolutions will inevitably produce white noise which will dominate on the largest scales. Non-observation of white noise on the Hubble scale precludes a power law extrapolation of the power spectrum below one comoving parsec and places severe constraints on a wide variety of phenomena in the early universe, including phase transitions, vorticity and gravitational radiation.