So if they are scale invariant then should fluctuations in cosmic density also be? Perhaps there is an upper limit on the scale of 50 Mpc or so?Heisenberg's uncertainty principle predicts that during the inflationary phase there would be quantum thermal fluctuations, which would be magnified to cosmic scale. These fluctuations serve as the seeds of all current structure in the Universe. Inflation predicts that the primordial fluctuations are nearly scale invariant and Gaussian, which has been accurately confirmed by measurements of the CMB.
Sorry if this is off topic, maybe it should be another thread.