Characteristic energy units of primordial fluctuations if gaussian

1. Jul 7, 2012

BillSaltLake

Characteristic energy "units" of primordial fluctuations if gaussian

Correct me if wrong, but I think a purely gaussian distribution of the primordial fluctuations could be characterized by a certain unit of energy (which I'll express as mass). If so, then the observed fluctuations are associated with an energy that is > 1040 in natural units. (There's nothing intrinsically wrong with that high of a number, but it seems as though it was chosen as the spectral amplitude without much justification as to why it should be so high.)
In a gaussian distribution, if a certain number of particles N is on average found in volume V, then the fractional standard deviation in the density N/V is N-1/2 in a sample with volume V. Crudely applying this to the last scattering surface, the density fractional deviation was ~ 10-5 over a length corresponding to half the horizon. A sphere with diameter of half the horizon contained energy ~1046kg. In order to get the correct deviation, there would need to be 1010 "particles" in that sphere, implying a "particle" energy (or intrinsic unit of energy) of ~1036kg, or about 1044 Planck masses.
If the 10-5 was already in effect earlier at the Planck time (ignoring inflation), the "particle" mass would need to be several orders of magnitude higher.
My understanding is that inflation smoothed out these fluctuations, which decreased the deviation in that length scale down to 10-5. If so, inflation would require even higher unit ("particle") energy.
Am I looking at this wrong, or is this high intrinsic unit of energy simply accepted in the model?

Last edited: Jul 7, 2012