Characteristic energy units of primordial fluctuations if gaussian

[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?

 

[AndyW]

I would like to clarify a few points about the characteristic energy units of primordial fluctuations in a gaussian distribution.

Firstly, the term "gaussian" refers to the shape of the distribution, not the units of energy. A gaussian distribution is a symmetrical bell-shaped curve that is commonly used to describe natural phenomena. It does not have any inherent units of energy associated with it.

Secondly, the observed fluctuations in the cosmic microwave background (CMB) radiation are not associated with a specific energy unit. The fluctuations in the CMB are a result of density variations in the early universe, which were caused by quantum fluctuations during inflation. These fluctuations are not particles, but rather fluctuations in the energy density of the universe.

Thirdly, the number and energy of particles in the early universe are not well-defined due to the extreme conditions and unknown physics at that time. Therefore, trying to assign a specific energy unit to these fluctuations is not a meaningful exercise.

Lastly, the energy scale of inflation is not well-constrained, and it is not necessary for the energy scale to be extremely high in order to explain the observed fluctuations in the CMB. Inflation is a proposed mechanism to explain the large-scale homogeneity and isotropy of the universe, and it does not necessarily require a high energy scale.

In summary, the concept of a characteristic energy unit for primordial fluctuations in a gaussian distribution is not a well-defined or relevant concept in the study of the early universe. It is important to be cautious when trying to assign specific units to phenomena that are not fully understood and have not been observed directly.