Link between Universe mass density and Cosmic Microwave Background energy

[johne1618]

Present critical density of Universe

rho_crit = 3 H^2 / 8 Pi G

H = Hubble Constant = 2.2E-18 sec^-1

rho_crit = 8.6E-27 kg / m^3

What particle mass does this represent?

The length scale associated with a quantum particle of mass m is
the Compton wavelength lambda where

lambda = h / m c

This translates to the following density:

rho_particle = mass / volume

rho_particle = mass / lambda^3

rho_particle = m / (h / m c)^3

rho_particle = m^4 c^3 / h^3

Let us equate the two densities:

rho_particle = rho_crit

m^4 = h^3 * 8.6E-27 / c^3

m = 1.7E-38 kg

m = 1 meV / c^2

The Cosmic Microwave Background has a photon energy of 1 meV.

Surprising coincidence or not?

I suppose this is not surprising if the mass and radiation energy at
the recombination time were similar.

Or maybe it is surprising as mass density is supposed to scale as R^-3 whereas radiation density scales as R^-4.

 

[zhermes]

What's the coincidence?
What are you asking here?
What is the purpose of this?

 

[johne1618]

I'm not sure what I'm getting at!

 

[Naty1]

johne: why not try to explain to yourself, that is write down and maybe post, what each of your results means to you...make an interpretation of the math...

When I was in college I always found I learned the most when I tried to explain to myself in my own words what I was trying to learn...

 

[sardar]

There may have been some fine-tuning in the early universe to result in this coincidence.

However, it is important to note that this is only the critical density of the universe and does not account for the actual mass density of the universe. The actual mass density of the universe may be significantly different from this value, depending on the amount of dark matter and dark energy present. Therefore, it is not entirely accurate to make a direct link between the universe's mass density and the energy of the cosmic microwave background. Further research and observations are needed to fully understand the relationship between these two factors.