Link between Universe mass density and Cosmic Microwave Background energy

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Discussion Overview

The discussion revolves around the relationship between the critical density of the universe and the energy of the Cosmic Microwave Background (CMB). Participants explore the implications of equating particle mass derived from critical density with photon energy from the CMB, considering both theoretical and conceptual aspects.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant presents the critical density formula and calculates a corresponding particle mass, suggesting a potential link to the CMB energy.
  • The same participant notes the scaling differences between mass density and radiation density, raising questions about the significance of their equivalence at recombination time.
  • Another participant questions the clarity and purpose of the initial post, seeking further explanation of the coincidence mentioned.
  • A different participant expresses uncertainty about the implications of their own contributions, indicating a lack of clarity in the discussion.
  • One participant encourages self-explanation as a learning tool, suggesting that articulating thoughts may lead to better understanding.

Areas of Agreement / Disagreement

The discussion contains multiple competing views and remains unresolved, particularly regarding the significance of the calculated mass and its relation to the CMB energy.

Contextual Notes

Participants have not fully clarified the assumptions behind their calculations or the implications of the scaling laws mentioned. The discussion reflects varying levels of understanding and interpretation of the mathematical results.

Who May Find This Useful

Readers interested in cosmology, the relationship between mass and energy in the universe, and the implications of the Cosmic Microwave Background may find this discussion relevant.

johne1618
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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.
 
Last edited:
Space news on Phys.org
What's the coincidence?
What are you asking here?
What is the purpose of this?
 
I'm not sure what I'm getting at!
 
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...
 

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