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Link between Universe mass density and Cosmic Microwave Background energy

  1. Sep 19, 2011 #1
    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: Sep 19, 2011
  2. jcsd
  3. Sep 20, 2011 #2
    What's the coincidence?
    What are you asking here?
    What is the purpose of this?
     
  4. Sep 20, 2011 #3
    I'm not sure what I'm getting at!
     
  5. Sep 25, 2011 #4
    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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