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Friedmann paradox

  1. May 8, 2004 #1
    Please show me how to solve this paradox
    cos the Friedmann equation is:
    [tex]
    H^{2}= \frac{8*pi*G*rho}{3}-\frac{k*c^{2}}{R^{2}}
    [/tex]
    but the concordance model says that k=0, so we can eliminate the last term of the equation
    then we isolate rho, the density of energy:
    [tex]
    rho=\frac{3*H^{2}}{8*pi*G}
    [/tex]
    but however, the formula for the critical energy density is
    [tex]
    rho_{crit}=\frac{3*H^2*c^2}{8*pi*G}
    [/tex]
    but the concordance model says that rho=rhocrit
    but you see that the 2 formulae are not equal, there's an extra c2 in the formula for rhocrit

    I can't figure where is the mistake
     
    Last edited: May 8, 2004
  2. jcsd
  3. May 8, 2004 #2

    Stingray

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    rho is mass density. rho_crit is energy density (as you wrote it). Mass and energy have different units, and you use c^2 to convert between them.

    Most people like to use units such that c=1, and then energy and mass are interchangable. This convention is so common that books are sometimes careless about distinguishing the two.
     
    Last edited: May 8, 2004
  4. May 8, 2004 #3
    please, take a look to this thread
    https://www.physicsforums.com/showthread.php?t=2864
    Here's jeff, and I think that he is a knowledgeable person, and says that rho includes all kinds of energy, not only mass

     
    Last edited: May 8, 2004
  5. May 8, 2004 #4

    Stingray

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    That's true. I was being a little sloppy myself. rho includes everything, but the way you wrote it, it has units of mass/volume, whereas rho_crit has units of energy/volume. Wherever you're quoting rho_crit from has a slightly different form for Friedmann's equation than you do, so their answer is different by c^2. This is just a convention. You can choose either mass units or energy units for rho as long as H works out as 1/time in the end.
     
  6. May 19, 2004 #5

    Chronos

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    use the conversion c^2=m/e
     
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