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What the Hubble constant must be set to if Univ is flat

  1. May 31, 2012 #1
    What must the Hubble constant be if the Universe is flat. At the Lamda CDM article on wiki it says 70.4 km/s mpc. I'm not sure if that's what it must be if the universe is flat or if that's what experiments have measured it to be, I'm 99% sure that it's the former but I want to be 100% sure. Also I've read the wiki article on the Hubble constant and all the various experiments that have been done to measure it so you don't need to tell me that.
     
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  3. May 31, 2012 #2

    Chronos

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    The hubble constant is a measured, not theoretical value. We currently cannot derive it from first principles.
     
  4. May 31, 2012 #3
    Could you give me some more info. I'm pretty sure what determine if the universe is flat is the density, but I forget what the equation is that determines omega.
     
  5. May 31, 2012 #4

    Chronos

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    Google on critical density of the universe.
     
  6. May 31, 2012 #5
    it says a'/a is the hubble parameter, and the friedman equation is

    (8piG rho + lamda c^2)/3 = (a'^2 + kc^2)/a^2

    So I would think that

    (8piG rho + lamda c^2)/3 - kc^2/a^2 is what the hubble constant would have to equal if the universe is flat, since I'm pretty sure the friedmann equation must equal 1 for a flat universe.
     
  7. May 31, 2012 #6
    The parameter 'k' measures the curvature. For a flat universe, you only need k=0. The scale factor and hence the Hubble Constant at any epoch then depend on the various densities (matter, radiation, dark energy).

    http://en.wikipedia.org/wiki/Friedmann_equations#The_equations
     
  8. May 31, 2012 #7
    am I right that a'^2/a^2 is the hubble parameter? I specifically remember reading in Sussking's the Cosmic Landscape that the Hubble constant must be a certain ratio in order for the universe to be flat. He writes:

     
    Last edited: May 31, 2012
  9. May 31, 2012 #8
    It doesn't have to be anything in particular. Once you have dark energy, then if you change hubble's constant, then you can change the dark energy component and still end up with a flat universe.

    It's a direct measurement. Also with our other observations we can tell that the universe as is flat within observational limits, but all of that are measurements.
     
  10. May 31, 2012 #9
    Once you add in dark energy, you have an extra variable that you can tweak.

    Also in the 1970's the fact that the universe seems close to flat was considered a "problem" but flat universes pop out naturally from inflation so it's no longer considered weird or unusual that the universe is flat.

    The other thing was that there's been a lot of talk about the anthropic principle, but the experience with inflation points out that one shouldn't go "anthropic" too early. In the 1970's, there were a lot of "weird coincidences" that suggested fine tuning, but inflation solved most of them without the need to go anthropic.
     
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