Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Universe density types equation

  1. Jun 7, 2015 #1
    I was searching a cosmology calculator and In one calculator I saw this equation.
    is that true true for all type universe's (open,flat,closed) ?
    and is here ##Ω_k={-k\over H^2_0 /a^2_0}## isnt it.
    (And If you can give me an article about this issue I will be very happy,I need exact proof)
    Last edited: Jun 7, 2015
  2. jcsd
  3. Jun 7, 2015 #2


    User Avatar
    Science Advisor

    It's true for globally isotropic universes with matter and cosmological constant. For proof, consult any introductory cosmology text.
  4. Jun 7, 2015 #3


    User Avatar
    Science Advisor

    That equation is part of the definition of the ##\Omega## parameters. It's true as long as there is no other component of the energy density (e.g. it's true as long as the radiation density is small enough to be ignored). If you have some other component, such as ##\Omega_r## for radiation, then you have to add that to the equation:

    [tex]1 = \Omega_k + \Omega_m + \Omega_\Lambda + \Omega_r[/tex]

    And yes, that equation for ##\Omega_k## is correct.
  5. Jun 7, 2015 #4


    User Avatar
    Science Advisor

    Sum = 1 implies a flat universe. > 1 implies closed, < 1 implies open.
  6. Jun 7, 2015 #5


    User Avatar
    Science Advisor
    Gold Member

    Not when [itex]\Omega_k[/itex] is included, as Chalnoth said the sum is unity; [itex]\Omega_k[/itex] absorbs the k term.

    [itex]\Omega_k[/itex] > 0 implies open, [itex]\Omega_k[/itex] = 0 implies flat and [itex]\Omega_k[/itex]< 0 implies closed, (see the OP definition of [itex]\Omega_k[/itex]).

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook