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What is the critical density of the universe?

  1. 3.6 nanojoules per cubic mile

    1 vote(s)
    33.3%
  2. 3.6 millijoules per cubic mile

    0 vote(s)
    0.0%
  3. 3.6 joules per cubic mile

    1 vote(s)
    33.3%
  4. 3.6 kilojoules per cubic mile

    1 vote(s)
    33.3%
  1. May 16, 2003 #1

    marcus

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    The critical density of the universe is

    (3c2H02)/8piG

    which is the average energy density required for flatness.
    And in fact recent measurements imply that our universe is indeed flat and therefore has this energy density.

    In addition, the Hubble parameter H0 has been
    determined in the past 5 years with remarkable accuracy
    and is 71 km/s per Mpc plusminus some modest uncertainty.
    So what is the density of our universe? We live here
    and ought to have some idea what it is.

    Presumably you know c, and G, and pi, and 71, so
    it should be a snap for you to guesstimate the rough size.

    Knowing this density can be handy because it lets one
    compare other energy densities to it----like the energy lost
    from the CMB thru expansion----and figure out what various
    fractions of it amount to, like the part of the energy that is visible matter and the part contributed by radiation and so on. But it's
    good as well because it gives a feel for how thinly or thickly space is occupied.
     
  2. jcsd
  3. May 16, 2003 #2

    chroot

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    cf. Carroll and Ostlie's "Introduction to Modern Astrophysics."

    - Warren
     
    Last edited: May 16, 2003
  4. May 16, 2003 #3

    marcus

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    Which of the four answers is closest to what Carroll and Ostlie say?

    I have high expectations of PF people----I expect them either to know the rough order of magnitude of rho crit, or else to
    be able to make a quick guesstimate using what they know
    about H0. Besides which it can be useful to know.
     
  5. May 16, 2003 #4

    chroot

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    What's with you and all this "I'm going to test PF" attitude? You've made it clear now in several threads that you really don't know as much as you think you know.

    - Warren
     
  6. May 16, 2003 #5
    I disagree. The critical density depends on the geometry of the entire universe.
     
  7. May 16, 2003 #6

    marcus

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    This is a possible objection. Bravo.
    You are objecting to the formula

    (3c2 H02)/8piG

    as a way to calculate rho crit.

    It is the standard Astro 1 formula for rho crit (not even Astro 101 :smile:) and comes right
    out of the second Friedmann equation.

    Because of that there are some underlying assumptions built into it of homogeneous isotropic.

    Everybody is allowed to doubt that on the large scale the U
    is homog and isotropic. And also to doubt that the Einstein
    equation of GR (which the Friedmann eqs derive from) is correct.

    But there is a widespread belief that these things are pretty darn near right. The people who are investigating the possibility that the universe looks like a donut are pretty far out on the margin. It is not really a hot research topic.

    So why not accept GR and Friedmann eqs and flatness and this resulting formula at least provsionally and see what it says about your universe?

    In which case, which of the four answers is the energy density
    that comes out of the formula?
     
    Last edited: May 17, 2003
  8. May 17, 2003 #7
    That value comes right out of specific solution to the field equations; the critical density depends on the behavior of the cosmological constant.
     
  9. May 19, 2003 #8
    Ok your super new fancy version of H = 2.3e-18 s-1
    c=3e8
    G=6.67e-11
    GMm/r=mv2/2 {v=c}
    2GM/c2=r
    M = (4/3)πr3ρ
    2G(4/3)πr2ρ/c2=1
    ρ=3c2/(8πGr2)
    r = c/H
    ρ=3H2/8πG
    =9.5e-27 kg/m3
     
    Last edited: May 19, 2003
  10. May 19, 2003 #9

    marcus

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    I will check your answer if you wish. Your figure for the Hubble time is 1/2.3E-18 seconds which works out to 13.8 billion years, so your figure for H is correct.

    Now let's look at the bottom line. You have it expressed as a mass density so I have to convert it to energy density, multiplying by 9E16 the square of the speed of light and that turns 9.5E-27 kg/m3 into 0.855E-9 joules per cubic meter.

    That is 0.855 joules per cubic kilometer!

    YIPPPEEEE!, now a cubic mile is about 4.2 cubic km so indeed your figure converts to 3.6 joules per cubic mile. This is one of the options on the poll.

    I mixed the units----joules per cubic mile----in the poll so that one could not simply copy something out of a book or off the web. Your value of around 0.86E-9 joules per cubic meter is a standard mainstream estimate of rho crit. Bravo and congratulations!!!!

    Especially since you did not merely copy it from somewhere but obviously went out on a limb and calculated it yourself.
    This shows that Foxans have the pioneer spirit or chutzpah or something.

    Put a click beside 3.6 joules per cubic mile, if you want.
     
  11. May 19, 2003 #10

    marcus

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    Jonathan Swift: "A Modest Proposal"

    SchwaR. your suggestion that our form of government is a
    kleptocracy reminds me of Swift's way of expressing his rage,
    which was to turn it into very funny satire. I think his best
    piece is not Gulliver but the short essay A Modest Proposal,
    which explains how to solve the problem of overpopulation
    and is even more relevant today than in the 18th. Have you
    read Swift by any chance? there is a kind of Irishness about
    his way of expressing outrage.

    I will match you in natural units

    For a metric user the Hubble time is 4.35E17 seconds
    (I have simply taken the reciprocal of your
    "2.3e-18 s-1")

    and for a natural user the same time is 8.06E60.

    A user of natural units simply divides (3/8pi) by the square of 8.06E60, and is done.

    A user of metric units would proceed rather much as you did.
    Divide (3/8pi) by 6.673E-11, multiply by the square of 3E8, divide by the square of 4.35E17----that gives 0.85 nanojoules per cubic meter, which is the right answer.
     
  12. May 20, 2003 #11
    your equation for ρ is incorrect
     
  13. May 20, 2003 #12

    marcus

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    in what way incorrect?

    Please be more specific. In fact I did give an equation for
    the critical energy density rho crit.

    And the formula I gave was

    (3c2 H02)/8piG

    Are you saying that formula is incorrect?

    There is no other formula in cosmology for the critical
    energy density, that I know of.
     
  14. May 20, 2003 #13
    ahh. alright, just dont get it confused with vacuum energy density.
     
    Last edited: May 20, 2003
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