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Thread: Universe size questions

  1. #31
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    Default Re: Universe size questions



    Quote Originally Posted by chas53 View Post
    hey nFA,
    I've read your post now. thank you again.

    here is another link to the FLRW metric, in case that one doesn't work:

    https://en.wikipedia.org/wiki/Friedm...3Walker_metric

    I have more reading to do at wikipedia.
    and I will continue to try to understand this better.
    thank you again for all of your excellent teaching.
    Charlie
    You're welcome. Sorry that the link I posted earlier to the FLRW metric seems to have been trashed on the forum. Copy / paste of links is another bug that needs to be worked out.

    Call the font police!
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  3. #32
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    Default Re: Universe size questions

    hahahahahahahaha

    nFA,
    I read about the radiation, matter and then (and current) dark helmet oops sorry, I meant dark energy,
    dominated eras in the scale factor wiki:

    https://en.wikipedia.org/wiki/Scale_factor_(cosmology)

    and the wheels start turning up stairs, and presto, a thought occurs to me.
    why is there no dark matter dominated era?
    any ideas ?
    Charlie

  4. #33
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    Default Re: Universe size questions

    Quote Originally Posted by chas53 View Post
    hahahahahahahaha

    nFA,
    I read about the radiation, matter and then (and current) dark helmet oops sorry, I meant dark energy,
    dominated eras in the scale factor wiki:

    https://en.wikipedia.org/wiki/Scale_factor_(cosmology)

    and the wheels start turning up stairs, and presto, a thought occurs to me.
    why is there no dark matter dominated era?
    any ideas ?
    Charlie
    It is easy. In the periods when different forms of mass and energy, what is the meaning of dominant? It’s that one form dominates the contribution to the equation of state, i.e. the pressure as a function of density. Because DM doesn’t interact with other forms, its pressure is zero or nearly so .
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  6. #34
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    Default Re: Universe size questions

    Here's a little more on how cold dark matter has zero pressure (and viscosity) and so never dominates the pressure of the universe even though gravitationally it dominates normal matter. The example is the Bullet Cluster:

    https://www.forbes.com/sites/startsw.../#47fd31611738

    Two galaxy clusters collide. Because cold dark matter exerts no fluid pressure force on the gas, the DM and galaxies pass through while fluid pressure and viscosity cause the gas to stick and stay behind.

    The equation of state of dark matter (pressure as a function of density) is, as far as we know, p = 0. This equation of state has a long history in cosmological models. In simple FLRW models the equations of state are listed here:

    https://en.wikipedia.org/wiki/Equati...te_(cosmology)
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  8. #35
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    Default Re: Universe size questions

    thank you very much nFA.
    all very interesting.

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    Default Re: Universe size questions

    Quote Originally Posted by not_Fritz_Argelander View Post
    Now for the factor of 1000 in CMB.....

    I'm going to be looking for a place to live today so not much time.

    There are two pieces that need to be looked at. One is the FLRW metric:

    https://en.m.wikipedia.org/wiki/Frie...Walker_metric

    The metric is fundamental for calculating distances. You'll notice that it contains the scale factor a(t). But further in the article there are three different choices of comoving coordinates: reduced circumference, hyperspherical, and Cartesian. These are all comoving coordinates with different underlying geometry. As the latter part of the article shows this a(t) contains all the information about the expansion of the universe. There is a separate article about the scale factor.

    https://en.wikipedia.org/wiki/Scale_factor_(cosmology)

    In this article note that how a(t) depends upon t depends on which form of matter-energy dominates the pressure-density relationship (equation of state) at what time. By pressure - density relationship I mean "how does the pressure of the stuff depend on its density". This is different for the radiation dominated, matter dominated and dark energy dominated epochs.

    The relationship between redshift and the a(t) ( 1 + z = a(now) / a(then) ) is derived from the FLRW metric here:
    https://en.wikipedia.org/wiki/Redshi...cal_derivation

    The CMB formed when electrons combined with protons to form hydrogen atoms which happened when the universe cooled to 3000K. The current temperature is about 3K. There is a direct relationship between the temperature of radiation in the universe and the scale factor a(t) provided by the redshift relation 1+z=a(now)/a(then).

    So this says that the universe expanded by about 1000 fold in the scale factor since the CMB was formed.

    But it is not directly interpretable as a distance just as differences in coordinates are not directly interpretable as distances.

    To calculate distances, assuming that they are along a radial line so we can neglect differences in the angular coordinates, one needs to specify t and r and integrate the metric. So one has at the time of emission a time and radius. We observe them at r=0 (here) now, t = 13 Byr. When we integrate the metric to r of that point of emission now we get 46 Bly.

    The 1000 scale factor and the 3.5 distance growth factor are only seemingly inconsistent. One uses the scale factor to calculate the distance growth factor. Algebra alone won't do it. One needs to do calculus and integrate the metric.
    hey nFA,
    if you feel like it, would you please say more about this?
    this is what in particular, I am thinking about. the 46 / 13 = ~3.5 value is
    very simple and easy to understand.
    the 1000 scale factor, I wonder a couple things.

    if the current value of the scale factor is 1,
    does that mean that the scale factor at the time the CMB was emitted,
    was .001?
    also, would you say more about the radiation temperature?
    and the direct relationship between it decreasing from 3000K to 3K,
    and the 1000 fold scale factor?

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    Default Re: Universe size questions

    Quote Originally Posted by chas53 View Post
    hey nFA,
    if you feel like it, would you please say more about this?
    this is what in particular, I am thinking about. the 46 / 13 = ~3.5 value is
    very simple and easy to understand.
    the 1000 scale factor, I wonder a couple things.

    if the current value of the scale factor is 1,
    does that mean that the scale factor at the time the CMB was emitted,
    was .001?
    Yes, exactly.

    also, would you say more about the radiation temperature?
    and the direct relationship between it decreasing from 3000K to 3K,
    and the 1000 fold scale factor?
    First a simple hand waving argument to show that for relativistic matter photons T ~ 1/a while for cold matter T ~ 1/(a^2).

    For a relativistic particle E = pc where p is the momentum so the dependence of the energy (and therefore temperature) of a photon is the same as the dependence of p on a.

    For a non relativistic particle (normal matter) E = p^2/(2m) so the dependence of the energy (and therefore temperature) of an atom or other material particle is the same as the dependence of p^2 on a.

    From the form of the FLRW metric we can guess that p ~ 1/a by dimensional analysis. (Momentum ~ Planck's constant / wave length.)

    So for a photon T ~ 1/a while for non relativistic particles T ~ (1/a)^2.

    So.... that's pretty hand waving. But if you want rigor and detail it gets ugly awfully fast!

    Here is a rigorous treatment for photons that deals with the thermodynamics of radiation as a prerequisite. It's the way I was taught in grad school.

    https://www.cv.nrao.edu/course/astr534/CMB.html

    Here is an even more beautiful and rigorous treatment that looks at solving the geodesic equations of motion in GR:

    https://arxiv.org/pdf/physics/0603087.pdf

    But you need to have comfort in the use of geodesic equations of motion and the Christoffel symbols of the FLRW metric.

    Cheers.
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    Default Re: Universe size questions

    a is wavelength, right?

    edit: yes I see it in your post now.
    thank you very much nFA!!
    Last edited by chas53; 04-17-2019 at 04:12 AM.

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    Default Re: Universe size questions

    Quote Originally Posted by chas53 View Post
    a is wavelength, right?

    edit: yes I see it in your post now.
    thank you very much nFA!!
    No... 'a' is the FLRW metric scale factor. The key point in the hand waving version is that momentum ~ Planck's constant / wavelength for light so since the wavelength scales as 'a' momentum scales as 1/a.

    Similarly for slow stuff energy ~ temperature ~ p^2 ~ (1/a)^2.
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  15. #40
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    Default Re: Universe size questions

    ah, ok.
    excellent.
    thank you very much nFA!!

 

 
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