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Understanding Cosmology (Post 3)

Discussion in 'Science and Religion' started by Meow Mix, Jun 24, 2021.

  1. Meow Mix

    Meow Mix Curious Kitty

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    In Post 2, we talked about the Friedmann equation and what we mean when we talk about various energy densities and density parameters (recall that the density parameters are just the energy density of a thing in relation to the critical density at which the geometry of the universe is spatially flat, which we know through observation, such that adding all density parameters should exactly equal one). I'll try to respond to any questions.

    So now we're going to start the first subject that everybody is asking about: dark matter. Why do we think there's dark matter, and what is it?

    Consider that we already know the universe is spatially flat, so we know that when we add all our density parameters together, we should get 1. We might wonder, "do stars make up a lot of the energy density of the universe?" Surely they would, right, because there's so many of them and they're so huge and massive?

    Actually, no. Using the mass-to-light ratio of stars within 100 Mpc (remember, this is about the scale at which the universe is homogeneous and isotropic), the density parameter of stars is about 0.003: that means stars only make up 0.3% of the energy density needed to have a spatially flat universe like the one that we observe!
    (There is a very low uncertainty in this number due to faint, low-mass stars; but even accounting for this, we still end up with a tiny density parameter, ~0.005.)

    Most of the "regular" matter (baryonic matter) in the universe is actually in the form of gas: galaxies' gas mass is roughly ten times that of their star mass. But there is also gas in the intergalactic medium, and this can be hard to count. If we wanted to count up how much baryonic matter we have in the universe, how would we do it?

    The answer is we can count up how much baryonic matter is in the universe by understanding how it was formed, nucleosynthesis. But this is a big subject (ask questions in the comments if you like), so I will tell you a few condensed facts:
    1. It was initially too hot for atoms to form because the temperature of the universe when the scale factor was very small (remember T is proportional to a^-1) was above or at the same order of the binding energy of atoms: so there would have been a period before atoms.
    2. Nucleosynthesis truly began when deuterium was able to form (deuterium is an isotope of hyrogen that has one proton and one neutron) because there are many viable paths involving deuterium to heavier elements.
    3. Less than 1% of atoms in the universe are heavier than helium. Why? Because of energy limitations, but also largely because of the neutron to proton ratio: free neutrons are unstable and decay; but were necessary for a lot of reactions to produce higher elements. So there was a scarcity of neutrons (about a 1:5 ratio of neutrons to protons), leading to nucleosynthesis being very inefficient.

    The final yield of each element in nucleosynthesis can be calculated with some complicated nuclear physics, as you can see above.

    We can calculate elemental abundances:

    ...and compare them to what we see in the universe. (This is an amazing piece of evidence for the Big Bang in general, by the way, but that is not the focus of this post).

    We can measure the primordial abundances of baryon number densities in untouched clusters of gas, for instance, to independently cross-check our work. There is also a complex relationship to photon number density that can be considered (skipping this here due to complication, ask questions if you want).

    We can calculate the density parameter for just baryons very accurately:

    0.048 (give or take some small change) is not very much, it doesn't go a long way towards giving us a universe that is spatially flat like the one that we observe!

    The conclusion is inescapable: most of the stuff in the universe is not the baryonic matter that we're used to seeing, like stars and gas!

    So what else is there if it's not baryonic matter? We're not to the "dark" part just yet. I suppose that will be on Post 4.
     
    #1 Meow Mix, Jun 24, 2021
    Last edited: Jun 24, 2021
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  2. Meow Mix

    Meow Mix Curious Kitty

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    A note on elemental abundances in the universe: some of you may already known that stars are mostly helium and hydrogen; and that planets get their heavy elements from supernovae.

    Interstellar and intergalactic gas then, it stands to reason, wouldn't have any heavier elements without said supernovae. So you can use this reasoning as a sanity check on some of the stuff above: stars make up an absurdly tiny fraction of the energy density of the universe, gas is mostly hydrogen and helium, so why would we expect there to be so much stuff in gas that it can flatten the universal geometry alone? There has to be something else! (Though, the measurement through nucleosynthesis and baryogenesis given in the main post is better, this reasoning is more accessible).
     
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  3. JoshuaTree

    JoshuaTree Flowers are red?

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    Aether?
     
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  4. Meow Mix

    Meow Mix Curious Kitty

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    No luminiferous ether, intergalactic gas is largely constrained in dark matter "tubules"/filaments, and this is a major source of gas for galaxies to make stars with as it gets infed. It doesn't permeate space.

    On Post 1, one of the first images is what the universe looks like zoomed out to hundreds of Mpc, the filamentous structure is where the gas is.
     
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  5. Heyo

    Heyo Well-Known Member

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    Not directly related to the post but in general to the topic:
    Do you have a (or several) mental model(s) for the universe, like the rubber sheet or balloon model? Or do you just SUAC?
    I have problems with incorporating a flat universe into my balloon model and still hope the existing measurement inaccuracies turn out to be enough for a closed universe.
    And if I turn to an infinite rubber sheet, for that sheet to be flat, there has to be a "bump" (equal in magnitude) for every depression (gravity well). I.e. the "bumps" are areas of negative gravity so that the sum of all "bumps" and of all mass is zero to maintain an overall flat sheet.
     
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  6. Meow Mix

    Meow Mix Curious Kitty

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    I usually use a balloon model myself.

    Just because the visible universe is flat doesn't mean the external universe is flat; it could well be curved. Inflation and dark energy just drive a given region, small compared to the rest of the universe, towards flatness.

    If it is flat though and we do have a sheet everywhere, inflation has your bumps covered: its opposition to the gravitational potential is in fact what even drives the inflation; which would be ongoing today in eternal inflation (just not here).
     
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  7. Heyo

    Heyo Well-Known Member

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    Thanks. For me it helps a lot if I can visualize something. The numbers have to "mean something". It is also great for quick sanity checks. If the numbers and equations don't fit the model it can be that the model is not applicable but often it means that something is wrong with the numbers.
     
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  8. Meow Mix

    Meow Mix Curious Kitty

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    I feel the same! ^.^
     
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