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How big was the big bang?

  1. Apr 18, 2010 #1
    "The whole universe was in a hot, dense state, when nearly 14 billion years ago expansion started .."

    The big bang (BB) is often recapitulated by noting the times when the universe was the size of a proton, or the size of a grapefruit, or the size of our solar system. This is most easily understood as the times when our currently observable universe was the size of a proton, grapefruit, etc. What is more difficult to understand (or calculate) is the extent of
    the entire of the universe at those same times. Most discussions of BB suggest that the primordial universe (the whole thing, not just our observable seed) was a finite expanding sphere. Our observable universe was a small piece of that sphere.

    So how big was it? The question came up as part of the "What is beyond the observable universe?" thread. In that discussion it was suggested that current models, either for simplicity sake, or to match the data most closely, presume that what is beyond the current observable universe is just more of the same. Carried to its logical extension, that would imply the universe is now infinite. It seems that if it is now infinite, then it must have been infinite to start with. I don't think there's any way to get to a currently infinite universe if we started with a finite universe.

    So far the best answer is: we don't know for sure, but we do know that it (the whole universe) is much larger than our observable universe. So I have a few questions for this thread:

    1) I would like to know if it is possible that the primordial universe (the whole thing) was infinite in extent. Does GR allow such a beginning? Could it have started out infinite, and very dense, and then started expanding, creating more space everywhere at once and continuing to do so?

    2) On the other extreme, if the primordial universe was finite, how small could it have been before we would notice it now? How we would tell (1) from (2)?

    3) If the primordial universe was finite, and we (our observable universe) were just a small part of it, does it matter where we were within that sphere? It seems that if we were near one edge of the sphere, the CMB would be highly lopsided now. Since it isn't, does that mean we were within at least X% of the center?
  2. jcsd
  3. Apr 19, 2010 #2


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    Definitely! That is what is most commonly assumed by cosmologists. It could have been finite at the start of expansion, but the simplest thing to assume is infinite.

    The standard cosmo model LCDM (or LambdaCDM) comes in several versions, most common one has infinite extent at start of expansion.

    Definitely! GR can accomodate either infinite or finite at start of expansion. The standard cosmology model LCDM is based on GR.

    Good question. This was answered in the WMAP5 report (5th year WMAP data, implications for cosmology, Komatsu et al) The typical finite case considered is where space is a hypersphere---the 3D analog of the 2D surface of a balloon. There is no center in space away from which things are expanding, every point is equal, just like on a balloon but 3D.

    The official NASA WMAP5 report gave a 95% confidence figure for the LOWER BOUND OF THE HYPERSPHERE RADIUS. It has to be at least 100 billion lightyears as of today or with 95% confidence we would notice conflict with data. The data is consistent with either infinite or, in the finite case, with a > 600 billion lightyear circumference expanding balloon analog----a > 600 billion lightyear circumference hypersphere.

    So you take it from there. If it is finite we know that it at least so and so big. (Or we would notice conflict with data.) So extrapolate back to when it was a billion or a trillion times smaller!

    However no one knows what things were like at the VERY BEGINNING of expansion. According to some models there was a bounce when the density reached about 40% of planck density. So contraction stopped and turned around and expansion started at around Planck density, or half or 40% whatever.

    Physical models of right around the start of expansion is part of quantum gravity research. It is current ongoing research. It's not time yet to be forming definite ideas.
    Plus we only have 95% confidence lower bounds on the size. the real thing could be much much bigger than the lower bound established by WMAP. Next year with more datat they may have a still higher lowerbound. Improving data typically pushes up the estimated lowerbounds. If this isn't clear, ask more questions. Let me know if I'm not making sense to you.

    Think of the 2D balloon surface, all existence on that sphere, no space inside or outside. All points equally central. A 2D creature living in the 2D surface cannot point with its flipper in any direction that is not in the 2D surface. All locations are equal. It does not matter where we are. Same with a 3D hypersphere. (Typical finite case considered.)

    There is no edge and no central point as far as we know. In standard LCDM cosmology matter is assumed to be approximately uniformly distributed throughout all space. If space is finite there is finite matter, evenly distributed. There is no boundary or edge. If space is infinite there is infinite matter, evenly distributed. Again there is no boundary or edge. For the finite case, again think of the analogy of the 2D balloon. All existence, all directions, all space, all matter, concentrated on the 2D surface. No edge or boundary.

    Some people speculate about higher dimensional surroundings but most working cosmologists keep it simple. No frills. The simplest mathematical model that fits the data. No evidence for edges or boundaries or surrounding higher dimensional space, so they don't consider them. Occam's razor. Don't need that stuff so chuck it. A few fantasizers make up more elaborate models but on the whole most pros don't bother to fit data to them.
    Last edited: Apr 19, 2010
  4. Apr 19, 2010 #3
    What boggles my mind with the balloon analogy is, that 2D creatures living there shouldn't notice growth of their world at all, since all their "space" expands equally, so that relative distances stay the very same.
    Thus, by that analogy, it is not explained why we observe galaxies heading away from us, since we should grow at the same rate, and as such our relations too.

    In my understanding, this picture would only work, if there constantly is some rubber inserted (instead of stretched), but less in places of high matter density.

    Also, if we dismiss the idea of additional dimensions: In what would our "3D balloon" be inscribed?

    I know that there are arguments like: Space is only defined where something is, whereby one may measure distance, and thus our universe is creating it's own space all by itself. I somehow doubt that, and would think that there always was a "potential" space where things can be put into, but bare of our universe, there was no means of measuring it (provided there was some kind of a massless observer). The notorious "nothing" if you wish to call it that.

    My point being: Even imagining our universe as a hypersphere doesn't really answer much, but introduces new questions along the way.

    A little question that just came to my mind: If black holes may "pack" arbitrary amounts of mass into one singular point without size - what would forbid packing all matter and energy there is into one singular point, giving the option of a universe that somehow is an exploding uber-black-hole? (Which would contradict data if this would be happening in plain 3D space, since CBR is roughly the same all around - a minor quirk *cough*)
  5. Apr 19, 2010 #4


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    It sounds like you haven't watched the balloon model animation, and aren't picturing it right.

    Google "wright balloon model" and have a look.
    The galaxies are the 2D creatures in this case. They stay the same size. And they stay at the same latitude-longitude position on the balloon. But they get farther apart from each other.

    There are also photons of light that actually travel at a fixed speed across the face of the balloon, and are able to travel from one galaxy to another if the two are not too far apart.
    You can learn a lot by watching the computer-generated animation.

    It sounds from the rest of your post like you have several common misconceptions about expansion cosmology that this excellent SciAm article was written to relieve people of
    http://www.astro.princeton.edu/~aes/AST105/Readings/misconceptionsBigBang.pdf [Broken]
    How about reading the article (simply written and well illustrated) and then coming back with improved questions?
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  6. Apr 19, 2010 #5


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    Yah, you're not following.

    In both 2D and 3D:
    - creature-sized objects do not grow in size. In fact, nothing grows in size, including galaxies. Their own internal forces easily overwhelm the puny expansion factor of the universe. (Think of a penny glued to the balloon. You don't expect the penny to grow in size simply because it's sitting on the balloon.)

    - distances on the scale of creatures, and on the scale of galaxies do not increase either. At this scale, everything is gravitationally-bound, and again it overwhelms the puny expansion factor of the universe. (Think of multiple pennies on the balloon attached to each other with twine. You don't expect that an expanding balloon will snap all the pieces of twine.)

    - only on very large scales - where gravity between extremely distant objects (such as whole galaxy clusters separated by tens of millions of light years) is vanishingly weak - are the effects of expansion noticeable. (Think of multiple pennies so far apart on the balloon that there is no string between them. The pennies will move away from each other.)
    Last edited: Apr 19, 2010
  7. Apr 20, 2010 #6
    First, I think it is cool that we have measured the lower bound on the hypersphere.
    But I am still trying to figure out how to apply the balloon analogy. (perhaps I am personally in a dense state.) So here's a few questions:

    1) Is the balloon the entire universe or just our observable universe? (I think it is the whole thing.)

    2) If the balloon is the entire universe (expanding according to H), is our observable universe just a circular region on the surface (expanding at c)?

    3) If the universe is infinite, it seems the balloon would become very very large, and very very flat. I would have trouble distinguishing it from a flat plane anywhere on it. My observable universe is still a circular region on a (now) nearly flat plane. If the universe was infinite to start with, then my balloon analogy seems to have busted. The whole universe was a big flat sheet that was starting to stretch out.

    I fear I have taken a wrong turn here somewhere.
  8. Apr 20, 2010 #7
    I do know of this model, and how to see it. The fundamental difference that leads to my uncertainty is the question of the "fabric of space" itself. If space itself expands, one and the same region would grow in size from an outside observer in time, while for an insider it would stay the same.
    My main issue is to define whether "space" is where everything else flies around in (=the universe expands in, with universe meaning all particles there are), or if space itself is a property of the universe as well, and would be expanding with it.
    If the latter was an option, even gravitational bonding wouldn't resolve the issue of why far galaxies are red shifted, since from "in here" they always should look the same distance away.

    Or to keep it in the balloon world: One may disregard the actual surface of the physical balloon, and only refer to shape, or it may also be understood that the rubber may be a stand in for "empty space". There isn't any more rubber turning up between the glued coins when expanding, it stretches. That is where I have a problem with the balloon analogy.
  9. Apr 20, 2010 #8


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    I do too! The NASA report is mostly too technical to read but in case you are curious the PDF is online.
    Look at Table 2 on page 4, where it says "curvature radius". If you want help decoding it to get a figure in lighyears, just ask. It comes to slightly over 100 billion lightyears.
    More power to you!

    You are right. Whole thing. Ignore the rubber. Ignore the metaphorical air inside and outside the balloon. :biggrin: Concentrate on the pure mathematical 2D surface. The analogy is just there to help visualize changing distance relations among the photons and the galaxies. Geometry is essentially distance relationships. General Relativity is a theory of how geometry changes.

    Be sure you have watched the "wright balloon model" animation, paying attention to the photons as well as the galaxies. You can see them redshifting as time goes on, wave-lengthening. Think of them as always moving 1 millimeter per second over the balloon surface, no matter whether the balloon is small or large.

    Yes! However as a technicality the present radius of the observable (approx. the distance to the last scatter surface--the material that emitted the Cmb light we are now receiving) is about 45 and the hubble radius (distance that is increasing at rate c) is about 13 billion ly. We currently see stuff which is today way farther than the hubble distance. Hubble distance corresponds to redshift z = 1.4 and we see out beyond z = 1000.
    So you made a slight parenthetical error when you said "(expanding at c)". The observable is expanding faster than c.

    Read Lineweaver SciAm article to get explained how we can observe stuff whose distance from us is increasing faster than c.

    This sounds perfectly lucid to me! We always have to keep in mind that the universe might be infinite--like an infinite flat plane, in the 2D analogy.
    Then the balloon analogy is, strictly speaking, wrong! Busted, as you say.
    In that infinite case, the universe started out infinite, already infinite when it began expanding.

    Classical 1915 Gen Rel is incomplete in the sense that it does not have an description of the geometry at the precise moment expansion began (the word "singularity" means mathematical failure, gap in the story, where the equations break down, and it does not have to be confined to a single point.) Most cosmology is based on the vintage 1915 GR theory, so it does not cover the absolute start of expansion.

    You might get something out of the one-page essay at Einstein-Online called "A tale of two big bangs". I have the link in my sig, at the end of this post. It is a general audience non-technical discussion that goes a little into some tentative ideas researchers have about the very start. What should replace the singularlity---the failure of the classical model.

    Finite is always going to be easier to imagine, but we don't know which is correct. If infinite turned out to be correct I would personally go on imagining a "very big" balloon surface, almost flat, and therefore "almost infinite" in a certain half-baked sense.
    Last edited: Apr 20, 2010
  10. Apr 20, 2010 #9


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    Just looking at that one post I don't see any wrong turn. It all looks on track. But everybody has taken and will take wrong turns somewhere, wrong turns come with the territory :biggrin:

    Be careful, it is possible you don't. Did you google "wright balloon model" and actually watch?

    When you use the balloon picture, try imagining that the rubber isn't there. Only the pure 2D surface is there. At each moment, a geometry comprised of distance relations.

    In Gen Rel there is finally no fabric of space. There is no material called "space itself". There is no "rubber". You will understand the balloon model better if you train yourself not to think of space as a physical substance

    Neither alternative sounds quite right. Gen Rel is about geometry and how it responds to matter. Matter tells geometry how to curve, geometry tells matter how to flow.
    The GR equation is about the metric---that is about a distance function---it tells how the metric evolves and interacts with the flow of matter. The metric is a math description of geometry, the web of distance relations. Saying that the metric expands just means that distances between stationary objects are increasing according to a certain pattern.

    For concreteness, even though radar doesn't work over such long distances, you can imagine distances being measured by radar ranging. Timing how long it takes to bounce a beep off of something. The way hubble law distance is defined you can think of temporarily freezing the expansion process, so distances don't change during measurement, and then timing beeps. When I say the metric expands or the geometry expands I mean that distances to remote galaxies really are increasing, as you would measure by sending radar signals.

    But no "substance" being created. No "rubber". No "fabric". There's plenty more to discuss and ask about. But this is about all I can say for starters.

    The next thing you should probably try to understand is what it means to be stationary relative to the CMB (the background of ancient light.)

    Watch the movie---you will see that the galaxies stand still (lat. and long.) while the distances between them grow.
    That's what Cmb stationary means visually.
    Last edited: Apr 20, 2010
  11. Apr 20, 2010 #10
    Thanks for these answers, a lot!
    I really do get what the model intends to explain, it just was the alternative (layman's) interpretation that the rubber plays an actual role in the thing - which, with just looking at this model naively, can be misunderstood this way, that got me thinking.

    So in essence, space is thought to have always been there, and our universe (= all the particles that make it up, not more, not less) just moves through this space, basically not affecting it (if we disregard gravitational influences for a moment here). Was that more or less okay to say so?

    This now leaves me with another issue to think/read about. What then is this "space", and how can it be there? I know it's not a substance, but it's some kind of room, that must have come into existence somehow, or at least exist somewhere, and maybe even have a geometry by itself. Also: Are metrics like the planck length a property of the particles of our universe, or is it bound to this space? Is there a limit as to what particles and sizes may emerge/reside in this space, i.e. does it have some sort of structure by itself? Oh boy... I think I'll have to lock myself into some big library someday, and spend a few months there :)

    And I just realized, that I rushed in here and hijacked this thread a bit. I'm terribly sorry for that. Excitement overwhelmed my manners I fear.
  12. Apr 22, 2010 #11
    I've tried to get to this several times, to no avail. Google shows it, but site doesn't seem to work. Is anybody else having trouble? I'd like to see this.
  13. Apr 23, 2010 #12
    You cannot really say that 'space' is a "Property". A property has 'substance'. I guess you could call space an "Entity" inasmuch as an entity can be real, imaginary, metaphysical, or just a concept. Basically what throws people is their idea that if the Universe is expanding, 'space' must expand to accommodate said expansion. But since space is 'nothing' and nothing is everywhere 'something' isn't, space doesn't need to expand because it [nothing] is already there.
  14. Apr 23, 2010 #13


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    Pixchips thanks for telling me about the problem!


    I just tried it and it works fine. There could have been a temporary problem yesterday when you tried. Or there could be some difficulty with your browser. Give it a try and please let us know either way.
  15. Apr 26, 2010 #14
    I got it working! Something wrong with explorer and java scripts on this machine. I installed mozilla and java and it works fine. Thanks!
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