Does anyone have a link to a detailed description of the cosmological horizon problem?

PhotoSpiralysis Big Bang

(Photo credit: Absolute Chaos)

So, I’m trying to understand cosmic inflation a bit better, and I’ve concluded that I don’t understand one of the chief itches that it scratches.  I know the standard explanation about regions of space being too far apart to have ever interacted, but I don’t get why they couldn’t have interacted when the universe was the size of an atom.

If the answer is that there wasn’t enough time for the universe to expand without inflation, why the time limit?  Why can’t the solution be that the universe is a bit older?

If any of my readers with physics expertise know the answer, I’d be grateful.

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45 Responses to Does anyone have a link to a detailed description of the cosmological horizon problem?

  1. john zande says:

    Great question. I’ll be watching for replies.

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  2. Ignostic Atheist says:

    I was under the impression that they did interact when the universe was the size of an atom. Why don’t you think so?

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  3. My understanding is limited, but I can give it a try.

    As our imagination travels back in time, the universe getting denser, the expansion rate has to increase to counteract the gravity and avoid a collapse, allowing the sparse, rapidly expanding universe we see today. The alternative, the idea of a very dense universe expanding slowly seems implausible.

    So ultimately the observable universe had to be expanding much more rapidly than the speed of light. Indeed it is still going faster than light.

    So if the observable universe were always expanding faster than light, then what lies on our cosmic horizon in one direction could never have interacted with what lies on our cosmic horizon in the opposite direction, even when they were within a hydrogen atom’s radius apart, because they would have been so close for much less time than it would take for a signal to traverse even this tiny distance.

    But that doesn’t really explain why the interaction between different parts is accounted for by inflation. I think acceleration comes into the picture here. We can see that interactions took place between regions that are too far apart to have interacted without some massive acceleration of expansion at the beginning of time. The expansion was once slow enough to allow them to communicate, but was later fast enough to put them so far apart that a naive interpretation would have assumed communication was always impossible.

    I don’t know. This is just my waffle, trying to explain my limited understanding. I’m not sure it’s of much use. Hopefully you’ll get better responses!

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  4. Thanks DM and IA. The gravity issue makes sense. Maybe inflation was needed to get the expansion going? Although my understanding is that inflation was over 10-33 seconds after the big bang. I would think gravity would still have been an issue at that point, and that it was to an extent, slowing down the expansion until a certain point in the universe before dark energy started accelerating it again.

    But then I’m not clear on why the standard explanation is always about how homogeneous distant parts of the universe are. Why would we expect them to not be homogeneous if they were once within an atom’s diameter of each other?

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    • “Although my understanding is that inflation was over 10-33 seconds after the big bang.”

      Inflation was over quickly, but it was so rapid that the universe was much less dense by then and so the rate of expansion that remained was enough to overcome gravity.

      “But then I’m not clear on why the standard explanation is always about how homogeneous distant parts of the universe are. ”

      I too have problems understanding why homogeneity is a problem. Homogeneity doesn’t necessarily mean having communication. Correlation is not causation, but sometimes correlations reveal a common cause. For example, I used to be confused about how snowflakes grow to be symmetrical. How does one side of the snowflake know what the other is doing? What kind of process of communication is going on? But there is no such process. It’s just that the snowflake is a small object and conditions at one side of the snowflake match conditions at the other side and so they grow and develop deterministically in much the same way, seeded by an initial tiny crystalline structure.

      I don’t really understand why it could not be the same for the universe. Could the temperature of the universe not be a value that arises deterministically out of the physical constants? Why do we need to suppose that communication exists?

      I assume there must be some good answer. For example, perhaps QM predicts that the universe should be much less homogenous. Perhaps the initial fluctuations should have lead to more variation, and we need to have communication in order to allow this to even out to the extent that it has.

      “Why would we expect them to not be homogeneous if they were once within an atom’s diameter of each other?”

      I don’t think you are getting what an enormous distance an atom’s diameter is if the expansion rate is high enough. Given a fast enough expansion, it is a distance that prohibits all communication. For communication to be possible, the expansion rate must have once been relatively slow, which means that it must subsequently have been enormous (inflation) in order to catch up to what we see today. The period of slow expansion cannot have been long because the universe would have collapsed if it lasted longer than a few planck times.

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    • Ignostic Atheist says:

      Isn’t it more that we would expect it to not be homogenous if they weren’t so close together? What is suggesting otherwise?

      I’m not entirely sure about the gravity business, really. It would depend on when the Higgs field formed, right?

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  5. DM, it sounds like we’re in the same boat.

    On atom’s diameter, that was me using sloppy wording to refer to an arbitrarily close distance. From the initiation of the big bang to inflation, the universe should have been small enough for its components to interact and homogenize. From what I understand, inflation counts on that.

    Maybe, as you speculate, there’s some aspect of physics that says that the homogeneity would break down unless the expansion were very rapid.

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    • Hi SAP,

      “On atom’s diameter, that was me using sloppy wording to refer to an arbitrarily close distance.”

      I still don’t think you get it. Without inflation, then the rate of expansion of the universe is in some sense proportional to the size of the universe. It has to be to prevent collapse. The smaller the universe, the greater the rate of expansion. No matter how small the distance the rate of expansion is always great enough to prohibit communication between the two points we’re talking about.

      With inflation, this relationshp is broken. When the universe was very small, the rate was small enough to allow communication between the two points. Then the rate accelerated enormously so as to prevent communication. Then it settled back to something more in line with what we see today. So, because we observe homogeneity, inflation must be true.

      “Maybe, as you speculate, there’s some aspect of physics that says that the homogeneity would break down unless the expansion were very rapid.”

      That’s not what I’m saying. The reason the expansion had to be very rapid is because otherwise the universe would have collapsed. It simply cannot exist in a state of primordial density for very long without rapid expansion.

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    • “it sounds like we’re in the same boat.”

      Not quite. My confusion is about why homogeneity implies communication. Your confusion seems to be why communication implies inflation.

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  6. IA,
    Here’s my understanding of the standard big bang timeline
    1. It starts. Universe is close together, interacts, and homogenizes.
    2. Inflation happens. The observable universe is now about the size of a grape fruit,
    3. Expansion continues with the homogeneity achieved in 1 continuing.
    4. Current universe we observe today which is (mostly) homogeneous.

    My questions is why 2 is necessary for that homogeneity?

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    • Your understanding of the timeline is correct.

      1 is necessary for the homogeneity. 2 is necessary for 1 not to have collapsed the universe.

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      • I’d totally be prepared to buy that, if it was the explanation physicists usually gave. But they use the homogeneity one instead.

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        • “But they use the homogeneity one instead.”

          Ok, I haven’t explained this well.

          The important thing about (1) is not that the universe is close together. The important point is that it’s expanding slowly enough for relatively distant parts to communicate. This is only possible with inflation.

          The only reason to believe that inflation happened is because of the homogeneity. Without homogeneity, we can simply assume that expansion rate was always proportional to the density of the universe*. So the universe would still have been expanding at a tremendous speed at the big bang (I guess infinite at the theoretical singularity), but there was no special inflationary epoch which happened after the communication.

          So, in a way, the extraordinary thing about inflation is not just how fast expansion was at one point, but how slow it was before that point — much slower than a naive prediction based on today’s universe would have guessed.

          Do you get it now?

          (Oddly, the more I explain this and think about it the more I feel like I understand it, so thanks for that!)

          *When I say proportional I’m speaking loosely. I don’t actually know what the formula is. It may be proportional to the square of the density or something more complicated.

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    • Ignostic Atheist says:

      I typically run on the multiverse idea that inflation is a constant. That, unlike in the big bang model where there was a start and stop period of inflation, it was already happening at that first moment, and that something (gravity?) caused it to stop. At that first moment, there were no particles to consider to be “close together”, they were just energy all wrapped up in a pretty little uniform package. Perhaps it was a single, arbitrarily high energy particle that spontaneously appeared and was ripped apart by inflation.

      Going off the rails, perhaps it was the particle/antiparticle annihilation that we expect in a quantum vacuum, but never allowed to annihilate due to inflation, unlike what we would expect inside our slowly inflating universe. In that case, there would be a sister dark matter universe, upside down and backward, that, depending on how far down determinism goes, could be otherwise identical to ours. Mmm, goosebumps.

      At any rate, the question to ask from the point of view of the multiverse isn’t why was inflation necessary for the homogeneity of the universe, but why’d it stop?

      But hey, I am in no way a physicist. I just love to imagine.

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      • I love to imagine too, so no worries. I’m reading Max Tegmark’s book on the mathematical universe, and I’m in the section reviewing cosmology, where he speculates that our universe may be one of the regions, bubbles, where inflation was interrupted. Beyond the confines of our bubble, it continues uninterrupted, except for perhaps other regions an unfathomable distance away.

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  7. James Pailly says:

    I’m not a scientist, only a science enthusiast, so take what I’m saying with a grain of salt. I think the key concept that you’ve overlooked is that in the immediate aftermath of the Big Bang, space expanded or “inflated” faster than the speed of light. This means that two points on opposite sides of the Big Bang would have been propelled away from each other faster than the light from one could reach the other. Therefore, they could never have interacted AFTER the Big Bang occurred.

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    • James, no worries. My science status is enthusiast also.
      What I’ve been struggling with is why the inflation step itself is proved by homogeneity. DM might have covered it and I’m about to respond to him.

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  8. DM,
    I’m grateful for your efforts.

    So I’m clear with the homogeneity magic of inflation not being inflation itself, but the fact that it didn’t start right away, allowing a period for homogeneity to happen.

    But if gravity is what makes inflation necessary, why wouldn’t gravity have collapsed everything before inflation started? Or afterward for that matter? It seems like if you needed inflation to prevent gravity from collapsing everything from 10-36 to 10-32 seconds, you also need it to prevent collapse from 10-43 to 10-36 seconds. That said, we’re talking about such short time scales that I could see the very shortness being a factor, though not once inflation was over.

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    • “why wouldn’t gravity have collapsed everything before inflation started?”

      Because it didn’t have time to. Anyway, inflation didn’t really “start”. It was going from the very beginning, but it was a (rapid) acceleration. This means that in the very first instants expansion was not quick. So expansion started slow and rapidly accelerated. Without inflation, expansion starts (infinitely?) fast and decelerates. This accelerating force was always there and was always counteracting gravity until inflation stopped.

      “Or afterward for that matter?”

      Because by the time inflation ended the universe was already expanding quickly enough and had lost enough density to coast for tens of billions of years without collapsing (if collapse it ever would).

      “It seems like if you needed inflation to prevent gravity from collapsing everything from 10-36 to 10-32 seconds, you also need it to prevent collapse from 10-43 to 10-36 seconds.”

      I think this is answered by my argument that inflation was there from the very beginning as an acceleration. The difference between the two periods is not whether inflation is there or not but whether the expansion has yet accelerated to speeds we recognise as characteristic of inflation.

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      • Ignostic Atheist says:

        Inflation isn’t really an acceleration though; it’s an expansion of space and doesn’t impart motion.

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        • I’m actually aware of this, but acceleration is often used to describe processes other than motion (e.g. accelerating economic growth). I find it hard to find another way of concisely communicating the idea that the rate of expansion of space was growing over time. Any suggestions?

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          • Ignostic Atheist says:

            Hrm, ok then, what makes you think that inflation accelerated from slow at the beginning to extremely fast, before it came back down to a nice slow inflation? And what does this say about the idea of the multiverse as a whole? Could other universes have smashed into ours because inflation is so pokey?

            The words you’re looking for are accelerating inflation.

            If space and time are linked, wouldn’t the inflation of space also make time run slower?

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          • “what makes you think that inflation accelerated from slow at the beginning to extremely fast”

            Have a look at this graph.

            Now, granted, only the very rapid part is described as inflation, but you’ll note that the expansion of the universe’s radius accelerates right from the beginning. Acceleration means going from slow to fast. Therefore it was slow at the beginning. In this graph the slope is pretty much 0 at the beginning. While inflation is usually described as the epoch of rapid expansion, I think it’s also reasonable to think of inflation as that which caused the acceleration to rapid expansion.

            “And what does this say about the idea of the multiverse as a whole?”

            Not a lot? I think I’m just describing the standard inflationary model. So, whatever that says about the multiverse.

            “Could other universes have smashed into ours because inflation is so pokey?”

            No, because universes are regions where inflation has ceased. They are separated by regions where inflation has not ceased. The distances between universes grow exponentially so they can never collide.

            “The words you’re looking for are accelerating inflation.”

            I think that’s what I’ve been saying!

            “If space and time are linked, wouldn’t the inflation of space also make time run slower?”

            I imagine it would make time run quicker if anything. Strong gravitational fields slow down time, so I would imagine that time runs slower in a dense universe. Inflation causes the universe to get less dense. But I don’t know, really.

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          • Ignostic Atheist says:

            But by your description, universes are defined more as regions where inflation has occurred, rather than regions where inflation has ceased. The slope of inflation begins at close to zero, which suggests that the rate of inflation outside of a universe is rather wimpy.

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          • ” which suggests that the rate of inflation outside of a universe is rather wimpy.”

            No matter how fast inflation ever gets, there will always be parts of an inflating space which are only inflating slowly. Two objects a nanometer apart separate much more slowly than two objects a meter apart. So if the inflation rate of a region is in some sense proportional to the size of the region (as seems to be the case in the graph I linked to), then no matter when you start, if you look at a region in an inflating space small enough you will find that the inflation rate of that region is correspondingly small. The multiverse may have been inflating for eons, but if our universe started as a bubble a planck-length across then that bubble would have been expanding relatively slowly at first.

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          • Ignostic Atheist says:

            Ah, that is what I get for confusing a graph of the radius of the universe with a graph of the rate of inflation.

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          • I think that this zoom of the Mandelbrot Set might help as a visualisation.

            As you watch the video, which zooms eternally, you can imagine that what you see represents space inflating eternally. The rate at which shapes grow is geometric, not arithmetic. When you first make out a shape appearing, it’s growing at a relatively low rate (e.g. 10 pixels per second). By the time it slips out of the field of view, it is growing at perhaps 100 pixels per second.

            You can imagine each such shape is a bubble universe. Expansion of that universe starts slowly but rapidly accelerates. Globally, the rate of exponential acceleration remains constant, but it is not wimpy. Universes will not collide because even as they grow bigger, the space between them grows even bigger again.

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          • “Ah, that is what I get for confusing a graph of the radius of the universe with a graph of the rate of inflation.”

            Actually, the two should look similar, if we think of the rate in terms of metres per second, say. The bigger the universe is, the faster the rate is.

            But if you think of the rate in terms of “time taken to double in size” then it’s different.

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          • Ignostic Atheist says:

            My thought is if you take a thimble full of inflating cosmos, after a fraction of a second it will be a certain size and that experiment holds steady, not accelerating. This is ignoring the fact that the thimble would be annihilated or start a universe of its own.

            So your second option.

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          • “My thought is if you take a thimble full of inflating cosmos, after a fraction of a second it will be a certain size and that experiment holds steady, not accelerating. ”

            I think this is correct. However, there is still an acceleration in play. If you take a car doing 0mph and accelerate at 5mph per second, then it will have travelled a certain distance after 10 seconds, and that experiment holds steady. But just as with the expansion of inflating space, the relationship between the distance travelled and time elapsed is not linear.

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          • Ignostic Atheist says:

            Ok, let’s put it this way,

            Some volume of inflating space V(n) = V(n-1) * R, where R is the rate of inflation. You say it is accelerating because dV increases over time, I say it is constant because R is constant.

            Can we subscript in comments? What the hell, I’ll try: Vn = Vn-1 * R

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          • Subscript or not, I understand what you’re saying. But it’s both constant and acceleration, because it’s constant acceleration!

            When I say the rate of expansion of the universe, I mean the delta in the radius of the universe over time. You seem to mean the delta of the delta.

            Car analogy: the radius of the universe is the distance travelled. The rate of expansion of the universe is the velocity of the car. The rate of change of the rate of expansion of the universe (what you seem to mean by rate) is the acceleration of the car, and this remains constant.

            I think mine is the way these terms are normally interpreted, but I understand what you mean.

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          • Ignostic Atheist says:

            And I was given the impression that you were saying that the constant was accelerating. That’s really all there is to this.

            I like to view it as an expansion of space, rather than the change in radius of the universe compounded since the beginning of the universe, because nothing is actually being moved due to inflation. Points become more distant, but this is not due to a force being applied to them. This is unlike a car analogy where a car on the edge of the universe is being blasted through the speed of light. The car’s not moving, it’s the center of the universe that is moving away from the car. This applies to every single point in the universe – no force is acting upon it. Ignoring local forces, it is essentially stationary, with the universe running away from it.

            What it comes down to, is I’m not thinking of the universe specifically. I’m thinking of pre-universal inflation (I’s got the multiverse on the mind), for which there is no metric like the size of the universe to compare to. The only way to adequately explain that is to refer to the constant inflation’s effect on a unit cube or sphere, or whatever geometry exists.

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          • Excellent discussion guys. I’m just jumping in here to note that there is energy being applied to the expansion of space, but no one knows what it is, which is why it’s usually called dark energy.

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          • Ignostic Atheist says:

            I once thought that maybe, instead of everything in the universe flying apart, everything was shrinking and the size of the universe is static.

            Never did find a way to tell the difference between the two.

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          • I had the same thought. It is true, from a certain point of view. The ratio of matter to volume of space is shrinking. Of course, the reverse ratio of space volume to matter is expanding.

            If space is composed of irreducible pixels, say maybe at the planck length, then saying that matter is shrinking might only be accurate if that matter were composed of fewer and fewer pixels, existing at a lower and lower resolution (the universe might end in a great pixelation). Of course, if the pixel/matter ratio was staying the same, you could say that the pixels themselves were shrinking, which puts us back to the first paragraph. Although the number of pixels in the universe would still be increasing.

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          • I get that this idea is just a fun thought experiment and not something you intend seriously, but I think it raises some interesting issues so I’m going to take it seriously, if you don’t mind.

            I think the idea that stuff within the universe might be actually shrinking only makes sense if you think there is a sensible absolute measurement of distance that could be used only by an observer standing outside the universe. But there isn’t. The only way we can make sense of the size of the universe is in terms of stuff in the universe, i.e. a particle moving at the speed of light. In order to work with a model that has the universe shrinking, pretty much every physical constant would have to be changing in concert. It’s like using epicycles to support geocentrism – mathematically it can be made to work but it’s perversely complicated and there’s no reason to do it (except for fun, perhaps!). Since there can in principle be no observer to settle the question of whether it’s “actually” expanding or everything is shrinking, it’s a mistake to think that there is an answer at all. In truth, it’s a meaningless question, but parsimony demands that we consider the universe to be expanding.

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          • Ignostic Atheist says:

            Well maybe you can stop by sometime and let me know what you think of the Conformal Cyclic Cosmology put forth by Roger Penrose. It’s one of my new favorite things. 😀

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      • Thanks DM. That seems plausible (at least in my inexpert judgment). I’m going to have to mull it over. Maybe re-read Tegmark’s chapter on inflation.

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  9. There isn’t an answer; I’m saying. The problem begins at the beginning. The big bang itself isn’t probable in my opinion… and it cannot be shown to have occurred as an explosion. I like better a theory that the energy more or less pours into space-time… not that it ever exploded. Letus now if you come up with an actual iron-clad answer to the problem of the cosmological horizon.
    Thanks,
    ~ Eric

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    • There’s actually a lot of evidence for the big bang, that is, the known universe starting in a hot dense state about 14 billion years ago and expanding and cooling ever since then.

      I don’t have an iron clad answer yet, but from our discussion here, and from what I’ve been able to read, I think the answer is that under the classic big bang expansion rate, the cosmological horizon is always smaller than what is now the observable universe, even from the earliest instances.

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