Big-bang versus observational event horizon

[tamurphy]

Cosmologists seem to refer interchangeably both to a big-bang origin just beyond the limit of present observation, and to an observational horizon where the rate of expansion of the universe exceeds the speed of light.

The notion that looking out in space entails looking back in time gives rise to the conception that the most distant observations are of a much shrunken early universe that is projected to have originated in a big bang some 13.75 billion years ago. In the meantime, expanding spacetime has stretched this observational bubble to about 25 billion light years in radius.

Concurrently there are credible suggestions of a mega-universe that extends, perhaps infinitely, beyond the event horizon of local observation. This horizon occurs at the distance where the rate of expansion of the universe with respect to the observer exceeds the speed of light.

At least these are my understandings.

My question is, how are these two conceptions reconciled? A mega-universe would seem to imply that, if there were a big bang, it must have occurred beyond the local event horizon. On the other hand, a big-bang singularity that lies within the local event horizon, albeit at the de facto limit of observation, would seem to render the notion of a mega-universe moot. Perhaps more to the point, how is the observational event horizon related to the big-bang?

 

[Chalnoth]

Cosmologists seem to refer interchangeably both to a big-bang origin just beyond the limit of present observation, and to an observational horizon where the rate of expansion of the universe exceeds the speed of light.

Er, this isn't actually true. By most measures you would want to use of recession velocity, most of the observable universe is and always has been receding at faster than the speed of light. The horizon isn't caused by any sort of speed limitation (there is no speed of light limitation between distant objects in GR, only at single points). Instead, it's just caused by how far light can get, which can be very different than any sort of speed differential between distant objects.

The reasoning for this is pretty simple, actually: the speed between two objects separated by some distance in General Relativity is arbitrary. It depends entirely upon your choice of coordinates. If the speed depends upon something as arbitrary as what numbers you decide to apply to space-time, then obviously there can be no limit placed upon it (I can just pick my numbers so that the speed comes up to whatever value you want!).

That said, if you take coordinates that move along with the expansion, then in those coordinates we see galaxies today that are and always have been moving away faster than light. The way it works is this: the galaxy emits a photon towards us. That photon travels in our direction, but the space between us and the photon is expanding faster than light. The photon makes some headway, but then there's more distance left to travel. This goes on for some time, but in the meantime the expansion rate is slowing down. The photon is still closer than the galaxy, so the recession velocity is less, even though it's moving away. Eventually, if the expansion rate slows enough, the photon will no longer have a recession velocity, and will actually start moving towards us, while the galaxy, which is much further away by now, will still be receding at faster than the speed of light. The photon doesn't care, though: it long ago left that galaxy and it doesn't matter how fast the galaxy is receding.

The notion that looking out in space entails looking back in time gives rise to the conception that the most distant observations are of a much shrunken early universe that is projected to have originated in a big bang some 13.75 billion years ago. In the meantime, expanding spacetime has stretched this observational bubble to about 25 billion light years in radius.

Well, the cosmic microwave background is today about 48 billion light years away from us (in those same coordinates that move along with expansion that I mentioned earlier). This is the limit of our vision because before then, our universe was opaque.

My question is, how are these two conceptions reconciled? A mega-universe would seem to imply that, if there were a big bang, it must have occurred beyond the local event horizon. On the other hand, a big-bang singularity that lies within the local event horizon, albeit at the de facto limit of observation, would seem to render the notion of a mega-universe moot. Perhaps more to the point, how is the observational event horizon related to the big-bang?

It all comes down to how the expansion rate has changed over time. At very early times, during inflation, the expansion rate was nearly constant. This means that if you ask, "if an object is one million light years away, how fast, on average, is it receding?" you'll get the same answer whether you're talking about objects one second or the next: objects one million light years away always recede at roughly the same average velocity.

Note that this means that objects are actually accelerating away from one another: an object one million light years away now will, in the next second, have moved away, where objects are on average receding even faster.

In the very early universe, this acceleration was absolutely massive, so that an area of space-time smaller than the size of a proton would have been blown up to be many light years across in less than a second. Because you can start from such a small area that gets huge in very little time, everything that came from this one event could well be so vastly larger than what we can see that it boggles the mind: if inflation lasted only twice as long as is required to explain the flatness of the observable universe, it would have produced a universe around 10^30 times larger in each direction than what we can see.

 

[Ich]

On the other hand, a big-bang singularity that lies within the local event horizon, albeit at the de facto limit of observation, would seem to render the notion of a mega-universe moot.

I don't understand what you're trying to say here. The big bang certainly lies in the causal past of everything in the universe, so why do you think it should be outside the observable universe of each observer?
BTW, the limit of the observable universe is normally not called an event horizon.

 

[tamurphy]

Cosmologists seem to refer interchangeably both to a big-bang origin just beyond the limit of present observation, and to an observational horizon where the rate of expansion of the universe exceeds the speed of light.

Er, this isn't actually true. By most measures you would want to use of recession velocity, most of the observable universe is and always has been receding at faster than the speed of light.

Thanks for your comments.

Just to be sure we're on the same page, when I refer to an 'observational universe,' I mean the spacetime domain that is observable from a particular point in spacetime. For all practical purposes, such a point could be regarded as virtually identical for contemporary denizens of planet Earth. I've tended to visualize this as a Minkowski past light cone.

With this as background, I don't understand your statement that "most of the observable universe is and always has been receding at faster than the speed of light," as light emitted from such locales wouldn't be observable from the present perspective.

 

[Chalnoth]

Thanks for your comments.

Just to be sure we're on the same page, when I refer to an 'observational universe,' I mean the spacetime domain that is observable from a particular point in spacetime. For all practical purposes, such a point could be regarded as virtually identical for contemporary denizens of planet Earth. I've tended to visualize this as a Minkowski past light cone.

With this as background, I don't understand your statement that "most of the observable universe is and always has been receding at faster than the speed of light," as light emitted from such locales wouldn't be observable from the present perspective.

Ah, well, you can view space-time as Minkowski locally, but not globally. It starts to break down as you get to distances that are significant compared to the space-time curvature, which in an expanding universe is around a Hubble radius. Since we're talking about the horizon here, we definitely have to take into account the curvature to talk about things in a meaningful manner.

 

[tamurphy]

Looking into deep space with optical telescopes yields images that are more and more redshifted with distance (and time). Attempting to look further would require infrared telescopes. This is being done. To look even further requires us to use radio telescopes whereupon we observe the cosmic microwave background radiation. We cannot look any further because the CMB will block our view.

It is interesting and perhaps relevant that we have a coincidence between our limit of observation established by the speed of light (our light cone) and the interference effect by the CMB. Why should our light cone just barely subsume the CMB? Is this another case of fine tuning?

Thank you very much. You've addressed the question I intended to ask regarding the curious coincidence between the observational limit imposed by the speed of light and what you refer to as "the interference effect by the CMB." Perhaps not surprisingly, I find the notion of fine tuning to be unsatisfying. Among other things, I'm wondering whether the CMB, inflation and imputed big-bang are simply the appearance of a local event horizon a la the notions of a holographic universe.

Remember, we must be seeing back to the big bang as a sort of delocalized "center" in a spacetime which has a minimum of 4 dimensions. Then, our line of sight constitutes a radius. If we were a point on the circumference of a circle, we might look back in time and distance toward the center.

But, our line of sight could not enclose more than the center and also points within the circle and on the circumference less than a single radius distant. This would represent only a fraction of the area of the circle. Now, the fraction of the universe that we can actually see when the universe is considered to be at least 4 dimensional is even less than this. The universe that we can see is what we would call a "lens" shape in 3 dimensions and in 4 dimensions might be called a "hyperlens".

I don't have a clear mental image of this. Perhaps such is unobtainable by a mode of perception that's conditioned to represent its stimuli in three or even four dimensions? Still, that concern doesn't prevent trying.

I'm confused by your statement "our line of sight could not enclose more than the center [big-bang?] and also points within the circle and on the circumference less than a single radius distant." Using your analogy, my comprehension of a light cone suggests that it flares out toward the center from a singular point of view on the circumference, thereby preventing perception of any other points on the circumference. Also, owing to the notion of expansion, it seems that cross-sections of the 'light cone' must narrow as they approach the central singularity. What am I missing here?

 

[tamurphy]

Ah, well, you can view space-time as Minkowski locally, but not globally. It starts to break down as you get to distances that are significant compared to the space-time curvature, which in an expanding universe is around a Hubble radius. Since we're talking about the horizon here, we definitely have to take into account the curvature to talk about things in a meaningful manner.

Right on! How would this curvature affect something like the Minkowski representation of an individual perspective? I've been inclined to think that negative spacetime curvature would be reflected in an outward flaring of the cone. However, as I mentioned elsewhere, this would seem to conflict with the notion that everything observable emanates from a big-banging singularity located within this cone.

One way I've tried to deal with this is to conceptualize a toroidal configuration with a non-dimensional singularity at its center. The focus of perception is then oriented in one direction from this singularity; the big-bang is oriented in the other direction; and the perceptual event horizon is the decohering interface between them.

Okay...let the guffaws begin...

 

[marcus]

...With this as background, I don't understand your statement that "most of the observable universe is and always has been receding at faster than the speed of light," as light emitted from such locales wouldn't be observable from the present perspective.

It is explained in the Lineweaver SciAm article linked here (princeton.edu link at the end of this post).
Most of the galaxies we now see were receding at rates greater than c, as per Hubble law, at the time they emitted the light we are getting from them. How this happens is explained in lay terms in the Lineweaver article.

What you quote from Cronos is quite legit---basic to the standard cosmo picture. If you look at the SciAm article and still don't understand, you are welcome to ask for help here.

 

[Chalnoth]

Right on! How would this curvature affect something like the Minkowski representation of an individual perspective? I've been inclined to think that negative spacetime curvature would be reflected in an outward flaring of the cone. However, as I mentioned elsewhere, this would seem to conflict with the notion that everything observable emanates from a big-banging singularity located within this cone.

Well, yes. This is known as the "horizon problem", the solution to which is positing a fast, accelerated expansion during early times (as compared to a matter or radiation-dominated expansion that is always decelerating).

 

[tamurphy]

It is explained in the Lineweaver SciAm article linked here (princeton.edu link at the end of this post).
Most of the galaxies we now see were receding at rates greater than c, as per Hubble law, at the time they emitted the light we are getting from them. How this happens is explained in lay terms in the Lineweaver article.

What you quote from Cronos is quite legit---basic to the standard cosmo picture. If you look at the SciAm article and still don't understand, you are welcome to ask for help here.

Thanks, Marcus. I didn't see the link you referred to. Is that because of a setting I may have?

 

[Chalnoth]

Thanks, Marcus. I didn't see the link you referred to. Is that because of a setting I may have?

It's in his signature.

 

[marcus]

Okay...let the guffaws begin...

It is in no one's interest to guffaw. Everybody's interest to get you up to speed.

Check out Ned Wright's tutorial. Just google ned wright. Cosmo prof at UCLA with a good website. Note the teardrop shape past lightcones (plotted using proper distance, the measure appropriate to Hubble law expansion.)

No need to worry about toroids at this point.

Also Wright has an online "cosmo calculator" that embodies the standard model (with, note this, these values of the three main parameters .27 for matter fraction, .73 for cosmo constant, 71 for current Hubble parameter).

Another thing that might help you is Morgan's online calculator. Google "cosmos calculator".
To get started with that one you need to put in the parameters .27, .73, 71. You will see which boxes to type in. Then you put in any redshift and it will give distances and recession rates.

You will see that any galaxy which we observe with redshift 1.7 or more was receding at more than c, at the moment when it emitted the light which we are now getting from it.

And of course, most of the galaxies we see have redshift greater than 1.7.
We see them out past z = 7, after all. And the CMB has z = 1090.

 

[marcus]

Thanks, Marcus. I didn't see the link you referred to. Is that because of a setting I may have?

Sorry about insufficient clarity. I'll get some links:

Lineweaver Sci Am article
http://www.astro.princeton.edu/~aes/AST105/Readings/misconceptionsBigBang.pdf [Broken]

Ned Wright cosmo tutorial
http://www.astro.ucla.edu/~wright/cosmo_01.htm
http://www.astro.ucla.edu/~wright/cosmolog.htm

Wright online calc.
http://www.astro.ucla.edu/~wright/CosmoCalc.html

Morgan online calc. (specially fond of this one because it gives recession rates )
http://www.uni.edu/morgans/ajjar/Cosmology/cosmos.html

Wright animated picture of expansion with stationary galaxies and wiggly photons moving between them
http://www.astro.ucla.edu/~wright/Balloon2.html
(galaxies stationary relative to the microwave Background, keeping same latitude longitude)

 

[Chalnoth]

It is in no one's interest to guffaw. Everybody's interest to get you up to speed.

Aye, almost nothing's more fun on these forums than somebody who is honestly inquisitive :)

 

[tamurphy]

It's [link] in his signature.

Thanks...I turned off signatures in an attempt to eliminate their repetition. Guess I'll have to turn them back on.

 

[tamurphy]

Sorry about insufficient clarity. I'll get some links:

Lineweaver Sci Am article
http://www.astro.princeton.edu/~aes/AST105/Readings/misconceptionsBigBang.pdf [Broken]

Ned Wright cosmo tutorial

Wright online calc.
http://www.astro.ucla.edu/~wright/CosmoCalc.html

Morgan online calc. (specially fond of this one because it gives recession rates )
http://www.uni.edu/morgans/ajjar/Cosmology/cosmos.html

Thanks again to you all. Now I have some homework to do before proceeding with this line of inquiry.