yet another Big Bang question

Pavel

I watched the Big Bang show on the History channel and a couple of things they had said raised my eyebrows. I wanted to ask you guys what you think.

First, they said that the Universe is 156 billion light years across. Where do they get that number? Is that based on the rate of inflation? But I thought they really don't know how much (precisely) it expanded. Otherwise, isn't the visible Universe 13.7 x 2 billion light years across? So do we now know how far it extends beyond the horizon?

Second, speaking of inflation, they said that the reason the inflation broke the cosmic speed limit (c) is because when it expanded, the forces were all united and therefore the physical laws-including the speed of light-didn't apply. But I thought that inflation has nothing to do with the speed of light. When space expands, the fabric itself stretches, not that the physical objects travel faster than speed of light. Isn't the same true for inflation as well? Besides, I thought inflation happened after the gravity split from the superforce. When do the laws of the speed limit start applying? After the electroweak force split into electromagnetic and weak ones??

Thanks,

Pavel

Chronos

The 156 billion light years thing is how big the universe really is 'right now'. This is a pretty useless piece of information since the light being emitted 'right now' won't be reaching us for a very long time. Only light emitted during the first 13.5 billion years of existence is reaching us at present. Inflation almost certainly occured before the electroweak break. It is not clear if it occured before gravity emerged. By most accounts, inflation was over by the time the Planck clock began ticking.

hellfire

If you had sent a photon 13.7 Gyr ago then this photon would not be at 13.7 GLyr away from you, but at about 46 GLyr. This is because in the time the photon traveled away from you, space between you and the photon expanded. By the way, the 156 GLyr number is wrong, the correct value is 92 GLyr.

One can consider objects to be at rest in space during expansion. The speed that one can calculate making use of Hubble's law v = H d, is an "apparent" recession speed of objects, but not a proper speed. Therefore, the limitation of v < c does not apply. You can see that, if d > c / H, then v > c. This limit c / H is called "Hubble distance". There is nothing special about this distance and every cosmological model in which space is big enough will have superluminal recession speeds. This has nothing to do with inflation or unification of forces.

George Jones

See this post by me.

Pavel

I see, well, I knew there was much more than we see, because we can see in all directions 13.7 Glyrs, but we can't presume (by Copernicus principle) that we happen to be at the center of the Universe; but I didn't know there is actually a number of how much further the real horizon extends. By the way, do you mind showing how you derive 92GLyr? With all due respect, the show had all the poster boys: Green, Tyson, Kraus, etc. They say 156 :). Hasn't Hubble constant been at a specific value (~71km/s Mp) only for a few billion years? And is there an agreement on how much inflation blew up the Universe? I've seen numbers from "up to a meter" to "beyond the visible Universe". Without this esitmate, how can you calculate the present size?


Chronos and George, thanks for your insigtful replies as well. I wanted to ask you about this "right now" in the context of SR, but perhaps some other time.

Thanks,

Pavel.

granpa

i believe the hubble constant only tells you the age of the universe.

marcus

I think that particular number is an AT LEAST estimate arrived at by looking for hall-of-mirrors-type repeat patterns in the CMB map.

that particular number came up in a paper by Neil Cornish and David Spergel (prominent reputable) in a paper around 2004-2005
then they confirmed and improved in a second paper in 2006 after more CMB data came out.

they never said the universe wasnt infinite. they never suggested it couldnt be 400 billion or 500 billion across either

they said it had to be AT LEAST 78----somehow because of confusion about the definition of the size parameter some people doubled this to 156----like talking about a circle the farthest away a point can be is 78 but the circumference is 156---technicalities.

HOW DID THEY GET IT? they said well the universe could be spatial infinite but suppose it WERE finite, like the surface of a balloon except 3D, or some other finite shape that has no boundary---say the surface of a donut. I know a donut sounds silly but SUPPOSE.

OK if it is a finite boundaryless 3D shape then if it is small enough for light to have come to us around both sides of the circle then we should see DUPLICATIONS in opposite sides of the sky in the very oldest structure available to us----the CMB map.
We should see REPEAT PATTERNS in the map. OK, so they figured out what "small enough" means----say it means 78 billion.

then they looked for repeat patterns and they DIDNT FIND ANY.

So they concluded that it must be AT LEAST 78, because if was anything less than this they would have seen repeat patterns.

they are good scientists. they are not trying to tell you the universe is 78 or 156, only that it has to be at least that, on good evidence.
==================

there are other ways to estimate the spatial size of the U, if it is finite. In January 2007 Ned Wright posted a paper which contains a suggestion that if it is finite a 'best fit' idea of size would be a radius of curvature of 130 billion.
that is speculative but gives some notion. a 4D ball with a 3D skin called a "3-sphere" analogous to the 2D surface of a balloon except it is 3D. A 3-sphere with radius 130 billion lightyear.

this is consistent with Cornish and Spergel because they were not talking radius their numbers are more like a circumference or half-circumference. So multiply the 130 by pi and it is at least what Cornish et al said. Nobody is being terribly precise at this stage anyway.

hellfire

I can show you the calculation, but it is easier if you go to any of the cosmological calculators in the web, like mine and check the "Radius of the observable universe now" output. If nevertheless you are interested in the calculation, then I will explain it here for you.

The value 46 GLyr is the radius of the observable universe, i.e. the radius of the causally connected patch today in the LCDM cosmological model. The start for the formation of the causally connected patch is usually defined at the epoch of formation of the CMB. There is no way that photons can reach farther away than this distance today, if we assume the validity of this model.

Thus, I simply cannot imagine how it can be possible, by any experimental means based on photons (or CMB), to infere about a lower bound for the radius of the universe that is larger than the causally connected region today. This is the reason for me to believe that this 156 GLyr value is wrong, and I guess that the confusion arises from some press article. If you think it is not, or you know about a reference where this is mentioned (a paper but not a press release please), please tell me.

By the way, I have searched now for the 2003 Cornish paper: Constraining the Topology of the Universe and I think I have found the source of confusion, that seams to be somehow what marcus already mentioned. In the abstract it is mentioned that:

I assume that someone was not careful enough and translated this into GLyr (78 GLyr) assuming that it was meant a lower bound for the radius. However, if you read the paper you will see, in the middle of the right column of page 4, that this value is a lower bound for the diameter.

Pavel

Greatly appreciate the insight, guys. Thank you for the references too.