# ΛMarch 12, 2008 2:28 PM   Subscribe

How is the universe 156 billion light years across if it is only 13.7 billion years old?
posted by plexi to Science & Nature (17 answers total) 15 users marked this as a favorite

Inflation. Where are you getting 156bn light years across from?
posted by caek at 2:30 PM on March 12, 2008

Because the Big Bang wasn't matter exploding into space, it was space itself expanding.
posted by BitterOldPunk at 2:32 PM on March 12, 2008

q.v. Superluminal space expansion.
posted by zamboni at 2:34 PM on March 12, 2008

Heh. Not that I would have looked there, but this is addressed in the 2nd paragraph of Universe:
Since special relativity states that matter cannot exceed the speed of light in a fixed space-time, it may seem paradoxical that two galaxies can be separated by 93 billion light years in 13 billion years; however, this separation is a natural consequence of general relativity. Stated simply, space can expand with no intrinsic limit on its rate; thus, two galaxies can separate more quickly than the speed of light if the space between them grows.
posted by smackfu at 2:36 PM on March 12, 2008

More from wikipedia: Observable universe.
posted by nat at 2:39 PM on March 12, 2008

Where are you getting 156bn light years across from?

NASA and the BBC, but Wikipedia says that figure is meaningless. Wikipedia doesn't cite why it is meaningless, it only references 3 articles that state the Universe is 156 billion light years across.

Is Wikipedia really the definitive source on cosmology?
posted by plexi at 2:48 PM on March 12, 2008

Yeah, it's pretty meaningless. What you mean by "across" depends on the geometry of the universe. More meaningful (but still on dodgy ground) to talk about the separation of two specific objects, which still begs your questions, since there are plenty of galaxies further than 14bn light years away. Play with "z" here and look at the luminosity distance, which is roughly the number you're talking about. A pretty small z of about 3 will get you up to 100bn light yr. We know of galaxies at z = 6 or greater.
posted by caek at 2:52 PM on March 12, 2008

Wikipedia is certainly not the definite source on cosmology, but more often than not it gives a good, well thought out and easily understandable discussion. I was going to write something up-- but the several folk who've edited the "Observable universe" article have done a better job than I could do on any reasonable time scale.

Wikipedia does discuss why that figure is meaningless: It is simply a doubling of the 78 billion lightyear estimate. Can you be more specific about what sort of reference you would like?
posted by nat at 2:54 PM on March 12, 2008

And of course at the big bang, z is a very big number indeed, so all bets are off.

Our Cosmic Habitat by Martin Rees is the best, least "whoa, gimme another hit of that bong" popular cosmology book by the way.
posted by caek at 2:54 PM on March 12, 2008

The figure you're talking about is probably an estimate of the width of the observable universe, which has a technical cosmological definition. For all we know, the universe currently may extend infinitely in all directions and may have extended infinitely in all directions at the point of the Big Bang.

Scientific American article Misconceptions About the Big Bang.
posted by XMLicious at 2:56 PM on March 12, 2008

Infinitely and non-repeatingly, I should say; caek makes a good point about cosmological geometry.
posted by XMLicious at 3:00 PM on March 12, 2008

Spacetime compression near the edges could pretty much make it infinite in size (in the sense that you would never reach the edge).
posted by blue_beetle at 3:07 PM on March 12, 2008

I suggest you listen to the always excellent Astronomy Cast. The current episode is in fact about the size of the Univers.
posted by McSly at 3:10 PM on March 12, 2008 [1 favorite]

blue_beetle: based upon that Scientific American article and from what I've read elsewhere about cosmology, there aren't necessarily any edges and compression need not have anything to do with an infinite universe. The universe may extend infinitely in every direction as flat spacetime and that would be consistent with Big Bang theory and the rest of modern cosmology, I believe.
posted by XMLicious at 4:02 PM on March 12, 2008

I've seen the 156 billion number before. I'm pretty sure it's one reporter or astrophysicist's mistake that's been seen and repeated. The right value is half that, roughly.

caek gives the link I always give people. The distance in question would usually actually be to the CMB - that's the point at which light is basically scattered all the time so it's as far back as you can see (the universe past that point is basically like a thick hot fog - completely impossible to see through). That's at a redshift of 1100. The big bang itself is at a redshift of infinity, but you'll see that as you increase the redshift the lookback time converges on the age of the universe, and the various distances will do peculiar things (luminosity distance will reach infinity, angular diameter distance will reach zero, and comoving distance probably some finite value a little larger than the one everyone talks about).

The reason it's bigger is most easily explained as the first light year the light covered was in the universe when it was very small, and it's since expanded, so that first light year of distance is now more like a thousand. The last light year, well, that's still pretty much a light year. Integrate it all up properly (as the Javascript calculator does) and you get the 46 billion light year comoving radius that you could double to about 90 billion light years diameter.

Now 156 billion light years is obviously not 2x 46 billion, or 4x it allowing for the doubling error. The 156 billion figure actually comes from an analysis of the patterns of fluctuations in the cosmic microwave background in a paper by Key et al. What they did was try to see if they could find if the universe was 'repeating' so that you could travel off in some direction and land up back where you started. To do this, you can look for the same patterns of fluctuations in two different parts of the sky. They found no repeating circle patterns larger than 20 degrees across. There's a diagram in that paper showing the universe overlapping with itself, with the CMB being an outer surface of a sphere which overlaps with an identical copy (really not a copy but the same universe again) and the intersection of the two spheres has an angular radius of 20 degrees. It's the intersecting ring that should be measurable on opposite sides of the sky, and which they didn't find any larger examples of.

Now, if you take that 20 degree number, and do the appropriate trigonometry with the radius of the sphere being my previously mentioned 46 billion light years you get a size of the universe that's less than 46 by
46*2*(1-cos(20 degrees))
which is 40.5 which is 81 billion light years. Double that again by mistake and you get 162, and the difference from that and 156 is entirely explicable by the roundings I've done in the process, the roundings done in the paper and roundings done converting between the parsecs astronomers more usually use and the light years that newspapers prefer.

And please, if you see that 156 billion number anywhere else, try to get it corrected.
posted by edd at 6:44 PM on March 12, 2008 [2 favorites]

Hmm, in fact I'm not even sure that geometry I did was right (I did it ages ago when the same issue came up somewhere else, and it seemed right at the time and fitted the numbers). I think the factor of 2 should be dropped. Which doesn't make it fit the given figures so nicely, but that is probably explainable by more rounding, slightly different cosmological parameters, and possibly them making exactly the same mistake I did. Unfortunately Key et al don't really explain the last bit of their estimate and just go from 20 degrees to 24 Gpc.
Anyway, basic principle is all the same.
posted by edd at 7:05 PM on March 12, 2008