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universe expanding forever? Answered

I saw this article on the BBC news site:


which has some astronomers apparently claiming that they have now worked out the fate of the universe from measurements on distant stars magnified through a galactic cluster. The final quote is:

Professor Priyamvada Natarajan of Yale University, a leading cosmologist and co-author of this study, said that the findings finally proved "exactly what the fate of the Universe will be".

This seems like a pretty bold claim to me - I was thinking that even if we had a lot of such measurements then we would still only be working out the geometry of space/time in the region of our universe that we are capable of seeing. This is likely to be only a small part of the whole universe due to the galactic horizon imposed by the age of the universe against the speed of light.

Also, even assuming that the whole universe of 3D space and time that we live in behaved the way they are saying, this is still only working out what would happen due to the universe's own internal dynamics - there are ideas coming out now about our universe being part of a wider multiverse outside the realm that we experience as normal space and time, so even if the universe did expand into a "cold dead wasteland", then something could possibly infringe upon it from outside space/time and make something different happen at any time in the future.

Some of what's going on here is just bad journalism - there's a longer article here:


which gives a fuller version of the same quote:

"The geometry, the content and the fate of the Universe are all intricately linked," says Natarajan. "If you know two, you can deduce the third. We already have a pretty good knowledge of the Universe's mass-energy content, so if we can get a handle on its geometry then we will be able to work out exactly what the fate of the Universe will be."

This is a bit more cautious but there's still this idea that by making measurements like this from just one point in space and time we can work out the fate of the whole universe, which I don't really believe.

So I reckon these sort of predictions should be taken with a massive pinch of salt, rather than definite statements of what we know. Which may be obvious, but I wanted to say it and see what anyone else thinks?


This is an excellent writeup! Thank you for posting it!

I must say that I'm rather taken aback by just how crappy the BBC's quote was, and in particular about how taking it out of context completely changed the meaning. I shouldn't be too surprised, given their long descent into Murdochian sensationalism, but still...

Natarajan's actual statement is accurate, so far as it goes. If we assume GR, then the geometry (curvature) of the Universe is determined by its content; the time evolution is fully deterministic. So indeed, given any two of those, you can solve for the third. At the moment, we think we know the mass-energy content (Omega ~= 1, when quintessence or whatever and dark matter are included), which implies a flat geometry.

We don't have a sufficiently solid independent measure of flatness to use as a constraint, however. The data coming from Planck (in particular, the E- and B-polarization results) should be sufficient to determine whether the geometry was flat on the surface of last scattering (and hence is still flat).

Now all of that is based on the presumption that general relativity is the correct description of cosmology. There's a very nice preprint out today (arXiv:1008.3392) which addresses this issue, and shows that several upcoming missions can constrain or falsify GR on cosmological scales at the 5-10% level.

Thanks - I'm trying to get my head round this stuff again after a long break so I'm glad you liked it. Are you saying that in GR the geometry of the universe has in some way to be the same thoughout? I thought it was possible for things to get a lot stranger than that, with different regions of space maybe curved differently. How does the curvature of the universe as a whole differ from the local curvature you get around massive bodies like the sun or a black hole etc.?

You asked, "Are you saying that in GR the geometry of the universe has in some way to be the same thoughout?"

Oh, no; sorry for misleading you. What I meant was that if we assume GR is correct, then we know how to calculate the curvature, both locally (within the solar system, or near a black hole, or whatever) and globally. If you throw out GR (or try to modify it to something else) then we don't necessarily know how to calculate the geometry based on mass-energy density.

The curvature of "the universe as a whole" is an average, based on the smeared out mass-energy density. The local curvatures (solar systems, black holes, etc.) are modifications on top of that average curvature. This statement, of course, assumes homogeneity and isotropy on the largest scales.

Kelsey, I agree with you that the universe's scale is changing rather than something actually traveling, but it's recession veloctiy is only dictated by the pressure of dark energy, according to the paper. Yes it's true that the further the object is the faster it's relative velocity, but this dependence cannot be linear because this apparent velocity could never surpass c. If what you say is the cause of the cosmological horizon, then there would be no hope of seeing past a certain distance because all apparent velocities would exceed c. But we know this not to be true because the longer we look not only do we see further in time but also in space.

.  While, as far as I can tell, the BBC has an excellent reputation for journalistic integrity, doing their homework, and such, but they do aim for a more "popular" market than peer-reviewed scientific publications. So, yes, you do have to take them with a large pinch of salt. Learn to ignore absolutes and superlatives.
.  As for whether any or all of it is true, I dunno. Maybe someone like kelseymh can point you in the right direction.
.  What makes you so sure the Universe is any larger than the "galactic horizon"?

Yup, you're dead on. The cosmological horizon is classically the bound beyond which we cannot receive information. That bound, of course, increases with time; it's currently something like 46 Gly in radius.

There are some models which permit inference of structure beyond the horizon. In particular, BAOs with wavelengths larger than the Hubble distance could induce gravitational flow effects or multipole alignments (the so-called "axis of evil" :-), which are inexplicable on the basis of the matter distribution within the horizon.

I personally find such arguments overly speculative, given the uncertainties in the data. Nevertheless, they can't be discounted outright.

It's not that I'm completely against people trying out arguments like this, which are really just testing the possible implications of our observations, I just don't like the way they get stated in such a definite way when really they are more tenuous than that.

I completely agree! And as you yourself noted, the physicists themselves tend to be more circumpsect than the reports describing their work. This happens even with good science reporting (even the Nature and Science new summaries, let alone New Scientist!).

> this sets a limit to the region of space/time that we can even possibly know
. Excellent point
. Just thinking out loud: If the extents of the Universe were contained in a singularity at the time of The Big Bang, wouldn't the speed of light also set the limit for the size of the Universe now?

> cosmological horizon
.  Yeah. I figured you didn't really want to limit yourself to a galaxy but I was too lazy to try to figure out what the proper phrase was so I just put it in quotes. :)

You asked, "If the extents of the Universe were contained in a singularity at the time of The Big Bang, wouldn't the speed of light also set the limit for the size of the Universe now?" No, for two reasons.

First, the cosmological expansion is not a "speed" in the sense of anything moving anywhere. The "scale" of spacetime is changing, and the objects (or regions of locally high curvature :-) embedded in that spacetime are merely "coming along for the ride." Because it's a scale change, the effect, as seen by any observer on any of those objects, is an apparent recession "velocity" which increases linearly with distance from the observer to what's being clocked.

At some far distance, that apparent "velocity" equals c, and light from that distant object can never reach the observer. It's this effect, that things emitting light seem to be moving away from us faster than the light can get here, which results in the cosmological horizon. There are almost certainly objects beyond our horizon (and we'll get to see them in the future), but we can't see them now.

Second, in the current "concordance" cosmological model (also called Lambda-CDM), the initial singularity expanded exponentially, undergoing something like 60 e-foldings in the first 10-33 seconds or so. If you work out the apparent recession velocity under those conditions, it's really really big (e60 = 1.14 × 1026).