Critical Density and the expanding universe

[Matt Walker]

Okay, here's my problem. I've recently read that physicists believe that all the mass and dark energy in the universe do indeed add up to the critical density, which means that the universe will continue to expand forever, at zero curvature, and is either finite (like a torus) or infinite. And apparently many physicists suspect it to be infinite. Now, my question is, how on Earth can something that is already infinite expand? And also how could the universe possibly have been infinite at t=0 when it was also impossibly dense?

Just a heads up - I'm not a particularly 'mathematically inclined' reader.

If anyone has an answer I'd like to hear it :D

 

[mikeph]

I suspect the problem behind your first question is that you imagine expansion as defined by the distance between the ends of an object, i.e. a rubber band expands when you pull the two ends apart. But this isn't entirely neccesary for the definition: you can define a local expansion as the change in distance between two nearby points on the rubber band, for example if you put two ink dots 1mm apart and then stretched the band, you can measure the new distance between the dots and then measure the local expansion. Nowhere in this measurement do you need any information about the ends of the band. This is similar to what we do in cosmology- we measure the change in distance between two "local" points, which are nearby galaxies, and find the distance is increasing. We don't know anything about whether the universe is infinite or not, but we know the two galaxies are moving further apart, and we find this for lots of galaxies.

So we deduce that the universe is expanding without being able to make any concrete deductions about its overall extent.

Regarding the second question, my understanding of the big bang theory is that there are no assertions about what happens at t=0, only at certain times afterwards, e.g. after 300 seconds we know that nucleosynthesis occurred, and after 300,000 years we know recombination and then decoupling of photons and electrons occurred. We don't know that the universe was infinitely dense at t=0 or what happened at this time. Someone else might be able to be more specific in response to this question.