inflation model of the universe

audioloop

cp = two principles of spatial invariance. The first invariance is isomorphism under translation = homogeneity (uniformity would be independent of the location one chooses to make the observations)
invariance as isomorphism under rotation = isotropy (direction, such as North or South, can not be distinguished).

bapowell

Although the two principles are not independent: global isotropy implies homogeneity.

enasset90

Heck, what I wanna know is this:
If during the first second of the "Big Bang" space grew larger than light could travel, how big could the universe be?

We have "figured out" the age of the universe, yet we have not "figured out" the expanse or breadth of it.
Ed

phinds

It is likely that we will never figure out the expanse. It MAY have started off infinite in extent, in which case it still is (just bigger than it used to be), or it may have started off finite, in which case it still is (just bigger than it used to be). No one knows and I've seen estimates that put the minimum size as not much bigger than the observable universe (which I think is ridiculous) to dozens of orders of magnitude times the size of the observable universe.

enasset90

If I understand correctly, space is expanding at a given rate, faster than gravity is able to pull all things together. Yet, on a smaller scale, gravity is doing things, like keeping the earth around the sun and causing Andromeda to collide with our galaxy, the Milky Way. So, things are being pulled together by gravity, but space (the distance between one atom to another) is growing longer...one year it is a yard, one million years later it is 1.001 yards. Sorry for all you EU guys... one year it is a meter, one million years later it is 1.0012 meters.
If this is correct, why couldn't the Professor speak this way?

Chalnoth

On average, overall, the expansion is simply too rapid to pull things together. However, there are places in the universe that are more dense than average, dense enough that gravity is strong enough to pull the local matter together into clumps. So most of the stuff in the universe is getting further apart, but the universe is becoming more clumpy.

phinds

Because it is not correct. NOTHING inside of gravitationally bound systems is being affected by dark energy. Atoms are NOT moving apart. If you put a ruler in deep space it will not change size.

A meter is a meter.

Thinks outside gravitationally bound systems DO get farther apart but that does not mean space, as a thing itslef, is expanding. See Metric Expansion (there's a link in this page: www.phinds.com/balloonanalogy and some further discussion of expansion)

Chalnoth

Pedantic correction:
Nothing inside of gravitational systems is being affected by the expansion. Dark energy still has an effect, but it's small. The expansion has no effect.

phinds

But if dark energy DOES have an effect, then the size of atoms would change, yes? Is this an interpretational statement or accepted fact?

Chalnoth

Well, no. This can perhaps be understood by considering that the attractive gravitational force between two objects with a cosmological constant in the Newtonian limit:

[tex]F = {GMm \over r^2} - {\Lambda m c^2 \over 3} r[/tex]

Here we imagine that [itex]M[/itex] is some large mass (such as the Sun), [itex]m[/itex] is the mass that is orbiting this large mass, and [itex]r[/itex] is the distance from the center of this large mass. The force, then, is the force the orbiting mass feels towards the larger one. You can see that the cosmological constant reduces the attractive force of gravity by some small amount. For atoms, this would have the effect of making atoms ever so slightly larger than they otherwise would be (the difference really is utterly negligible, however). Even for something as large as the solar system, the difference is much too small to measure, because [itex]\Lambda[/itex] is so tiny. The two forces only become comparable when the distance between objects is exceptionally large.

phinds

OK, thanks for that correction. I've been saying here in several posts that it has NO effect inside galactic clusters, rather than negligible effect, so I'll change my tune.

Paul