By local, of course, I mean “within our limit of observation”; so within our 13 billion light-year observation bubble.
Do we know that the current model of accelerating expansion holds true everywhere? Or is that an assumption we make? Is it possible we could be in a region that is expanding faster than elsewhere?
Is it - to put it more simply - possible that the cosmological principle is not true and that the universe is* not* homogenous and isotropic at much larger scales than we are able to detect?
I’m not all that cognizant of the more philosophical area of astrophysics. I know that we assume we do not exist in a special or unique location; does that merely facilitate our ability to conduct further reasoning, or is there some evidence to support it?
The ultimate answer is that we don’t; the relationship between the global and local structure of spacetime in general relativity is infact quite tenuous. E.g.even fixing the global geometry doesn’t fix the global topology (each of the homogenous spactial geometries admit various different topologies, the extra assumption of global isotropy is needed to fix teh topology)
However we can I think fairly reasonably assume that if there are very large variations on very large scales, then those scales must be larger than the observable universe. The simple reason for this is, if that were not the case then we would have to be sitting pretty much slap bang at the centre of this particular homogenous patch of space, which even if you are going to drop the strongest form of the cosmological principle, will be unacceptable to most.
An argument in favour of the cosmological principle (in it’s strongest form) is that if the universe on the very largets scale isn’t homogenous or isotropic then, how do you explain the inhomogenties and anistropies? What physical processes give rise to them?
Wouldn’t the colliding branes model predict a non-homogeneous universe? The portion of the brane near where a collision took place would be different from portions further away. We’d still need to assume the effect was pretty large so that the visible universe appeared isotropic. We wouldn’t have to be near the center, we’d just have to be far enough from an “edge”. An edge in this case would be something more like a decaying function I’d think rather than something sharp.
Oh, I get that. The scale of our “region” (should it exist) would need to be enormous to not put us in the centre of it. I wasn’t trying to suggest it might just beyond our observable limit.
That might be the answer to my question - if I knew what it meant! What are inhomogenties and anistropies, and how do they fit in to question?
In the framework of eternal inflation, the universe is actually fractal at the largest scales, comprised of many ‘bubbles’, one of which corresponds to what we observe as our universe; I’m no expert, but I don’t think all of these bubbles are expected to undergo accelerated expansion.
Yep, it’s just a point that if we consider ourselves as having an equal chance of being anywhere a homogenous regio’ of the universe, then unless that region exists on a scale much larger than the observable universe there’s a quite a high chance that we would be able to observe one of the edges of the region.
Inhomogenous = not the same everywhere
Anistropic= not the same in every direction.
A feature which stops the universe from being homogenous would be described as an inhomogenity, etc.
The thing is physical laws tend to be very homogenous and isotropic in nature and anistropies and inhomgenities on a small scale tend to average out on a large scale. It’s just difficult to imagine the kind of physical processes that can create large scale inhomogenties or anistropies.
HMHW has pointed out that some inflationary models do actually postulate a universe with quite distinct regions though.