Further Thoughts On Homogeneity/Isotropy

[Robert L. Oldershaw]

Phil Helbig has posted the following highly interesting comment
regarding homogeneity/isotropy on Sean Carroll's blogsite.

"Third, the assumption that we can extrapolate what we observe in
the observable universe to all of the universe, namely homogeneity
and isotropy on large scales, to the entire universe, might not be
right. In that case, what we observe might tell us nothing about
whether the universe is finite or not."

I appreciate this new candor and hope to see it often.

RLO
http://www3.amherst.edu/~rloldershaw

PS: All-Caps is definitely shouting. Italics are indicated by
astericks before and after, as in *qed*. Hope this helps!

[[Mod. note -- I have seen different conventions for what *asterisks*,
/slash marks/, and _underscores_ denote -- all usually mean some sort of
emphasis, but which might be bold vs italics vs some other typographical
distinction may vary. Indeed, I think that over the years I myself
have used different conventions. :)

In any case, ASCII typography is at a minimum quite peripheral to our
newsgroup's focus (research in astronomy/astrophysics), and it could
reasonably be said to fall outside our newsgroup charter altogether.
So, let's focus on discussing astronomy/astrophysics instead.
-- jt]]

[Phillip Helbig (undress to reply)]

In article <167256d8-8365-4ca1...@googlegroups.com>,
"Robert L. Oldershaw" <rlold...@amherst.edu> writes:

> Phil[lip] Helbig has posted the following highly interesting comment

> regarding homogeneity/isotropy on Sean Carroll's blogsite.
>
> "Third, the assumption that we can extrapolate what we observe in
> the observable universe to all of the universe, namely homogeneity
> and isotropy on large scales, to the entire universe, might not be
> right. In that case, what we observe might tell us nothing about
> whether the universe is finite or not."
>
> I appreciate this new candor and hope to see it often.

It's not new. It is also obvious: by definition, we can observe only
the observable universe. Anything we say about what is outside is an
extrapolation. Of course, if the extrapolation is sensible, then we can
have some confidence in it. For example, it would be strange if an
assumption happened to break down just at the edge of the observable
universe, especially since the size of the observable universe changes
with time, so it would be even stranger if it broke down at the edge of
the observable universe now.

The remark was an answer to the question whether the observed flatness
of the universe implies that it is infinite. The question is thus about
the largest possible scale in the universe, which might be infinite.
Had we observed significant positive or negative curvature, then we
could make a statement about the finiteness or lack thereof of the
universe with some confidence, since a wrong extrapolation would imply
that the universe beyond the particle horizon (the edge of the
observable universe) is substantially different to what is inside.
However, what we observe is a universe which is at least very close to
flat (i.e. the sum of the density parameter and cosmological constant,
Omega+lambda, is equal to 1 to within a per cent or better), so just a
small difference between the observable universe and the rest of it
could in principle lead to the opposite conclusion. (If the universe is
exactly flat then, of course, we could never prove this exactly by
observation. If it is not exactly flat then, in principle, we could
hope to observe non-zero curvature, i.e. rule out the flat case with
high confidence, though the caveat discussed above still applies.)