inflation vs topology

[boud]

hi bartek, everyone,

On Mon, 14 Apr 2003, szajtan odwieczny wrote:

> I'm wandering if inflation scenaries of cosmological evolution,
> discriminate the possibility for non trivial topology of the
> universe (eg.  some torus topology) of circumference smaller than
> the hubble radius. I had short talk about that with Boud but perhaps
> it was too short. If I understand well, in case of such non trivial
> topolology, there should be some, outstanding (special) directions
> in the CMB sky seen in multipole distribution just for the few
> lowest multipoles (on the biggest anular scales). On the other hand,

Well, multipoles are a *bad* way of trying to detect topology, but
it's correct that there should be something funny in the low l
multipoles for a multiply connected universe.

> one of the predictions of the inflationary models is that
> fluctuations in gravitational potetial ( in the biggest angular
> scales ) are gaussian and have random phases - so there should be no
> outstanding directions in CMB.

Up to the scale of the inflationary bubble, yes.

> (So far there is no evidence for
> deviations from gaussianity).

There were several COBE analyses such as  Pando, Valls-Gabaud & Fang:

http://de.arxiv.org/abs/astro-ph/9810165

that showed non-Gaussianity. Since the WMAP map looks similar to COBE
on large scales, i guess there should still be the same non-Gaussianity.

Do you know of an article that claims Pando et al were wrong?


> To me these two things are contrary to each other. Mae they exist
> together ? Can anybody shed  some light on this ?

If there is detectable non-trivial topology, then it's likely that if
the data is analysed *assuming* trivial topology, then there is a
non-Gaussian signal.

> Another thing is about the size of the universe. I mean, how it is possible
> for the universe to have topological circumferece smaller than (for example)
> the hubble radius, when we assume that every distance has been blown by the
> factor of 10^54 ever since the world begun ? Or maeybe these two facts also
> remain without any mutual confict ?

This is the fine-tuning problem. How is it possible for the cosmological
constant/quintessence parameter to be approximately equal to the matter
density parameter today (a factor of 2.3 is not much ;) rather than at
some more "random" time in the past or future?

First some corrections:

- the Guth value was (i think) 55 e-foldings, i.e. e^55 \approx 10^{24}

- it's not "since the world begun", it's since some early time such
as t = 10^{-33}s

Answer: It's sufficient that the injectivity diameter ("topological
circumference") was just a bit smaller than
10h^-1 Gpc/10^24 \approx 500m at t = 10^-{33}s.

Fine-tuning inflation is required to get Om_Lambda/Om_m \approx 10^0;
fine-tuning inflation is required for observable topology.

Fine-tuning inflation is also needed for observable curvature
(e.g. Om_total = 1.02).

We only know that the first one is correct - so far - but maybe all
three are correct, and are linked.

We'll see soon, i hope :)  Good PhD thesis topic ;)
boud