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