inflation vs topology

[szajtan odwieczny]

> > 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.

Well, you observed the maps composed of the sum of some few first
multipoles, and ..."saw the thing". Thats what I ment. There
mae be several sky maps resulting in the same C_l spectra, and that's
why it can be difficult or impossible to get the direction from C_l
(but that's not importand.)

>
> > 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.

Could you put this in full sentence ?
Do you mean that the topological radius (of eg. n-torus) is to be at least
as big as the radius of the inflationary bubble ? (That would be really
large radius).

>
> > (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?
I didn't read that paper, but I just rely, on the papers released
along with WMAP data (eg. astro-ph/0302223 and many references therein
among others the one of Pando 98) so maeybe I should write "so far there
is no significant cosmological non-Gaussianity". And WMAP data are found
to be consistent with assumption of Gaussian primordinal fluctuations.

btw. if the non-gaussianity is found then whole my work with masterthesis
is "o kant" - in a way useless - ;) If I remember well that would
be inconsistent with one of the assumptions of the cmbfast. (I don't know
about the size of the effect), but C_l couldn't be a good fluctuations
tracer, and the probability of model must have been computed directly
from the map.

>
>
> > 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?

"Another thing" was the same problem as the first one but attacked from
another side. My point was rather like: does the topological radius (
circumference) grows with the inflation ? Or it was once set by
something and doen't change in time.

...hm, you write about the quintessence. But what does it have to do with
the inflation, and to the problem ? Let's assume the inflation is
already finished. the "graceful exit problem" suggests that we mae
consider it as finished by the time of some 10^-33 s, and in this case
dark energy has nothing to do with activity of false vacum. In the early
universe (even in radiation dominated era) the density of dark energy was
negligible small. Unitl now when it starts to be importand. I don't know
about
some fine tuning with inflation ? It's rather cosmological constant that
should be tuned. I don't know maeybe false vacum was the priomridal origin
of the quinessence which starts dominating our universe recenly :), and
this is interesting topic itself, but it wasn't the point of my question.

>
> First some corrections:
>
> - the Guth value was (i think) 55 e-foldings, i.e. e^55 \approx 10^{24}
I wrote it from memory, but you're right, the factor is some 10^29. It
depands on how long we assume the inflation lasts.

>
> - it's not "since the world begun", it's since some early time such
> as t = 10^{-33}s
of course but even if it was from the beginning (whatever that means) or
from 10^-43 s it wouldn't change anything in sizes.
10^-33 s - 10^-43 s = 10^-33 s - 10^-35 s = 10^-33 s  (approxiamately)
(but these are details)

>
> 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.
Where does it come from ? (any references to read?). So from this I assume
that the injectivity diameter grows with time. Is that right ?
And btw. (probably it's another word, with no polish translation), but  is
there some polish equivalent for injectivity diameter ? (and btw. for
fundamental polyhydron
(or something like that) as well. Request for polish translation -
anyone ? )

>
> Fine-tuning inflation is required to get Om_Lambda/Om_m \approx 10^0;
mmm, isn't it the problem of quintessence tuning not inflation?

> fine-tuning inflation is required for observable topology.
What do you mean ?

>
> Fine-tuning inflation is also needed for observable curvature
> (e.g. Om_total = 1.02).
fine tuning here ? probably yes, maeybe just tuning is ok.
As just for the flatness problem, there is no lower limit set for flatness
(upper limit for inflation duration), but if inflation lasts too
long it would never stop, or universe might get too heavy or so, and we
wouln't have cmb fluctuations at level 10^-5 which in turn might would
have catastrofical consequencies for us :).

>
> We only know that the first one is correct - so far - but maybe all
> three are correct, and are linked.
>
...it's a long road, just to come to terms with the above.

b.