inflation vs topology (fwd)

[Boud Roukema]

> ---------- Forwarded message ----------
> Date: Thu, 17 Apr 2003 13:34:35 +0200 (CEST)
> From: Boud Roukema <boud...
> To: szajtan...
> Subject: Re: inflation vs topology

* Shouldn't this be on shape-univ ? i think this could be
interesting for others.

hi,

On Wed, 16 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.
>
> 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.)

i think we agree here. The "bad" is only a criticism of Tegmark et al's
approach. Maybe "bad" is too strong.  The sky maps are a little bit
better than C_l spectra, and they give a hint ("clue") to topology, but
not a good analysis.

> >
> > > 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 ?

Yes. The physical Universe cannot be bigger than itself.

> (That would be really
> large radius).

Maybe, maybe not. There are many, many inflationary models.

> >
> > > (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.

Don't believe everything you watch/read on/in CNN/BBC/ApJ/MNRAS/A&A/...

In professional astronomy research articles, people often write sentences
which sound good, but are vague, misleading and sometimes simply wrong.
It's not because they want to be wrong, it's just that they don't have
the time to do the analysis properly and they're under pressure to publish
and to conform.

If you can find a WMAP analysis which shows that Pando et al 9810165 are
wrong, that would be interesting.


> 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.

For an exact calculation, it's true that your analysis is probably
*slightly* wrong if it assumes gaussianity on all scales.

So you have to choose whether to live life in the real world and
accept that your results may be nearly right, but a little bit
wrong, or you could wait until there is a definite answer on topology,
but this might be long after the deadline to write your master's thesis.

In fact, Spergel et al 0302209 and Tegmark et al 0302496 seem to show a
definite non-gaussianity on the biggest observable scales. I'm not
sure if there is a way that you could include this in your analysis
*without* making an assumption on the physical origin of the
non-gaussianity. But maybe there is.

IMHO, non-gaussianity on a big scale is not a big problem for your
analysis.



>
> >
> >
> > > 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 ?

The injectivity diameter (what you call "topological radius") is
comoving. So it grows with inflation.

> Or it was once set by
> something and doen't change in time.

No, it's comoving.


> ...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.

I was including cosmological constant and quintessence together.
Let's call it dark energy.

Even if it was "negligibly small" at 10^-33s, it had to be just big
enough, and not too big, so that today it is 2.3 times bigger than
Omega_m.

> >
> > 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.

OK.

> >
> > - 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)

OK

> > 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?).

Do you mean "where does the injectivity diameter come from"?

If you mean some ideas on quantum gravity or quantum cosmology
(apparently quantum cosmology is *simpler* than quantum gravity),
look up the references in the 2nd last paragraph of Section 2
of Luminet & Roukema astro-ph/9901364

> 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?

I guess it could be either.


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

I mean just what you're saying ;). The amount of inflation needs
to be enough so that the injectivity diameter is not too big, not
too small, today.  Just as quintessence/cosmological constant needs to
be fine-tuned (either from inflation or independently) so that it's
not too big, not too small, today.

> > 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.

I disagree. Again this a question over many, many orders of magnitude.

> 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.

Last time i tried to understand inflation, i ended up discovering
that there was a fundamental thing that most people had forgotten -
topology. Maybe if you try to understand the above, you'll come up
with something else that most people (including me) have forgotten...

b