Well this sure was really hard week with fluid mechanics and stuff but now eventually back to cosmology Hi Boud, shape-univ

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If we assumed some multiply-connected space-time within some model (eg. dodecahedral) then my question is whether is leads to nongaussian (NG) features in CMB. I think it definitely should.

In principle, yes. In practice, maybe.

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Such spacetime, gives a modified power spectrum of fluctuations, limited to fundamental domain size and there should be repercusions of this size in harmonic modes that are natural multiple of that size. Then given a feature at one length scale should automatically give features at other scales - hence vialation of gaussianity. This could be investigated by bi- or tri-spectrum optimalized for these particular perturbation modes that come from the model. Given NG simulations one could estimate the sensityvity of this approach. This is also a test of the multiply connected space hypothesis.

Is that right ?

In principle, yes.

Hajian & Souradeep (2006) measure the bispectrum from several different version of WMAP-1st-year and claim no significant deviations from gaussianity: http://arxiv.org/abs/astro-ph/0501001

This is definitelly interesting paper. They deal with tests od SI violation and what are possible sources of such violation - eg. nonuniform sky noice. This is of particular interest to me recently since, I was calculating the variance (related to power spectrum amplidute) in separate region on the sky of WMAP and clearly I see nonuniform pattern of even with small scale signal removed. So I don;t quite understand that no strong IS violation was found, unless they mean the primordial SI is not viiolated after accounting for non-uniform noice in the map. BTW. they calculate Bipolar power spectrum, NOT bispectrum IMHO. and where is it about gaussianity ? are you talking about astro-ph/0501001 ? well maybye a bit but they sure don't test it.

But they don't model the *expected* signature of the PDS (poincare

dodecahedral

space) in 0501001.

In Hajian & Souradeep (2003), they model the expected signature from various specific versions of the T^3 model: http://arxiv.org/abs/astro-ph/0301590

again, this is not about the bispectrum. In any case with BiPS it's not possible to detect NG (non-Gaussainity), now is it ? it's on;y a measure of SI. I guess what I've jsut said above about their lack of detection is correct in light of what they say in conclusions of this paper. The question is whether it will ever be possible give such an answer. Meaning that is we knew what comes from noice, then why simply not to remove if from the map and then make a SI tests. If this is not possible then all that will be possible is to give comments like "it remains unprooved that the SI violation is of primordial origin". especially when there is not spectral dependence. However, in 0501001 I guess that they filtered the maps before analysis strongly removing anything for l>100. At such large scales the nonuniform noice distribution shouldn't be important at all. This is probably why they didn't find any SI violation at these scales.

i've only looked at this quickly, but it seems that they do not necessarily expect a strong (or any non-zero) signal.

In any case, back in 2003, there was little discussion of the PDS - the

paper

is dated 11 Aug 2003, and the Luminet et al. paper came out around Oct 2003. Hmmm... i guess at least, there was no pressure for them to study PDS. :P

So working out what bispectrum is expected from the PDS has (maybe) not been done yet.

well, this was only a loose thought. calculating bispectrum involves calculating alm compontnts first which involves technics that are generally as much CPU consuming as calculating bispectrum itself (because of the 3J symbols) - i'm not ready yet to do that with my soft :(

Hmm: better check the Aurich, Lustig, Steiner and Gundermann papers - they might have tried this.

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What I would need is to have a full fourier space of perturbations with topology encoded in it.

The PDS is a positive curvature model: you can't do fourier analysis in

curved that's true generally. (but it's ok to do it in flat sky approx. - i.e. for large k or l)

space. You need the full set of eigenmodes of the PDS itself. and that's more less what I've said. i need \Phi(kx,ky,kz) for PDS topology aren't these the eigen-modes in topology nomenclature ?

Tarou-san has done lots of cosmic topology eigenmode modelling - if you want to do something like this, you might want to visit him:

Kaiki Taro Inoue kinoue phys kindai ac jp

:) one of these days, one of these days :)

Or maybe your idea is more like making simulations, then making measurements of the bispectrum parameters, and then comparing them to the analytical calculations in Hajian & Souradeep (2003)? Hmmm... well, this would only function as a check that HS2003 have not made any errors.

But then you could presumably think of something new and interesting as a followup step - you can add stuff to simulations which can be (in some sense) difficult to add to analytical calculations.

I have to stick with NG I guess not SI. however there is so much independent sources of NG... my primary target is to deal with NG as an one of the observales (currently achievable) to constrain inflationary models. But seems to me that also A ans n_s and tensors are of very high competitive interest. I'm not yet sure which of these are better way of doing that, sure they are independent and NG will continoue to be sexy in cosmology for many years. :) BUT... since topo-stuff can also be a source of NG - which is primordial - so it surly is within my interest. pozdr. Bartek