A discussion at this week's CosmoCoffe revealed to me that there is a claim of observing non-Gaussianity in the Cosmic Microwave Background. Inflation produces approximately Gaussian primordial fluctuations if the inflaton fluctuations around the background behaved roughly as a free field, so that its different frequencies oscillate independently. This is what happens in simplest models of slow-roll inflation. Non-Gaussianity appears when the dynamics of inflaton fluctuations is affected by sizable non-linearities.

The CMB plot we see most often, that with the acoustic peaks, is the power spectrum of the 2-point correlation function. If the primordial fluctuations were Gaussian, all higher-point correlation functions would be determined by the two-point one. Searching for non-Gaussianity thus requires studying the 3-point correlation function of the CMB. In principle, non-Gaussianity should be described by a function of momenta, but it is often simply parametrized by a number called $f_{NL}$. Single field slow-roll inflation predicts $f_{NL} < 1$, (see for example this cute paper by Maldacena). Such a small effect would be overshadowed by cosmic variance and thus not observable. There exist, however, many inflationary models that can accommodate larger non-Gaussianity.

The WMAP 3-year analysis quotes the constraint

$-54 < f_{NL} < 114$. A month ago, Amit Yadav and Benjamin Wandelt presented their own analysis that yields $27 < f_{NL} < 147$ at 95% confidence level. This is 3 sigma away from zero! If confirmed, this observation would rule out single field slow-roll inflation and point to a more complicated mechanism of inflation.

Of course, the sigmas are not the same in cosmology so no reasons to get excited yet. But it's worth to keep an eye on future developments, since the implications of non-Gaussianity would be quite profound. The nice thing is that the Planck satellite, who will be launched this autumn, is sensitive down to $f_{NL} \sim 5$. If the effect is really up there, we shall know it soon.

## 6 comments:

It is very interesting.

Yadav and Wandelt also stressed that the shape of large non-Gaussianity is squeezed type which means k_1 is much smaller than k_2 and k_3. Curvaton scenario provides a possible explanation on it. I found that the author in 0801.0467 claimed that the inflation scale should be roughly at GUT scale in order to obtain such a large squeezed type non-Gaussianity in curvaton model.

What do you think about it?

I don't think much because i dont know much about CMB analyses. But, as far as i think, 1) Y&W don't claim the non-gaussianity is squeezed, they just didn't do their analyses for other types 2) At this stage it's far too early to discriminate between the models. Curvaton is a possible explanation, but just one of many.

Yes. I agree that curvaton is just a possible explanation. For example, Ekpyrotic scenario is an alternative model. ^-^

I also checked the paper by Y&W. They claimed that they found a large positive local(squezzed) type non-Gaussianity in the abstract.

Where can i find a formal mathematical derivation of the Gaussianity of CMB?

many thanks

There is no derivation really. Gaussianity follows when the inflaton scalar field behaves as a free field in a curved background, so that its different Fourier frequencies oscillate independently. For a derivation of density perturbations from inflation see for example Lyth Riotto hep-ph/9807278.

For an excellent review see astro-ph/0406398.

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