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### [astro-ph/0607160] Ellipticity in Cosmic Microwave Backgrou

Posted: January 29 2008
The paper claims that the observed CMB ellipticity is very discrepant with the LCDM prediction.

At a quick glance, I don't quite understand what is going on. This ellipticity would mean that the CMB is not a Gaussian field, no? Is the analysis reliable?

An earlier paper on this was brought up in http://cosmocoffee.info/viewtopic.php?t=195 .

### [astro-ph/0607160]

Posted: January 31 2008
Elliptical spots does not necessarily imply non-Gaussianity !!
One can have very well have a Gaussian field that is not statistically isotropic (SI). The statistics is still completely represented by the two point correlation alone

The correlation function of temperature in two directions is not simply a function of the angular separation between n & n' : $$\langle\Delta T(n) \Delta T(n')\rangle \equiv C(n,n') \not\equiv C(n\cdot n')$$.
In particular, hot/contours spots will not have circularly symmetric contours -- elliptical contours is a simple special
case of that.

In harmonic space, SI condition implies the matrix $$\langle a_{lm} a_{l'm'} \rangle= C_l \delta_{ll'} \delta_{mm'}$$ is diagonal in $$(l,m)$$ space. Violation of SI
implies non-zero `off diagonal terms'

For discussion of non stat. iso. CMB
Please see (among many others referred in these papers)
Astrophys.J. 597 (2003) L5-L8
arXiv:astro-ph/0501001

(Should clarify I am not supporting that the observed ellipticity is correct. We never found any significant SI
violation in WMAP maps)