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When we are speaking about gaussianity and non-gaussianity in a cosmological context, what is gaussian or non-gaussian in the CMB?
What would a non gaussian CMB look like compared to a gaussian one?
Is it just the profile of every overdensity $\delta = \frac{\rho-\rho_0}{\rho_0}$ which look like a gaussian and not an exponential or a sine?
It means, that the cosmological perturbations satisfy Gaussian initial conditions. This means, that the probability of the perturbation amplitude has a Gaussian shape about the mean value.
Considering linear perturbation theory, the initial Gaussian probability distribution will remain Gaussian for all times, e.g. today. It means, that there is e.g. no washout of the perturbations.
Well, since we see the CMB today, the question is more like: How should the initial conditions have been to see the CMB we observe today, given they are non-Gaissian? Since we then no longer consider linear perturbation theory, the answer might not be that simple. This paper from Bruni, Hidalgo, Meures and Wands may give some hints and ideas.
