What is primordial non gaussianity?

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Can anyone give an idea about primordial non gaussianity in a popular way??

mathman
Where did you see this expression, or did you make it up?

Chronos
Gold Member
Primordial non-Gaussianity is simply a term fo the non Guassian distribution detected in the temperature anisotropy of the cosmic microwave background. One of the better known discussions of this phenomenon is probably https://arxiv.org/abs/0712.1148, Detection of primordial non-Gaussianity (fNL) in the WMAP 3-year data at above 99.5% confidence.

kimbyd
Gold Member
Can anyone give an idea about primordial non gaussianity in a popular way??
The super short version is that it's all about the statistical properties of the temperature variations in the CMB.

Those temperature variations are sound waves, and at each frequency and direction of motion, if they are Gaussian, the amplitude of the resulting wave is drawn from an independent Gaussian distribution (also known as a Normal distribution). Deviations from this strict Gaussianity come in two ways:
1. The amplitudes of the waves can be correlated with one another.
2. The distribution of amplitudes differs from a Gaussian distribution (typically having fatter tails, meaning large deviations are more frequent than expected from a pure Gaussian).

The benefit of having Gaussian-distributed waves is that they can be perfectly-described by what is known as the two-point correlation function (which is the statistical variance between two points as a function of distance between the two points, independent of direction). This fact has a lot of really neat mathematical properties which make understanding the statistics of the CMB really easy. It means, for example, that all of the information about the temperature variation of the CMB is encoded in its power spectrum.

But what if this assumption isn't the case? Lots of more complex inflation models predict significant deviations from Gaussian behavior. These deviations can become far more challenging to investigate, just due to the more complex mathematics involved. So far, there is no evidence of deviation from Gaussianity:
https://arxiv.org/abs/1502.01592

Thanks Chronos and Kimbyd.