## Nongaussiantiy in cosmology June 1, 2009

Posted by keithkchan in Cosmology.

It seems that I haven’t talked about physics for some time. After all, in the About of this blog, it says it is mainly about physics. Obviously that’s because of my limited knowledge, and most people are are not interested in my research area. Anyway, even if you are not interested in I still introduces it a little bit.

Recently nongaussianity is rather popular topic in cosmology. The primordial density fluctuations in the early universe is very Gaussian. What I mean is that one can think of the density fluctuations drawn from a Gaussian distribution. The Gaussian field is completely characterized by its 2-point correlation function (or power spectrum in Fourier space.) Inflation, at least in simple models, predicts that the fluctuations are highly Gaussian. Because of the nonlinearity of gravity, a small amount of nongaussianity is generated. But the amount is not possible to detect in foreseeable observations (although some claim that 21 cm may do it). The common parametrization for nongaussianity is $\Phi_{\rm NG}=\phi + f_{\rm NL} \phi^2$, where $\phi$ is the Gaussian potential. That is the nongaussianity is generated by the nonlinear in $\phi$. This is a phenomenological expansion in $\phi$, and you can add more terms if you like. The current observational efforts are to constrain the value of $f_{\rm NL}$.

There are two kind of observations that allow people to probe nongaussianity. They are cosmic microwave background and large scale structure. Gaussian field has zero 3-pt function (or bispectrum in Fourier space). So people look for bispectrum in these observations. So far the best limit on $f_{\rm NL }$ is from WMAP data, but obtained by a group other than the WMAP team. The limit is $-4 < f_{\rm NL} < 80$ (95% confidence level). It will be really interesting if the future data exclude 0.

I may talk about nongaussianity more in future if I run out of stuffs to say.