Constraining Inflationary Models III: Primordial Non-Gaussianity.

It used to be the case that the spectral index n_s and the tensor-to-scalar ratio r were two of the only constraints we could use in distinguishing between inflationary models.  Unfortunately, this really isn't enough.  Too many models predict values for the quantities that are well within the error bars and probably will remain so forever.

However, new hope has emerged from primordial non-Gaussianity.  Gaussianity is the idea that all the n-point correlation functions are described in totality by the two point correlation function plotted above. Non-Guassianity describes departures from this.

Now, what is a correlation function?  A 2 point correlation function tells you how 2 points are related to each other.  A three point correlation functions tells you how three points are related to each other, etc...  For example, a non-zero 3 point function tells you that the three different points in spacetime had some way of influencing each other: interactions.

Therefore it turns out, physically how you get a departure from Gaussianity is by having interactions between the quantum fields/branes/etc... driving inflation.  A measurement of non-Gaussianity gives is a measurement directly on how these fields were interacting and therefore contain a wealth of information about the character of these fields/branes/etc...!

In cosmology we can plot these correlation functions versus the multiple moments l as shown in the plot.  The lower the multiple show how points far away from each other were interacting.  The higher multiple moments show how points close together were interacting.

The three point function, or bispectrum, gives rise to three independent quantities that parametrize non-Gaussianity.  The four point function, or trispectrum gives rise to two more parameters.  

The interesting thing is each inflation model makes different predictions for the values of each of these parameters.  Combined with n_s and r we will have 7 parameters to highly constrain inflationary models and weed out the rest.

This may help us finally understand what drove inflation.