# Avignon Day 1: Calculating Non-Gaussianities

Greetings from Avignon, where I’m attending a conference on “Progress on Old and New Themes” in cosmology. (Name chosen to create a clever acronym.) We’re gathering every day at the Popes’ Palace, or at least what was the Pope’s palace back in the days of the Babylonian Captivity.

This is one of those dawn-to-dusk conferences with no time off, so there won’t be much blogging. But if possible I’ll write in to report briefly on just one interesting idea that was discussed each day.

On the first day (yesterday, by now), my favorite talk was by Leonardo Senatore on the effective field theory of inflation. This idea goes back a couple of years to a paper by Clifford Cheung, Paolo Creminelli, Liam Fitzpatrick, Jared Kaplan, and Senatore; there’s a nice technical-level post by Jacques Distler that explains some of the basic ideas. An effective field theory is a way of using symmetries to sum up the effects of many unknown high-energy effects in a relatively simple low-energy description. The classic example is chiral perturbation theory, which replaces the quarks and gluons of quantum chromodynamics with the pions and nucleons of the low-energy world.

In the effective field theory of inflation, you try to characterize the behavior of inflationary perturbations in as general a way as possible. It’s tricky, because you are in a time-dependent background with a preferred (non-Lorentz-invariant) frame provided by the expanding universe. But it can be done, and Leonardo did a great job of explaining the virtues of the approach. In particular, it provides a very nice way of calculating non-gaussianities.

At a first approximation, cosmological perturbations are gaussian: the fluctuations at every point are drawn from a normal (bell curve) distribution. That’s the basic prediction of inflation, and it’s consistent with what we observe. But a more careful calculation shows that perturbations from inflation can be slightly non-gaussian; the search for such a signal in the data is a primary goal of current cosmological observations.

What the EFT of inflation lets you predict is what form the non-gaussianities can take. One way of characterizing the deviation from gaussianity is using the bispectrum, the correlation between fluctuations (in Fourier space) with three different wave vectors.

$latex langlePhi_{vec{k}_1}Phi_{vec{k}_2}Phi_{vec{k}_3}rangle = 2pi^{(3)} delta^3left(sum vec{k_i}right)F(k_1, k_2, k_3) $

Although it looks like *F* depends on the three wave numbers, scale invariance implies that it really only depends on the ratios *k*_{2}/*k*_{1} and *k*_{3}/*k*_{1}. (The directions don’t matter because of rotational invariance.) Long story short, you can plot the possibilities in terms of a function on a two-dimensional parameter space, like so:

The EFT of inflation lets you predict the shape of this function for any given inflationary model. Keep in mind: we haven’t yet observed *any* non-gaussianity, although we are trying. But it’s a reminder that there’s potentially a wealth of information about the early universe yet to be extracted from observable features today.

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