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The Planck satellite has been presented and awaited for a long time as the ultimate experiments for measuring temperature fluctuations in the cosmic microwave background (CMB) over the full sky.

One of the big questions that still need answer and that Planck might help clarify is about the dynamics and driving mechanisms in the first phases of the universe, in particular in the period called inflation.

Thankfully there is room for improvements at small scales, i.e. small pieces of sky observed with extremely high resolution, and more importantly for experiments to measure the polarisation of CMB. I know that for the next years a number of polarisation experiments, mostly from ground and balloons, are planned (I'm not sure about satellites).

For sure some of these result will rule out some of the possible inflationary scenarios, but to which level?

Will we ever be able to say: "inflation happened this way"?

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I'm not prepared to write a full post on the topic at this moment, but one of the big things researchers are interested in measuring is a very special parameter labeled f_nl. This parameter has to do with what's known as primordial non-Gaussianity, which essentially introduces the idea that the power-spectrum of the universe is not scale-free. – astromax Oct 2 '13 at 16:38
right. I forgot about non gaussianity. – Francesco Montesano Oct 3 '13 at 12:08
@astromax I would be interested in an answer here too, if you find time for it. – Dilaton Oct 5 '13 at 15:21

This is a great question. I know of a couple of really big things about inflation people want to be able to nail down by using the cosmic microwave background.

The first is measuring what are known as E- and B- modes, which are the curl-free and divergence-free components to the modes of cmb radiation:


Essentially, measuring large scale Gaussian B-modes from primordial gravitational waves will help constrain the energy scale of inflation. It may also be able to rule out most ekpyrotic and pure curvaton/inhomogeneous reheating models (same source).

The other thing people are looking at is this idea of primordial non-Gaussianity, which are second order corrections to the Gaussian fluctuations present in the cmb (review article; early planck results). Measuring a parameter called $f_{nl}$ (deviation from Gaussianity) has been a fairly crucial part of current and future studies and will also help rule out various inflationary models. This $f_{nl}$ parameter is defined as follows:

In this case the multipole coefficients $a_{lm}$ of the CMB temperature map can be written as $$a_{lm} = a_{lm}^{(G)} + f_{nl} a_{lm}^{(NG)} $$ where $a_{lm}^{(G)}$ is the Gaussian contribution and $a_{lm}^{(NG)}$ is the non-Gaussian contribution.

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