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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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    $\begingroup$ 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. $\endgroup$
    – astromax
    Commented Oct 2, 2013 at 16:38
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    $\begingroup$ right. I forgot about non gaussianity. $\endgroup$ Commented Oct 3, 2013 at 12:08
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    $\begingroup$ @astromax I would be interested in an answer here too, if you find time for it. $\endgroup$
    – Dilaton
    Commented Oct 5, 2013 at 15:21
  • $\begingroup$ Related meta post: How much is astrophysics, cosmology, and theoretical astrophysics on topic? $\endgroup$
    – called2voyage
    Commented Oct 15, 2013 at 18:44
  • $\begingroup$ We had a guest lecturer at the Uni giving a talk about the Planck satellite. He compared the map by WAMP with the much better spatial resolution of Planck and made the remark that Planck has, in terms of spatial resolution, reached the limit of real physical sizes of structures in the CMB. So, he claimed, next generation CMB-telescopes (if they are to be built) won't have better spatial resolution, because this won't be able to improve the image resolution. This is an anecdotal piece of knowledge about our limits, I hope you can look it up somehow, if you care. $\endgroup$
    – NeStack
    Commented Jun 16, 2021 at 7:18

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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:

E/Bmodes

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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Although this is late, I think an update to this thread would be interesting. As of 2022, satellite-based CMB experiments like PICO, LITEBIRD, and CMB-Bharat are coming up. These experiments would target scales for polarization observation as large as the dipole with a sensitivity of the order of $\sigma(r) \sim 10^{-4}$. The idea is to reach enough sensitivity in order to constrain the tensor-to-scalar ratio,r. This parameter is tied to the amplitude of B mode polarization sourced by primordial gravitational waves.

This would be a great leap from SIMONS Observatory which plans to have a sensitivity of a goal sensitivity $\sigma(r) \sim~ 10^{-3}$.

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