It shows the constraints on the spectral index

*ns*and the tensor-to-scalar ratio

*r*of the CMB fluctuations, compared to predictions of various single-field models of inflation. The limits on

*ns*changed slightly compared to the previous release, but the more important progress is along the y-axis. After including the joint Planck/Bicep analysis (in the plot referred to as BKP), the combined limit on the tensor-to-scalar ratio becomes r < 0.08. What is also important, the new limit is much more robust; for example, allowing for a scale dependence of the spectral index relaxes the bound only slightly, to r< 0.10.

The new results have a large impact on certain classes models. The model with the quadratic inflaton potential, arguably the simplest model of inflation, is now strongly disfavored. Natural inflation, where the inflaton is a pseudo-Golsdtone boson with a cosine potential, is in trouble. More generally, the data now favors a concave shape of the inflaton potential during the observable period of inflation; that is to say, it looks more like a hilltop than a half-pipe. A strong player emerging from this competition is R^2 inflation which, ironically, is the first model of inflation ever written. That model is equivalent to an exponential shape of the inflaton potential,

*V*=c[1-exp(-a φ/MPL)]^2, with

*a=sqrt(2/3)*in the exponent. A wider range of the exponent

*a*can

*also fit the data, as long as*

*a*is not too small. If your favorite theory predicts an exponential potential of this form, it may be a good time to work on it. However, one should not forget that other shapes of the potential are still allowed, for example a similar exponential potential without the square

*V*~ 1-exp(-a φ/MPL), a linear potential

*V*~

*φ*, or more generally any power law potential

*V*~φ^

*n*, with the power

*n≲*1. At this point, the data do not favor significantly one or the other. The next waves of CMB polarization experiments should clarify the picture. In particular, R^2 inflation predicts 0.003 < r < 0.005, which is should be testable in a not-so-distant future.

Planck's inflation paper is here.

## 6 comments:

I would not trust too much this bound on r: it is based on a global fit that relies on many many assumptions. Surely Planck makes a careful job, but as usual various uncertainties are a matter of opinion, being defined only up to O(1) factors. Global fits for r will soon become irrelevant: clearly the future is going for direct measurements

Thanks for this picture Jester: it clarifies all recent developments.

Let me point out that Weinberg, in his "Cosmology" (2008) book, rules out in p.488 the exponential potentials. But the potentials that last constrains favor are: squared Ricci scalar & alpha-attractors (that correspond to exponential squared potentials).

It looks like the collaboration submitted 17 papers to the arXiv, all in the span of ~30 seconds on Thursday afternoon. I can't decide if this is an impressive display of collaboration discipline or a sign of attention to detail that borders on the pathological.

Right, by "exponential potential" I meant ~(1 - e^{-a \phi}) or ~(1 - e^{-a \phi})^2. I clarified this in the text.

Can you write something on polarization by dust grains? If grains consist of trillions and trillions of different kind of molecules as I think,how does it polarize micro waves and how confident one can be in these calculations?

Oh, that's way beyond my expertise :) Planck had a few papers about it, e.g. 1405.0872 or 1409.2495, though I think they don't know for sure either...

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