Saturday, 7 February 2015

Weekend Plot: Inflation'15

The Planck collaboration is releasing new publications based on their full dataset, including CMB temperature and large-scale polarization data.  The updated values of the crucial  cosmological parameters were already made public in December last year, however one important new element is the combination of these result with the joint Planck/Bicep constraints on the CMB B-mode polarization.  The consequences for models of inflation are summarized in this plot:

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:

Anonymous said...

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

Antonio (AKA "Un físico") said...

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).

Anonymous said...

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.

Jester said...

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

Unknown said...

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?

Jester said...

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...