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.