What Do Planck 2015 Results Reveal About Power Law Potential Models?

[JD_PM]

TL;DR

I am trying to understand why the simple inflationary model with potential $V(\phi) \propto \phi^2$ is disfavored compared to models predicting a smaller tensor-to-scalar ratio.

I am reading Planck 2015 results. In particular, I focused on "Power law potentials" subsection.

The issues I have are

1. I do not understand why the validity of the model can be determined by the value of the $B$ mode.
2. Why the $B$ mode values $\ln B = −11.6$ and $\ln B = −23.3$ for the cubic and quartic potentials , respectively, are regarded as "strongly disfavored" and $\ln B = −4.7$ for the quadratic potential as "moderately disfavored"? What I mean is: what is the threshold value at which we can consider the potential as favored and why?

Thank you!

 

[kimbyd]

Different inflationary potential shapes predict different relationships between the tensor perturbations and scalar perturbations. The scalar perturbations contribute primarily to the temperature variations across the sky. The tensor perturbations contribute primarily to the polarization of the observed CMB.

The observed E-mode spectrum is dominated by effects after inflation such as structure formation, so it isn't a very good measure of the tensor perturbations.

The large-scale B-mode spectrum is mostly independent of late-time effects, so it's a nearly direct measurement of the tensor perturbations produced during inflation. So far all we've been able to say is that the magnitude of these perturbations is too small to be detected (yet).

Quadratic potentials for inflation typically predict that we would have detected the tensor perturbations by now. This is shown in Fig. 12 in that paper.