The challenge for single field inflation with BICEP2 result
  The detection of B-mode power spectrum by the BICEP2 collaboration constrains
the tensor-to-scalar ratio $r=0.20^{+0.07}_{-0.05}$ for the lensed-$\Lambda$CDM
model. The consistency of this big value with the {\em Planck} results requires
a large running of the spectral index. The large values of the tensor-to-scalar
ratio and the running of the spectral index put a challenge to single field
inflation. For the chaotic inflation, the larger the value of the
tensor-to-scalar ratio is, the smaller the value of the running of the spectral
index is. For the natural inflation, the absolute value of the running of the
spectral index has an upper limit.
