Take up the challenge for a single field inflation after BICEP2

The measurement of the tensor-to-scalar ratio $r$ shows a very powerful constraint to theoretical inflation models through the detection of B-mode. In this paper, we propose a single inflation model with infinity pows series potential called the Infinity Power Series (IPS) inflation model, which is well consistent with latest observations from \textit{Planck} and BICEP2. Furthermore, it is found that in the IPS model, the absolute value the running of the spectral index increases while the tensor-to-scalar ratio becomes large, namely both large $r \approx 0.20$ and $|n_s'|\gtrsim \mathcal{O}(10^{-2})$ are realized in the IPS model. In the meanwhile, the number of e-folds is also big enough $N\approx 35\sim45$ to solve the problems in Big Bang cosmology.

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