Constraints on the extensions to the base ΛCDM model from BICEP2, Planck and WMAP

Recently Background Imaging of Cosmic Extragalactic Polarization (B2) discovered the relic gravitational waves at $7.0\sigma$ confidence level. However, the other cosmic microwave background (CMB) data, for example Planck data released in 2013 (P13), prefer a much smaller amplitude of the primordial gravitational waves spectrum if a power-law spectrum of adiabatic scalar perturbations is assumed in the six-parameter $\Lambda$CDM cosmology. In this paper, we explore whether the $w$CDM model and the running spectral index can relax the tension between B2 and other CMB data. In particular, we find that a positive running of running of spectral index is preferred at $1.7\sigma$ level from the combination of B2, P13 and WMAP Polarization data.