Reducing the tension between the BICEP2 and the Planck measurements: A complete exploration of the parameter space

A large inflationary tensor-to-scalar ratio r0.002=0.20−0.05+0.07 is reported by the BICEP2 team based on their B-mode polarization detection, which is outside of the 95%95% confidence level of the Planck best fit model. We explore several possible ways to reduce the tension between the two by considering a model in which αsαs, ntnt, nsns and the neutrino parameters NeffNeff and ΣmνΣmν are set as free parameters. Using the Markov Chain Monte Carlo (MCMC) technique to survey the complete parameter space with and without the BICEP2 data, we find that the resulting constraints on r0.002r0.002 are consistent with each other and the apparent tension seems to be relaxed. Further detailed investigations on those fittings suggest that NeffNeff probably plays the most important role in reducing the tension. We also find that the results obtained from fitting without adopting the consistency relation do not deviate much from the consistency relation. With available Planck, WMAP, BICEP2 and BAO data sets altogether, we obtain r0.002=0.14−0.11+0.05, nt=0.35−0.47+0.28, ns=0.98−0.02+0.02, and αs=−0.0086−0.0189+0.0148; if the consistency relation is adopted, we get r0.002=0.22−0.06+0.05.