Reducing the Tension Between the BICEP2 and the Planck Measurements: A
  Complete Exploration of the Parameter Space
  A large inflationary tensor-to-scalar ratio $r_\mathrm{0.002} =
0.20^{+0.07}_{-0.05}$ is reported by the BICEP2 team based on their B-mode
polarization detection, which is outside of the $95\%$ 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 $\alpha_\mathrm{s}$,
$n_\mathrm{t}$, $n_\mathrm{s}$ and the neutrino parameters $N_\mathrm{eff}$ and
$\Sigma m_\mathrm{\nu}$ 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
$r_\mathrm{0.002}$ are consistent with each other and the apparent tension
seems to be relaxed. Further detailed investigations on those fittings suggest
that $N_\mathrm{eff}$ 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 datasets all together, we obtain
$r_{0.002} = 0.14_{-0.11}^{+0.05}$, $n_\mathrm{t} = 0.35_{-0.47}^{+0.28}$,
$n_\mathrm{s}=0.98_{-0.02}^{+0.02}$, and
$\alpha_\mathrm{s}=-0.0086_{-0.0189}^{+0.0148}$; if the consistency relation is
adopted, we get $r_{0.002} = 0.22_{-0.06}^{+0.05}$.
