Cosmological parameter fittings with the BICEP2 data

Combining the latest Planck, Wilkinson Microwave Anisotropy Probe (WMAP), and baryon acoustic oscillation (BAO) data, we exploit the recent cosmic microwave background (CMB) B-mode power spectra data released by the BICEP2 collaboration to constrain the cosmological parameters of the $\Lambda$CDM model, esp. the primordial power spectra parameters of the scalar and the tensor modes, $n_s,\alpha_s, r, n_t$. We obtained constraints on the parameters for a lensed $\Lambda$CDM model using the Markov Chain Monte Carlo (MCMC) technique, the marginalized $68\%$ bounds are $r = 0.1043\pm_{0.0914}^{0.0307}$, $n_s = 0.9617\pm_{0.0061}^{ 0.0061}$, $\alpha_s = -0.0175\pm_{0.0097}^{0.0105}$, $n_t = 0.5198\pm_{0.4579}^{0.4515}$. We found that a blue tilt for $n_t$ is favored slightly, but it is still well consistent with flat or even red tilt. Our $r$ value is slightly smaller than the one obtained by the BICEP team, as we allow $n_t$ as a free parameter without imposing the single-field slow roll inflation consistency relation. If we impose this relation, $r=0.2130\pm_{0.0609}^{0.0446}$. For most other parameters, the best fit values and measurement errors are not altered much by the introduction of the BICEP2 data.