Cosmological parameter fittings with the BICEP2 data

Abstract

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.