Pursuing the Amplitude of Tensor Mode Power Spectrum in Light of BICEP2

Abstract

In this brief report, we try to constrain general parameterized forms of scalar and tensor mode power spectra, $P_{s}(k)\equiv A_s(k/k_0)^{n_s-1+\frac{1}{2}\alpha_s\ln(k/k_0)}$ and $P_{t}(k)\equiv A_t(k/k_0)^{n_t+\frac{1}{2}\alpha_t\ln(k/k_0)}$ by the recently released BICEP2 data set plus {\it Planck} 2013, WMAP9 and BAO. We loosen the inflationary consistence relations, and take $A_s$, $n_s$, $A_t$ and $n_t$ as free model parameters, via the Markov chain Monte Carlo method, the interested model parameter space was investigated, we obtained marginalized $68\%$ limits on the interested parameters are: $n_s=0.96339_{-0.00554}^{+0.00560}$, $n_t=1.70490_{-0.56979}^{+0.56104}$, ${\rm{ln}}(10^{10} A_s)=3.08682_{-0.02614}^{+0.02353}$ and ${\rm{ln}}(10^{10} A_t)=3.98376_{-0.54885}^{+0.86045}$. The ratio of the amplitude at the scale $k=0.002 \text{Mpc} ^{-1}$ is $r=0.01655_{-0.01655}^{+0.00011}$ which is consistent with the {\it Planck} 2013 result.