Constraints on the primordial gravitational waves with variable sound speed from current CMB data

Understand

We make a comprehensive investigation of the observational effect of the inflation consistency relation.

• We focus on the general single-field inflation model with the consistency relation $r=-8c_s n_t$, and investigate the observational constraints of sound speed $c_s$ by using the Seven-Year WMAP data, the BICEP tensor power spectrum data, and the constraints on $f_{\rm NL}^{\rm equil.}$ and $f_{\rm NL}^{\rm orth.}$ from the Five-Year WMAP observations.
• We find that the constraints on the tensor-to-scalar ratio $r$ is much tighter if $c_s$ is small, since a large tilt $n_t$ is strongly constrained by the observations.
• We obtain $r<0.37, 0.27$ and 0.09 ($dn_s/d\ln k=0$) for $c_s$=1, 0.1 and 0.01 models at 95.4% confidence level.