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We make a comprehensive investigation of the observational effect of theinflation consistency relation. We focus on the general single-field inflationmodel with the consistency relation $r=-8c_s n_t$, and investigate theobservational constraints of sound speed $c_s$ by using the Seven-Year WMAPdata, the BICEP tensor power spectrum data, and the constraints on $f_{\rmNL}^{\rm equil.}$ and $f_{\rm NL}^{\rm orth.}$ from the Five-Year WMAPobservations. We find that the constraints on the tensor-to-scalar ratio $r$ ismuch tighter if $c_s$ is small, since a large tilt $n_t$ is stronglyconstrained by the observations. We obtain $r<0.37, 0.27$ and 0.09 ($dn_s/d\lnk=0$) for $c_s$=1, 0.1 and 0.01 models at 95.4% confidence level. When takingsmaller values of $c_s$, the positive correlation between $r$ and $n_s$ alsoleads to slightly tighter constraint on the upper bound of $n_s$, while therunning of scalar spectral index $dn_s/d\ln k$ is generally unaffected. For thesound speed $c_s$, it is not well constrained if only the CMB power spectrumdata is used, while the constraints are obtainable by taking $f_{\rm NL}^{\rmequil.}$ and $f_{\rm NL}^{\rm orth.}$ priors into account. With theconstraining data of $f_{\rm NL}^{\rm equil.}$ and $f_{\rm NL}^{\rm orth.}$, wefind that, $c_s\lesssim 0.01$ region is excluded at 99.7% CL, and the $c_s=1$case (the single-field slow-roll inflation) is slightly disfavored at 68.3% CL.In addition, the inclusion of $f_{\rm NL}^{\rm equil.}$ and $f_{\rm NL}^{\rmorth.}$ into the analysis can improve the constraints on $r$ and $n_s$. Wefurther discuss the implications of our constraints on the test of inflationmodels.

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