Constraints on single-field inflation with WMAP, SPT and ACT data -- A last-minute stand before Planck

Abstract: We constrain models of single field inflation with the pre-\textit{Planck} CMB data. The data used here is the 9-year Wilkinson Microwave Anisotropy Probe (\textit{WMAP}) data, South Pole Telescope (SPT) data and Atacama Cosmology Telescope (ACT) data. By adding in running of spectral index parameter, we find that the $\chi^2$ is improved by a factor of $\Delta \chi^2=8.44$, which strongly indicates the preference of this parameter from current data. In addition, we find that the running of spectral index $\alpha_s$ does not change very much even if we switch to different pivot scales, which suggests that the power law expansion of power spectrum is accurate enough till the 1st order term. Furthermore, we find that the joint constraints on $r-n_{s}$ give very tight constraints on single-field inflation models, and the models with power law potential $\phi^{p}$ can only survive if $0.9 \lesssim p \lesssim 2.1$, so a large class of inflation models have already been ruled out before \textit{Planck} data. Finally, we use the $f_{NL}$ data to constrain the non-trivial sound speed $c_s$. We find that the current constraint is dominated by the power spectrum constraints which have some inconsistency with the constraints from $f_{NL}$. This poses important questions of consistency between power spectrum and bispectrum of \textit{WMAP} data.