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We investigate the effect of primordial non-Gaussianity on thecross-correlation between the CMB anisotropies and the 21 cm fluctuations fromthe epoch of reionization. We assume an analytic reionization model and anionization fraction with $f_{\rm NL}$ induced scale dependent bias. We estimatethe angular power spectrum of the cross-correlation of the CMB and 21 cm. Inorder to evaluate the detectability, the signal-to-noise (S/N) ratio for only asingle redshift slice is also calculated for current and future observations,such as CMB observations by Planck satellite and 21 cm observations byOmniscope. The existence of the $f_{\rm NL}$ increases the signal of thecross-correlation at large scales and the amplification does not depend on thereionization parameters in our reionization model. However the cosmic varianceis significant on such scales and the S/N ratio is suppressed. The obtained S/Nratio is 2.8 (2.4) for $f_{\rm NL}=10$ (100) in our fiducial reionizationmodel. Our work suggests in the absence of significant foregrounds andsystematics, the auto-correlations of 21 cm is a better probe of $f_{\rm NL}$than the cross-correlations (as expected since it depends on $b^2$), while thecross-correlations contain only one factor of $b$. Nevertheless, it isinteresting to examine the cross-correlations between 21 cm and CMB, as thesignal-to-noise ratio is not negligible and it is more likely we can ridourselves of systematics and foregrounds that are common to both CMB and 21 cmexperiments than completely clean 21 cm of all of the possible foregrounds andsystematics in large scales.

Constraining primordial non-Gaussianity with CMB-21cm cross-correlations?