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The large-scale CMB B-mode polarization is the direct probe to the lowfrequency primordial gravitational wave signal. However, unambiguousmeasurement of this signal requires a precise understanding of the possiblecontamination. One such potential contamination arises from the patchiness inthe spatial distribution of free electrons during the epoch of reionization. Weestimate the B-mode power spectrum due to patchy reionization using acombination of \emph{photon-conserving} semi-numerical simulation andanalytical calculation, and compare its amplitude with the primordial B-modesignal. For a reionization history which is in agreement with several latestobservations, we find that a stronger secondary B-mode polarization signal isproduced when the reionization is driven by the sources in massive halos andits amplitude can be comparable to the recombination bump for tensor to scalarratio $(r) \lesssim 5 \times 10^{-4}$. If contamination from patchyreionization is neglected in the analysis of B-mode polarization data, then forthe models of reionization considered in this analysis, we find a maximum biasof about $30\%$ in the value of $r=\,10^{-3}$ when spatial modes between $\ell\in [50, 200]$ are used with a delensing efficiency of $50\%$. The inferredbias from patchy reionization is not a severe issue for the upcomingground-based CMB experiment Simons Observatory, but can be a potential sourceof confusion for proposed CMB experiments which target to detect the value of$r< 10^{-3}$. However, this obstacle can be removed by utilizing the differencein the shape of the power spectrum from the primordial signal.

Is patchy reionization an obstacle in detecting the primordial gravitational wave signal?