The variance of dispersion measure of high-redshift transient objects as a probe of ionized bubble size during reionization

The dispersion measure (DM) of high-redshift $(z \gtrsim 6)$ transient objects such as Fast Radio Bursts can be a powerful tool to probe the intergalactic medium during the Epoch of Reionization. In this paper, we study the variance of the DMs of objects with the same redshift as a potential probe of the size distribution of ionized bubbles. We calculate the DM variance with a simple model with randomly-distributed spherical bubbles. It is found that the DM variance reflects the characteristics of the probability distribution of the bubble size. We find the variance can be measured precisely enough to obtain the information on the typical size with a few hundred sources at a single redshift.