  Fast Radio Bursts (FRBs) are a promising tool for studying the low-density
universe as their dispersion measures (DM) are extremely sensitive probes of
electron column density. Active Galactic Nuclei (AGN) inject energy into the
intergalactic medium, affecting the DM and its scatter. To determine the
effectiveness of FRBs as a probe of AGN feedback, we analysed three different
AGN models from the EAGLE simulation series. We measured the mean DM-redshift
relation, and the scatter around it, using $2.56 \times 10^8$ sightlines at 131
redshift ($z$) bins between $0 \leq z \leq 3$. While the DM-redshift relation
itself is highly robust against different AGN feedback models, significant
differences are detected in the scatter around the mean: weaker feedback leads
to more scatter. We find $\sim 10^4$ localised FRBs are needed to discriminate
between the scatter in standard feedback and stronger, more intermittent
feedback models. The number of FRBs required is dependent on the redshift
distribution of the detected population. A log-normal redshift distribution at
$z=0.5$ requires approximately 50% fewer localised FRBs than a distribution
centred at $z=1$. With the Square Kilometre Array expected to detect $>10^3$
FRBs per day, in the future, FRBs will be able to provide constraints on AGN
feedback.
