  Here we present stringent low-frequency 185MHz limits on coherent radio
emission associated with a short gamma-ray burst (SGRB). Our observations of
the short GRB 180805A were taken with the upgraded Murchison Widefield Array
(MWA) rapid-response system, which triggered within 20s of receiving the
transient alert from Swift, corresponding to 83.7s post-burst. The SGRB was
observed for 30m, resulting in a 3sigma persistent flux density upper-limit of
40.2mJy/beam. Transient searches were conducted at the Swift position of this
GRB on 0.5s, 5s, 30s, and 2m timescales, resulting in 3sigma limits of
570-1830, 270-630, 200-420, and 100-200mJy/beam, respectively. We also
performed a dedispersion search for prompt signals at the position of the SGRB
with a temporal and spectral resolution of 0.5s and 1.28MHz, resulting in a
6sigma fluence upper-limit range from 570Jyms at DM=3000pc/cm^3 (z~2.5) to
1750Jyms at DM=200pc/cm^3 (z~0.1). We compare the fluence prompt emission limit
and the persistent upper-limit to SGRB coherent emission models assuming the
merger resulted in a stable magnetar. Our observations were not sensitive
enough to detect prompt emission associated with the alignment of magnetic
fields of a binary neutron star just prior to the merger, from the interaction
between the relativistic jet and the interstellar medium or persistent
pulsar-like emission from the spin-down of the magnetar. However, in the case
of a more powerful SGRB (a gamma-ray fluence an order of magnitude higher than
GRB 180805A and/or a brighter X-ray counterpart), our MWA observations may be
sensitive enough to detect coherent radio emission from the jet-ISM interaction
and/or the magnetar remnant. Finally, we demonstrate that of all current
low-frequency radio telescopes, only the MWA has the sensitivity and response
times capable of probing prompt emission models associated with the initial
SGRB merger event.
