  With their smaller radii and high cosmic abundance, transiting planets around
cool stars hold a unique appeal. As part of our on-going project to measure the
occurrence rate of extrasolar moons, we here present results from a survey
focussing on eight Kepler planetary candidates associated with M-dwarfs. Using
photodynamical modeling and Bayesian multimodal nested sampling, we find no
compelling evidence for an exomoon in these eight systems. Upper limits on the
presence of such bodies probe down to $\sim0.4M_{\oplus}$ in the best case. For
KOI-314, we are able to confirm the planetary nature of two out of the three
known transiting candidates using transit timing variations. Of particular
interest is KOI-314c, which is found to have a mass of
$1.0_{-0.3}^{+0.4}M_{\oplus}$, making it the lowest mass transiting planet
discovered to date. With a radius of $1.61_{-0.15}^{+0.16}R_{\oplus}$, this
Earth-mass world is likely enveloped by a significant gaseous envelope
comprising $\geq17_{-13}^{+12}$% of the planet by radius. We find evidence to
support the planetary nature of KOI-784 too via transit timing, but we advocate
further observations to verify the signals. In both systems, we infer that the
inner planet has a higher density than the outer world, which may be indicative
of photo-evaporation. These results highlight both the ability of Kepler to
search for sub-Earth mass moons and the exciting ancillary science which often
results from such efforts.
