  Superluminous supernovae (SLSNe) have been detected to $z\sim4$ and can be
detected to $z\gtrsim15$ using current and upcoming facilities. SLSNe are
extremely UV luminous, and hence objects at $z\gtrsim7$ are detected
exclusively via their rest-frame UV using optical and infrared facilities.
SLSNe have great utility in multiple areas of stellar and galactic evolution.
Here, we explore the potential use of SLSNe type-I as high-redshift
cosmological distance indicators in their rest-frame UV. Using a SLSNe-I sample
in the redshift range $1\lesssim z\lesssim 3$, we investigate correlations
between the peak absolute magnitude in a synthetic UV filter centered at 250 nm
and rise time, colour and decline rate of SLSNe-I light curves. We observe a
linear correlation between $M_0(250)$ and the rise time with an intrinsic
scatter of 0.29. Interestingly, this correlation is further tightened
($\sigma_{int} \approx 0.2$) by eliminating those SLSNe which show a pre-peak
bump in their light curve. This result hints at the possibility that the
"bumpy" SLSNe could belong to a different population. Weak correlations are
observed between the peak luminosity and colour indices. No relationship is
found between UV peak magnitude and the decline rate in contrast to what is
typically found in optical band. The correlations found here are promising, and
give encouraging insights for the use of SLSNe as cosmological probes at high
redshifts using standardising relations in the UV. We also highlight the
importance of early, and consistent, photometric data for constraining the
light curve properties.
