  In the last decade, astronomers have found a new type of supernova called
`superluminous supernovae' (SLSNe) due to their high peak luminosity and long
light-curves. These hydrogen-free explosions (SLSNe-I) can be seen to z~4 and
therefore, offer the possibility of probing the distant Universe. We aim to
investigate the possibility of detecting SLSNe-I using ESA's Euclid satellite,
scheduled for launch in 2020. In particular, we study the Euclid Deep Survey
(EDS) which will provide a unique combination of area, depth and cadence over
the mission. We estimated the redshift distribution of Euclid SLSNe-I using the
latest information on their rates and spectral energy distribution, as well as
known Euclid instrument and survey parameters, including the cadence and depth
of the EDS. We also applied a standardization method to the peak magnitudes to
create a simulated Hubble diagram to explore possible cosmological constraints.
We show that Euclid should detect approximately 140 high-quality SLSNe-I to z ~
3.5 over the first five years of the mission (with an additional 70 if we lower
our photometric classification criteria). This sample could revolutionize the
study of SLSNe-I at z>1 and open up their use as probes of star-formation
rates, galaxy populations, the interstellar and intergalactic medium. In
addition, a sample of such SLSNe-I could improve constraints on a
time-dependent dark energy equation-of-state, namely w(a), when combined with
local SLSNe-I and the expected SN Ia sample from the Dark Energy Survey. We
show that Euclid will observe hundreds of SLSNe-I for free. These luminous
transients will be in the Euclid data-stream and we should prepare now to
identify them as they offer a new probe of the high-redshift Universe for both
astrophysics and cosmology.
