Testing Cosmological Models with Type Ic Super Luminous Supernovae
  The use of type Ic Super Luminous Supernovae (SLSN Ic) to examine the
cosmological expansion introduces a new standard ruler with which to test
theoretical models. The sample suitable for this kind of work now includes 11
SLSNe Ic, which have thus far been used solely in tests involving $\Lambda$CDM.
In this paper, we broaden the base of support for this new, important cosmic
probe by using these observations to carry out a one-on-one comparison between
the $R_{\rm h}=ct$ and $\Lambda$CDM cosmologies. We individually optimize the
parameters in each cosmological model by minimizing the $\chi^{2}$ statistic.
We also carry out Monte Carlo simulations based on these current SLSN Ic
measurements to estimate how large the sample would have to be in order to rule
out either model at a $\sim 99.7\%$ confidence level. The currently available
sample indicates a likelihood of $\sim$$70-80\%$ that the $R_{\rm h}=ct$
Universe is the correct cosmology versus $\sim$$20-30\%$ for the standard
model. These results are suggestive, though not yet compelling, given the
current limited number of SLSNe Ic. We find that if the real cosmology is
$\Lambda$CDM, a sample of $\sim$$240$ SLSNe Ic would be sufficient to rule out
$R_{\rm h}=ct$ at this level of confidence, while $\sim$$480$ SLSNe Ic would be
required to rule out $\Lambda$CDM if the real Universe is instead $R_{\rm
h}=ct$. This difference in required sample size reflects the greater number of
free parameters available to fit the data with $\Lambda$CDM. If such SLSNe Ic
are commonly detected in the future, they could be a powerful tool for
constraining the dark-energy equation of state in $\Lambda$CDM, and
differentiating between this model and the $R_{\rm h}=ct$ Universe.
