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.Comment: 33 pages, 9 figures, 1 table. Accepted for publication in AJ. arXiv admin note: text overlap with arXiv:1405.2388, arXiv:1410.0875; text overlap with arXiv:1409.4429 by other author