Testing cosmological models with type Ic super luminous supernovae

The use of type Ic super luminous supernovae (SLSNe 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 the Λ cold dark matter (ΛCDM) model. 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 $R_h=ct$ and ΛCDM 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 SLSNe Ic measurements to estimate how large the sample would have to be in order to rule out either model at a ∼99.7% confidence level. The currently available sample indicates a likelihood of ∼70–80% that the $R_h=ct$ universe is the correct cosmology versus ∼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 ΛCDM, a sample of ∼240 SLSNe Ic would be sufficient to rule out $R_h=ct$ at this level of confidence, while ∼480 SLSNe Ic would be required to rule out ΛCDM if the real universe is instead $R_h=ct$. This difference in required sample size reflects the greater number of free parameters available to fit the data with ΛCDM. 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 ΛCDM, and differentiating between this model and the $R_h=ct$ universe.