I was reading a paper from arxiv (https://arxiv.org/abs/1312.5798) when I stumbled upon this passage at pag 4
"However, even at low redshifts, there are limitations to how well the Type Ia supernova data can be interpreted with an empirical model such as $\Lambda$CDM, because the data cannot be determined independently of the assumed cosmology--- the supernova luminosities must be evaluated by optimizing at least 4 parameters simultaneously with those in the adopted model. This renders the data compliant to the underlying theory..."
but I know that supernovae distances are calculated by comparing the observed flux with the luminosity through the relation
$$ F = \frac{L}{4 \pi S_k (r)^2 (1+z)^2} $$
where $ 4 \pi S_k (r)^2 $ is the proper area and the $(1+z)^2$ comes from both the redshift of the photon wavelength and the time expansion, so i thought that the only thing that could influence the measure should be the value of the curvature parameter $ k$ , so what does the author mean with "optimizing at least 4 parameters simultaneously with those in the adopted model" ? thanks