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Originally Posted by Jerry
Did you even read my quote from the paper?
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Did I? Did you?
Your quote merely mentions that there is a theoretical model. It also mentions that there are empirical reasons for limiting SN Ia luminosity dispersion. If you bother to read the rest of the paper, or any other SN Ia paper, you will find that nothing rests on the theoretical model. Not even in that paragraph you quoted does anything rely on the theoretical model.
Indeed, the inference in the paper is the opposite of the one you imagine. That is, the authors are arguing
from the empirical information on regularity
to a possible explanation. They do not commit to the theoretical explanation, however.
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If you are arguing that 'the essential assumption' is not grammatically similar to 'Theoretical models suggested'; you are still missing the point. The spectra of the most distant supernova are very noisy - Read the Broder et al paper referenced by Antoinseb - it is an necessary assumption of every paper using supernova Ia for cosmological purposes that the distant sample has the same light-curve length/ magnitude relationship as the local sample.
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This "assumption" can be tested by a variety of methods. Yet this assumption also does not rely on the theoretical model of the ultimate constituents of SN Ia events.