Type Ia Supernovae, Evolution, and the Cosmological Constant

We explore the possible role of evolution in the analysis of data on Type Ia supernovae (SNe Ia) at cosmological distances. First, using a variety of simple sleuthing techniques, we find evidence that the properties of the high- and low-redshift SNe Ia observed so far differ from one another. Next, we examine the effects of allowing for an uncertain amount of evolution in the analysis, using two simple phenomenological models for evolution and prior probabilities that express a preference for no evolution but allow it to be present. One model shifts the magnitudes of the high-redshift SNe Ia relative to the low-redshift SNe Ia by a fixed amount. A second, more realistic, model introduces a continuous magnitude shift of the form δm(z) = β ln(1 + z) to the SNe Ia sample. The result is that cosmological models and evolution are highly degenerate with one another, so that the incorporation of even very simple models for evolution makes it virtually impossible to pin down the values of Ω_M and Ω_Λ, the density parameters for nonrelativistic matter and for the cosmological constant, respectively. The Hubble constant, H₀, is unaffected by evolution. We evaluate the Bayes factor for models with evolution versus models without evolution, which, if one has no prior predilection for or against evolution, is the odds ratio for these two classes of models. The resulting values are always of order 1, in spite of the fact that the models that include evolution have additional parameters; thus, the data alone cannot discriminate between the two possibilities. Simulations show that simply acquiring more data of the same type as are available now will not alleviate the difficulty of separating evolution from cosmology in the analysis. What is needed is a better physical understanding of the SN Ia process, and the connections among the maximum luminosity, rate of decline, spectra, and initial conditions, so that physical models for evolution may be constructed, and confronted with the data. Moreover, we show that if SNe Ia evolve with time, but evolution is neglected in analyzing data, then, given enough SNe Ia, the analysis hones in on values of Ω_M and Ω_Λ that are incorrect. Using Bayesian methods, we show that the probability that the cosmological constant is nonzero (rather than zero) is unchanged by the SNe Ia data when one accounts for the possibility of evolution, provided that we do not discriminate among open, closed, and flat cosmologies a priori. The case for nonzero cosmological constant is stronger if the universe is presumed to be flat but still depends sensitively on the degree to which the peak luminosities of SNe Ia evolve as a function of redshift.