More Evidence for the Redshift Dependence of Color from the JLA
  Supernova Sample Using Redshift Tomography
  In this work, by applying the redshift tomography method to Joint Light-curve
Analysis (JLA) supernova sample, we explore the possible redshift-dependence of
stretch-luminosity parameter $\alpha$ and color-luminosity parameter $\beta$.
The basic idea is to divide the JLA sample into different redshift bins,
assuming that $\alpha$ and $\beta$ are piecewise constants. Then, by
constraining the $\Lambda$CDM model, we check the consistency of cosmology-fit
results given by the SN sample of each redshift bin. We also adopt the same
technique to explore the possible evolution of $\beta$ in various subsamples of
JLA. Using the full JLA data, we find that $\alpha$ is always consistent with a
constant. In contrast, at high redshift $\beta$ has a significant trend of
decreasing, at $\sim 3.5\sigma$ confidence level (CL). Moreover, we find that
low-$z$ subsample favors a constant $\beta$; in contrast, SDSS and SNLS
subsamples favor a decreasing $\beta$ at 2$\sigma$ and $3.3\sigma$ CL,
respectively. Besides, by using a binned parameterization of $\beta$, we study
the impacts of $\beta$'s evolution on parameter estimation. We find that
compared with a constant $\beta$, a varying $\beta$ yields a larger best-fit
value of fractional matter density $\Omega_{m0}$, which slightly deviates from
the best-fit result given by other cosmological observations. However, for both
the varying $\beta$ and the constant $\beta$ cases, the $1\sigma$ regions of
$\Omega_{m0}$ are still consistent with the result given by other observations.
