Effects of time-varying in SNLS3 on constraining interacting dark energy models

It has been found that, for the Supernova Legacy Survey three-year (SNLS3) data, there is strong evidence for the redshift evolution of the color-luminosity parameter . In this paper, adopting the -cold-dark-matter (CDM) model and considering its interacting extensions (with three kinds of interaction between dark sectors), we explore the evolution of and its effects on parameter estimation. In addition to the SNLS3 data, we also use the latest Planck distance priors data, the galaxy clustering data extracted from sloan digital sky survey data release 7 and baryon oscillation spectroscopic survey, as well as the direct measurement of Hubble constant from the Hubble Space Telescope observation. We find that, for all the interacting dark energy (IDE) models, adding a parameter of can reduce by 34, indicating that a constant is ruled out at 5.8 confidence level. Furthermore, it is found that varying can significantly change the fitting results of various cosmological parameters: for all the dark energy models considered in this paper, varying yields a larger fractional CDM densities and a larger equation of state ; on the other side, varying yields a smaller reduced Hubble constant for the CDM model, but it has no impact on for the three IDE models. This implies that there is a degeneracy between and coupling parameter . Our work shows that the evolution of is insensitive to the interaction between dark sectors, and then highlights the importance of considering 's evolution in the cosmology fits.