the likelihood ($\chi^2$) approach. The black circle (gray square) is the best fit value for the likelihood ($\chi^2$). *Left panel:* Results for the MLCS2k2 version of the SDSS compilation. *Right panel:* Results for the SALT2 version of the SDSS compilation. \[fig:SDSS\_wCDM\_cosmopar\]](FIG2_a.eps "fig:"){width="49.00000%"} ![68% and 95% confidence level contours, in the plane $\Omega_{m0}\times w$, for the F$w$CDM model. We marginalized over all other parameters with flat prior. The solid (dashed) lines are the results for the likelihood ($\chi^2$) approach. The black circle (gray square) is the best fit value for the likelihood ($\chi^2$). *Left panel:* Results for the MLCS2k2 version of the SDSS compilation. *Right panel:* Results for the SALT2 version of the SDSS compilation. \[fig:SDSS\_wCDM\_cosmopar\]](FIG2_b.eps "fig:"){width="49.00000%"}

In Fig. \[fig:SDSS\_beta\_alpha\] we show the confidence contours for the SALT2 parameters $\boldsymbol{\delta}$ for both $\Lambda$CDM and F$w$CDM models. We can see that there is no significant difference in the constraints for $\alpha$. For $\beta$ we find a bias that is, however, small compared to the 68% confidence interval for this parameter.

![68% and 95% confidence level contours in the plane $\beta\times\alpha$. We marginalized over all other parameters with flat prior. The solid (dashed) lines are the results for the likelihood ($\chi^2$) approach. The 