Estimating the redshift error in supernova data analysis

Recent works have shown that small shifts in redshift -- gravitational redshift or systematic errors -- could potentially cause a significant bias in the estimation of cosmological parameters. I aim to verify whether a theoretical correction on redshift is sufficient to ease the tension between the estimates of cosmological parameters from SNe 1a dataset and Planck 2015 results. A free parameter for redshift shift($\Delta z$) is implemented in the Maximum Likelihood Estimator. Redshift error was estimated from the Joint Light-curve Analysis(JLA) dataset and results from the Planck 2015 survey. The estimation from JLA dataset alone gives a best fit value of $\Omega_m = 0.272$, $\Omega_{\Lambda} = 0.390$, and $\Delta z = 3.77 \times 10^{-4}$. The best fit values of both $\Omega_m$ and $\Omega_{\Lambda}$ disagrees heavily with results from other observations. Information criteria and observed density contrasts suggest that the current data from SNe 1a is not accurate enough to give a proper estimate of $\Delta z$. A joint analysis with Planck results seems to give a more plausible value of the redshift error, and can potentially be used as a probe to measure our local gravitational environment.