A new approach for obtaining cosmological constraints from Type Ia Supernovae using Approximate Bayesian Computation

Cosmological parameter estimation techniques that robustly account for systematic measurement uncertainties will be crucial for the next generation of cosmological surveys. We present a new analysis method, superABC, for obtaining cosmological constraints from Type Ia supernova (SN Ia) light curves using Approximate Bayesian Computation (ABC) without any likelihood assumptions. The ABC method works by using a forward model simulation of the data where systematic uncertainties can be simulated and marginalized over. A key feature of the method presented here is the use of two distinct metrics, the Tripp' and Light Curve’ metrics, which allow us to compare the simulated data to the observed data set. The Tripp metric takes as input the parameters of models fit to each light curve with the SALT-II method, whereas the Light Curve metric uses the measured fluxes directly without model fitting. We apply the superABC sampler to a simulated data set of $\sim$1000 SNe corresponding to the first season of the Dark Energy Survey Supernova Program. Varying $\Omega_m, w_0, \alpha$and$\beta$ and a magnitude offset parameter, with no systematics we obtain $\mathrm{\Delta }(w_0)=w_0^{\mathrm{t}\mathrm{r}\mathrm{u}\mathrm{e}}-w_0^{\mathrm{b}\mathrm{e}\mathrm{s}\mathrm{t}\mathrm{f}\mathrm{i}\mathrm{t}}=-0.036\pm 0.109$ (a $\sim 11$% 1$\sigma$ uncertainty) using the Tripp metric and $\Delta(w_0) = -0.055\pm0.068$(a$\sim7$$\sigma$ uncertainty) using the Light Curve metric. Including 1% calibration uncertainties in four passbands, adding 4 more parameters, we obtain $\mathrm{\Delta }(w_0)=-0.062\pm 0.132$ (a $\sim 14$% 1$\sigma$ uncertainty) using the Tripp metric. Overall we find a $17$% increase in the uncertainty on $w_0$ with systematics compared to without. We contrast this with a MCMC approach where systematic effects are approximately included. We find that the MCMC method slightly underestimates the impact of calibration uncertainties for this simulated data set.