Maximum Cosmological Information from Type-Ia Supernova Observations

Type-Ia supernova observations yield estimates of the luminosity distance, which includes not only the background luminosity distance, but also the fluctuation due to inhomogeneities in the Universe. In particular, the spatial correlation of the host galaxies is a dominant source of the fluctuation in the luminosity distance measurements. Utilizing the recent theoretical framework that accurately quantifies the information contents accounting for the three-dimensional correlation of the observables on the past-light cone, we compute the maximum cosmological information obtainable from idealized supernova surveys as a function of maximum redshift $z_m$. Here we consider two cosmological parameters $\Omega_m$ and $w_0$ and show that these parameters can be constrained at maximum 1% levels in an idealized survey with $z_m=1$. We discuss how these fundamental limits set by cosmic variance can be overcome.