Deciphering the cosmic star formation history and the nature of type Ia supernovae with future supernova surveys

We investigate the prospects of future supernova searches getting meaningful constraints on the cosmic star formation history ( CSFH) and the delay time of Type Ia supernovae from star formation ( tau(Ia)), based only on supernova data. Here we parameterized the CSFH by two parameters, alpha and beta, which are the evolutionary indices [proportional to( 1 + z)({alpha,beta})] at z >= 1 and less than or similar to 1, respectively, and quantitatively examined how well the three parameters ( alpha, beta, and tau(Ia)) can be constrained in ongoing and future supernova surveys. We found that the type classification of detected supernovae down to the magnitude of I-AB similar to 27 is essential for getting a useful constraint on beta. The parameter tau(Ia) can also be constrained to within an accuracy of similar to 1 - 2 Gyr without knowing alpha, which is somewhat degenerate with tau(Ia). This might be achieved by ground- based surveys but depends on the still highly uncertain type classification by imaging data. More reliable classification will be achieved by the SNAP mission. The supernova counts at a magnitude level of I-AB or K-AB similar to 30 will allow us to break degeneracies between alpha and tau(Ia) and independently constrain all three parameters, even without knowing supernova types. This can be achieved by the SNAP and JWST missions, which have the different strengths of larger statistics and reaching to higher redshifts, respectively. The dependence of observable quantities on survey time intervals is also quantitatively calculated and discussed.