Type Ia supernova counts at high z: signatures of cosmological models and progenitors

Determination of the rates at which supernovae of Type Ia (SNe Ia) occur in the early Universe can give signatures of the time spent by the binary progenitor systems to reach explosion and of the geometry of the Universe. Observations made within the Supernova Cosmology Project are already providing the first numbers. Here it is shown that, for any assumed SNe Ia progenitor, SNe Ia counts up to $m_{R}\simeq 23-26$ are useful tests of the SNe Ia progenitor systems and cosmological tracers of a possible non-zero value of the cosmological constant, $\Lambda$. The SNe Ia counts at high redshifts compare differently with those at lower redshifts depending on the cosmological model. Flat $\Omega_{\Lambda}$--dominated universes would show a more significant increase of the SNe Ia counts at $z \sim 1$ than a flat, $\Omega_{M} = 1$ universe. Here we consider three sorts of universes: a flat universe with $H_{0} = 65 km s^{-1} Mpc^{-1}$, $\Omega_{M} = 1.0$, $\Omega_{\Lambda} = 0.0$; an open universe with $H_{0} = 65 km s^{-1} Mpc^{-1}$, $\Omega_{M} = 0.3$, $\Omega_{\Lambda} = 0.0$; and a flat, $\Lambda$--dominated universe with $H_{0} = 65 km s^{-1} Mpc^{-1}$, $\Omega_{M} = 0.3$, $\Omega_{\Lambda} = 0.7$). On the other hand, the SNe Ia counts from one class of binary progenitors (double degenerate systems) should not increase steeply in the $z= 0$ to $z= 1$ range, contrary to what should be seen for other binary progenitors. A measurement of the SNe Ia counts up to $z \sim 1$ is within reach of ongoing SNe Ia searches at high redshifts.