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 .