Type Ia Supernovae ( SNe Ia ) are the best standard candles known today .
At high redshift ( z \sim 1 ) SNe Ia are used to determine the Cosmological Constant \Lambda with great success .
However the most serious concern is raised by the possible luminosity evolution of the SNe Ia explosion itself , i.e. , that their intrinsic luminosity might vary with the look-back time .
It is unknown to which extent high-redshift SNe Ia can directly be compared to near SNe Ia in order to determine \Lambda .
A possibility to circumvent this problem is to restrict the analysis to nearby SNe Ia situated preferably in E/S0 galaxies .
Since the signal will be much smaller , we have to consider an substantial sample .
As there are not enough data yet available , we conducted our analysis based on 200 synthetic SNe Ia with a luminosity scatter \sigma _ { \mathrm { m } } = 0. ^ { \mathrm { m } } 12 ( derived from observations ) assuming a homogeneous space distribution and a limiting distance of z \leq 0.16 .
We show that this kind of data , which we expect from future observations , will allow us to distinguish between a matter dominated or \Lambda -dominated ( \Omega _ { \mathrm { M } } = 0.3 , \Omega _ { \mathrm { \Lambda } } = 0.7 ) universe with a significance of up to 2-3 \sigma .