Supernova pencil beam survey

Type Ia supernovae (SNe Ia) can be calibrated to be good standard candles at cosmological distances. However, at $z\ga 1$, gravitational lensing leads to significant level of noise in a SN Hubble diagram. We propose a pencil beam survey of SNe Ia which would yield a significant number of SNe in redshift bins of 0.1 for $z$ up to 2. The SN number count can provide a direct probe of cosmology which is not sensitive to matter distribution in the universe. The large number of SNe in redshift bins at high $z$ would enable proper consideration of the effect of gravitational lensing. Gravitational lensing noise can be removed from the Hubble diagram by appropriate flux averaging of SNe in redshift bins. The distribution of SN magnitudes in a given redshift bin depends on $\Omega_m$, $\Omega_{\Lambda}$, the mass distribution in lenses, and is very sensitive to the fraction of matter in compact objects. The SN pencil beam survey can yield a wealth of data which should enable accurate determination of the cosmological parameters, constrain mass fraction in compact objects and the evolution of clustering, and provide valuable information on the formation and evolution of galaxies.