Supernova pencil beam survey

Type Ia supernovae (SNe Ia) can be calibrated to be good standard candles at cosmological distances. We propose a supernova pencil beam survey that could yield between dozens to hundreds of SNe Ia in redshift bins of 0.1 up to $z=1.5$, which would enable the proper consideration of the systematic uncertainties of SNe Ia as standard candles, in particular, evolution and gravitational lensing. We estimate the effect of gravitational lensing both in terms of an intuitive effective smoothness parameter and in terms of the dispersion in the SN Ia luminosities as function of redshift and the number of SNe available for flux-averaging at given redshift. The large number of SNe Ia in redshift bins at high $z$ would allow us to reduce gravitational lensing noise in the SN Ia Hubble diagram via appropriate flux averaging, and use the lensing induced redshift-dependent distributions of SN Ia luminosities to constrain mass fraction in compact objects and the evolution of clustering. The SN number count is not sensitive to matter distribution in the universe; it can be used to test models of cosmology and to measure the SN rate. The SN pencil beam survey can yield a wealth of data which should enable accurate determination of the cosmological parameters and the SN rate, and provide valuable information on the formation and evolution of galaxies. The SN pencil beam survey can be accomplished on a dedicated 4 meter telescope with a square degree field of view. This telescope can be used to conduct other important observational projects compatible with the SN pencil beam survey.