Determining H₀ and q₀ from supernova data

Since 1929 when Edwin Hubble showed that the Universe is expanding, extensive observations of redshifts and relative distances of galaxies have established the form of expansion law. Mapping the kinematics of the expanding universe requires sets of measurements of the relative size and age of the universe at different epochs of its history. There has been decades effort to get precise measurements of two parameters that provide a crucial test for cosmology models. The two key parameters are the rate of expansion, i.e., the Hubble constant (H₀) and the deceleration in expansion (q₀). These two parameters have been studied from the exceedingly distant clusters where redshift is large. It is indicated that the universe is made up by roughly 73% of dark energy, 23% of dark matter, and 4% of normal luminous matter; and the universe is currently accelerating. Recently, however, the unexpected faintness of the Type Ia supernovae (SNe) at low redshifts (z < 1) provides unique information to the study of the expansion behavior of the universe and the determination of the Hubble constant. In this work, we present a method based upon the distance modulus redshift relation and use the recent supernova Ia data to determine the parameters H₀ and q₀ simultaneously. Preliminary analysis from the data MLCS2k2 suggests the following ranges for H₀ and q₀, 54km/sec/Mpc < H₀ < 58km/sec/Mpc and 0.27 < q₀ < 0.38, which are different from the current theory.