Weak Lensing and the Measurement of q0 from Type Ia Supernovae

Abstract

On-going projects to discover Type Ia supernovae at redshifts z = 0.3 - 1, coupled with improved techniques to narrow the dispersion in SN Ia peak magnitudes, have renewed the prospects for determining the cosmic deceleration parameter q_0. We estimate the expected uncertainty in the Hubble diagram determination of q_0 due to weak lensing by structure in the universe, which stochastically shifts the apparent brightness of distant standard candles. Although the results are sensitive to the density power spectrum on small scales, the induced flux dispersion sigma_m < 0.04 Omega_{m,0}^{1/2} mag for sources at z \leq 0.5, well below the ``intrinsic&#34; spread of nearby SN Ia magnitudes, sigma_M \simeq 0.2 mag. Thus, density inhomogeneities do not significantly impact the current program to measure q_0, in contrast to a recent claim. If, however, light-curve shape and other calibrators can reduce the effective intrinsic spread to 0.1 mag at high z, then weak lensing could increase the observed spread by 30% in an Omega_{m,0}=1 universe for SNe at z > 1.