The three faces of Ωm:: testing gravity with low- and high-redshift SNe Ia surveys

Peculiar velocities of galaxies hosting Type Ia supernovae (SNe Ia) generate a significant systematic effect in deriving the dark energy equation of state w, at level of a few per cent. Here, we illustrate how the peculiar velocity effect in SNe Ia data can be turned from a 'systematic' into a probe of cosmological parameters. We assume a flat Lambda cold dark matter model (w = -1) and use low- and high-redshift SNe Ia data to derive simultaneously three distinct estimates of the matter density Omega(m) which appear in the problem: from the geometry, from the dynamics and from the shape of the matter power spectrum. We find that each of the three Omega(m)'s agrees with the canonical value Omega(m) = 0.25 to within 1 sigma, for reasonably assumed fluctuation amplitude and Hubble parameter. This is consistent with the standard cosmological scenario for both the geometry and the growth of structure. For fixed Omega(m) = 0.25 for all three Omega(m)'s, we constrain gamma = 0.72 +/- 0.21 in the growth factor of Omega(m)(z)(gamma), so we cannot currently distinguish between standard Einstein gravity and predictions from some modified gravity models. Future surveys of thousands of SNe Ia, or inclusion of peculiar velocity data, could significantly improve the above tests.