THE COSMOLOGICAL BULK FLOW: CONSISTENCY WITH ΛCDM ANDz≈ 0 CONSTRAINTS ON σ8AND γ

We derive estimates for the cosmological bulk flow from the SFI++ Tully–Fisher (TF) catalog. For a sphere of radius 40 h −1 Mpc centered on the Milky Way, we derive a bulk flow of 333 ± 38 km s −1 toward Galactic ( l , b ) = (276°, 14°) within a 3° 1σ error. Within a radius of 100 h −1 Mpc we get 257 ± 44 km s −1 toward ( l , b ) = (279°, 10°) within a 6° error. These directions are at 40° to the Supergalactic plane, close to the apex of the motion of the Local Group of galaxies after the Virgocentric infall correction. Our findings are consistent with the ΛCDM model with the latest Wilkinson Microwave Anisotropy Probe ( WMAP ) best-fit cosmological parameters, but the bulk flow allows independent constraints. For the WMAP -inferred Hubble parameter h = 0.71 and baryonic mean density parameter Ω b = 0.0449, the constraint from the bulk flow on the matter density, Ω m , the normalization of the density fluctuations, σ 8 , and the growth index, γ, can be expressed as σ 8 Ω γ − 0.55 m (Ω m /0.266) 0.28 = 0.86 ± 0.11 (for Ω m ≈ 0.266). Fixing σ 8 = 0.8 and Ω m = 0.266 as favored by WMAP , we get γ = 0.495 ± 0.096. The constraint derived here rules out popular Dvali–Gabadadze–Porrati models at more than the 99% confidence level. Our results are based on the All Space Constrained Estimate (ACSE) model which reconstructs the bulk flow from an all space three-dimensional peculiar velocity field constrained to match the TF measurements. At large distances, ASCE generates a robust bulk flow from the SFI++ survey that is insensitive to the assumed prior. For comparison, a standard straightforward maximum likelihood estimate leads to very similar results.