The cosmological bulk flow: consistency with $\Lambda$CDM and $z\approx 0$ constraints on $\sigma_8$ and $\gamma$

We derive estimates for the cosmological bulk flow from the SFI++ Tully-Fisher (TF) catalog. For a sphere of radius $40 \hmpc$ centered on the MW, we derive a bulk flow of $333 \pm 38\kms$ towards Galactic $(l,b)=(276^\circ,14^\circ)$ within a $3^\circ$ $1\sigma$ error. Within a $100\hmpc$ we get $257\pm 44\kms$ towards $(l,b)=(279^\circ, 10^\circ)$ within a $6^\circ$ error. These directions are at a $40^\circ$ with 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 $\Lambda$CDM model with the latest WMAP best fit cosmological parameters. But the bulk flow allows independent constraints. For WMAP inferred Hubble parameter $h=0.71$ and baryonic mean density parameter $\Omega_b=0.0449$, the constraint from the bulk flow on the matter density $\Omega_m$, the normalization of the density fluctuations, $\sigma_8$, and the growth index, $\gamma$, can be expressed as $\sigma_8\Omega_m^{\gamma-0.55}(\Omega_m/0.266)^{0.28}=0.86\pm 0.11$ (for $\Omega_m\approx 0.266$). Fixing $\sigma_8=0.8$ and $\Omega_m=0.266$ as favored by WMAP, we get $\gamma=0.495\pm 0.096$. The constraint derived here rules out popular DGP models at more than the 99% confidence level. Our results are based on a method termed \ace\ (All Space Constrained Estimate) which reconstructs the bulk flow from an all space three dimensional peculiar velocity field constrained to match the TF measurements. At large distances \ace\ generates a robust bulk flow from the SFI++ that is insensitive to the assumed prior. For comparison, a standard straightforward maximum likelihood estimate leads to very similar results.