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We derive estimates for the cosmological bulk flow from the SFI++Tully-Fisher (TF) catalog. For a sphere of radius $40 \hmpc$ centered on theMW, 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 $(l,b)=(279^\circ, 10^\circ)$ withina $6^\circ$ error. These directions are at a $40^\circ$ with the Supergalacticplane, close to the apex of the motion of the Local Group of galaxies after theVirgocentric infall correction. Our findings are consistent with the$\Lambda$CDM model with the latest WMAP best fit cosmological parameters. Butthe bulk flow allows independent constraints. For WMAP inferred Hubbleparameter $h=0.71$ and baryonic mean density parameter $\Omega_b=0.0449$, theconstraint from the bulk flow on the matter density $\Omega_m$, thenormalization 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 favoredby WMAP, we get $\gamma=0.495\pm 0.096$. The constraint derived here rules outpopular DGP models at more than the 99% confidence level. Our results are basedon a method termed \ace\ (All Space Constrained Estimate) which reconstructsthe bulk flow from an all space three dimensional peculiar velocity fieldconstrained to match the TF measurements. At large distances \ace\ generates arobust bulk flow from the SFI++ that is insensitive to the assumed prior. Forcomparison, a standard straightforward maximum likelihood estimate leads tovery similar results.

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