Dark Energy and the quietness of the Local Hubble Flow

The linearity and quietness of the Local ($<10Mpc$) Hubble Flow (LHF) in view of the very clumpy local universe is a long standing puzzle in standard and in open CDM cosmogony. The question addressed in this paper is whether the antigravity component of the recently discovered dark energy can cool the velocity flow enough to provide a solution to this puzzle. We calculate the growth of matter fluctuations in a flat universe containing a fraction ${\mathrm{\Omega }}_X(t_0)$ of dark energy obeying the time independent equation of state $p_X=w{\rho }_X$. We find that dark energy can indeed cool the LHF. However the dark energy parameter values required to make the predicted velocity dispersion consistent with the observed value $v_{rms}\simeq 40km\mathrm{/}sec$ have been ruled out by other observational tests constraining the dark energy parameters $w$ and ${\mathrm{\Omega }}_X$. Therefore despite the claims of recent qualitative studies dark energy with time independent equation of state can not by itself explain the quietness and linearity of the Local Hubble Flow.