The cosmological bulk flow in QCDM model: (In)consistency with $\Lambda CDM$

We study the bulk flow of the local universe using Type Ia supernova data by considering a class of cosmological model which is spatially flat,(FRW) space-times and contains cold dark matter and $Q$ component (QCDM models) of the fluid as a scalar field, with self interactions determined by a potential $V(Q)=V_{0}Exp(-\lambda Q)$ evolving in Universe. We use different cumulative redshift slices of the Union 2 catalogue. A maximum-likelihood analysis of peculiar velocities confirms that at low redshift $0.015 <z<0.1$, bulk flow is moving towards the $(l; b) = (302^{o}\pm20^{o}; 3^{o}\pm10^{o})$ direction with $v _{bulk} = 240\pm 25kms^{-1} $ velocity. This direction is aligned with direction of (SSC) and agreement with a number previous studies at $(1-\sigma)$, however for high redshift $0.1 <z<0.2$, we get $v _{bulk} = 1000\pm 25kms^{-1} $ towards the $(l; b) = (254^{+16^{o}}_{-14^{o}}; 6^{+7^{o}}_{-10^{o}})$. This indicates that for low redshift our results are approximately consistent with the $\Lambda CDM$ model with the latest WMAP best fit cosmological parameters however for high redshift they are in disagreement of $\Lambda CDM$ and support the results of previous studies such as Kashlinsky et. al, which report the large bulk flow for the Universe. We can conclude that, in $QCDM$ model, at small scales, fluctuations of the dark energy are damped and do not enter in the evolution equation for the perturbations in the pressureless matter, while at very large scales $(\sim > 100 h^{-1}Mpc)$, they leaving an imprint on the microwave background anisotropy.