5 on Data Release 3 (DR3; [38]) of the SDSS. Briefly, the C4 catalogue identifies clusters in a seven-dimensional ga la xy position and colour space (righ ascension, declina- tio n , redshift, u − g, g − r, r − i, i − z ) using the SDSS Main Ga la xy spectroscopic sample. This method greatly re- du c es the twin problems of projection effects and redshift sp a ce distortions in identifying physically–bound galaxy gr o ups. This catalogue is composed of ∼ 2000 clusters in th e redshift range 0 . 02 < z < 0 . 15. T he estimation of the correlation function relies cru- cia lly on our ability to compare the clustering of the data to t hat of a random field. Thus any artificial structures in t he data must be considered when constructing the ra n dom catalogue. These problems include incomplete- ne s s , such as the angular mask (e.g. survey boundaries, br ig ht stars and dust extinction in our own galaxy), and th e radial distribution where at large distances, the mean sp a ce density decreases as we approach the magnitude lim it of the survey. We have constructed random sam- ples which takes these issues into account, i.e., the angu- lar positions are randomly sampled from a sphere to lie within the DR3 mask, while the redshifts are obtained from a smooth spline fit to the real C4 redshift distri- bution (which removes true large scale structures). The random samples are then made to be 50 times denser than the real data to avoid Poisson noise. In Figure 3, we show our estimation of the ξ$_{s}$ ( σ, π ) binned into with 6 configuration–space bins up to 60 Mpc (one bin per 10Mpc). Separations of less than 10 Mpc are removed to reduce the FoG effect. Error on ξ$_{s}$ ( σ, π ) were derived using the jackknife method [39], which in- volves dividing the survey into N sub-sections with equal area (and thus volume) and then computing the mean and variance of ξ$_{s}$ ( σ, π ) from these N measurements of the correlation function with the i th region removed each time (where i = 1 ...N ). In our analysis, we divided the whole C4 area into N = 30 sub-subsections and determine the variance from [40], In this formula, there is a degeneracy between g ∗ b i and g ∗ Θ$_{m}$ i which cannot be solely broken by fitting ξ$_{s}$ ( σ, π ); instead we simultaneously fit for v i p and b i from the data and then marginalize over the bias to obtain v$_{p}$ (indepen- dent of b ) in that redshift bin. Therefore, if our statistical determination of the history of v i p can be combined with an independent measurement of bias, then v i p can be de- termined precisely. The scaled parameter g ∗ Θ$_{m}$ i depends on all shift factors; the primordial amplitude or the en- hancement of D$_{m}$ due to varying ω$_{m}$ , as well as later time Θ$_{m}$ evolution. But the estimation of v$_{p}$ from g ∗ Θ$_{m}$ i is independent of the uncertainty in the overall shifting. If the evolution of g ∗ Θ$_{m}$ is measured, it can be used to reconstruct other coherent growth factors. The coherent growth factor of Φ can be given using the Euler equation, FIG. 3: The 2-D two–point correlation function ( ξ$_{s}$ ( σ, π )) for the SDSS DR3 C4 cluster survey with a median redshift of ¯ z =0.1. The contours have been slightly smoothed.  (Mpc h −1 )  (Mpc h −1 ) −60 −40 −20 0 20 40 60 −40 −20 0 20 40 60 −2 −1.5 −1 −0.5 0 0.5 g ∗ Φ = 2 3 aH H 2 $_{∗}$ω$_{m}$ ( g ∗ θ$_{m}$ + dg ∗ θ$_{m}$ d ln a ) , (9) σ 2 $_{ξ}$( r$_{i}$ ) = N$_{jack}$ − 1 N$_{jack}$ N$_{jack}$ ∑ k =1 [ ξ$_{k}$ ( r$_{i}$ ) − ξ ( r$_{i}$ )] $^{2}$, (10) where no anisotropy condition is used. If the Poisson equation is validated then the re-constructed g ∗ Φ can be used to derive g ∗ δ$_{m}$ using the relation g ∗ δ$_{m}$ = ag ∗ $_{Φ}$. Then this estimated matter fluctuation evolution can be used to determine bias from the measured g ∗ b i as b = g ∗ $_{b i}$/g ∗ $_{δ$_{m}$}$. where N$_{jack}$ is the number of jackknife samples used and r$_{i}$ represents a single bin in the σ − π configuration space. Then we compute ξ ( r$_{i}$ ) = 1 N$_{jack}$ N$_{jack}$ ∑ k =1 ξ$_{k}$ ( r$_{i}$ ) , (11) C$_{ij}$ = N$_{jack}$ − 1 N$_{jack}$ k = N$_{jack}$ ∑ k =1 Δ k $_{i}$Δ k $_{j}$, (12) Δ k i = ξ$_{k}$ ( r$_{i}$ ) − ξ ( r$_{i}$ ) σ$_{ξ}$ ( r$_{i}$ ) . (13) III. REDSHIFT–SPACE DISTORTIONS FROM CLUSTERS OF GALAXIES As a demonstration of the parameterization discussed above, we present here a measurement of the redshift– space 2-D two–point correlation function ( ξ$_{s}$ ( σ, π )) for clusters of galaxies selected from the SDSS. We use an updated version of the C4 cluster catalogue [23] based where, and the normalised covariance matrix is estimated from [39],