The Cosmological Constant and Quintessence from a Correlation Function Comoving Fine Feature in the 2dF Quasar Redshift Survey

Local maxima at characteristic comoving scales have previously been claimed to exist in the density perturbation spectrum at the wavenumber $k =2\pi/L_{{\rm LSS}}$, where $L_{{\rm LSS}}\sim 100$–200 (comoving), at low redshift ($z\, \,\lower.6ex\hbox{$\buildrel z ”), $1.1 z ”) and $1.6 z ”). Because of the selection method of the survey and sparsity of the data, the analysis was done conservatively to avoid non-cosmological artefacts. (i) Avoiding a priori estimates of the length scales of features, local maxima in $\xi(r)$ are found in all three different redshift ranges. The requirement that a local maximum be present in all three redshift ranges at a fixed comoving length scale implies strong, purely geometric constraints on the local cosmological parameters, in which case the length scale of the local maximum common to the three redshift ranges is $2L_{{\rm LSS}}= 244\pm17$. (ii) For a standard cosmological constant FLRW model, the matter density and cosmological constant are constrained to $\Omega_{{\rm m}}= 0.25\pm0.10, \Omega_\Lambda=0.65\pm0.25 $ (68% confidence), $\Omega_{{\rm m}}= 0.25\pm0.15, \Omega_\Lambda=0.60\pm0.35 $ (95% confidence), respectively, from the 2QZ–10K alone . Independently of the type Ia supernovae data, the zero cosmological constant model ($\Omega_\Lambda=0$) is rejected at the 99.7% confidence level. (iii) For an effective quintessence ($w_{{\rm Q}}$) model and zero curvature, $ w_{{\rm Q}} from the 2QZ–10K alone . In a different analysis of a larger (but less complete) subset of the same 2QZ–10K catalogue, Hoyle et al. ([CITE]) found a local maximum in the power spectrum to exist for widely differing choices of $\Omega_{{\rm m}}$ and $\Omega_\Lambda$, which is difficult to understand for a genuine large scale feature at fixed comoving length scale. A resolution of this problem and definitive results should come from the full 2QZ, which should clearly provide even more impressive constraints on fine features in density perturbation statistics, and on the local cosmological parameters $\Omega_{{\rm m}},$ $\Omega_\Lambda$ and $w_{{\rm Q}}$.