Tangential Large Scale Structure as a Standard Ruler: Curvature Parameters from Quasars

Several observational analyses suggest that matter is spatially structured at $\approx 130h^{-1}Mpc$ at low redshifts. This peak in the power spectrum provides a standard ruler in comoving space which can be used to compare the local geometry at high and low redshifts, thereby constraining the curvature parameters. It is shown here that this power spectrum peak is present in the observed quasar distribution at $z\sim 2$: qualitatively, via wedge diagrams which clearly show a void-like structure, and quantitatively, via one-dimensional Fourier analysis of the quasars’ tangential distribution. The sample studied here contains 812 quasars. The method produces strong constraints (68% confidence limits) on the density parameter ${\mathrm{\Omega }}_0$ and weaker constraints on the cosmological constant ${\lambda }_0$, which can be expressed by the relation $ \Omega_0 = (0.24 \pm0.15)

• (0.10\pm0.08) \lambda_0 $\mathrm{.}Independentlyof$\lambda_0$(intherange$\lambda_0 \in [0,1]$),theconstraintis$0.1 < \Omega_0 < 0.45$. Combination of the present results with SN Type Ia results yields $\Omega_0 = (0.30\pm0.11) + (0.57\pm0.11) (\lambda_0-0.7),$ $0.55<{\lambda }_0<0.95,$ (68% confidence limits). This strongly supports the possibility that the observable universe satisfies a nearly flat, perturbed Friedmann-Lema^{\i}tre-Robertson-Walker model, independently of any cosmic microwave background observations.