Using the Comoving Maximum of the Galaxy Power Spectrum to Measure Cosmological Curvature

The large-scale maximum at k ≃ 0 . 05 h/ Mpc identified in the power-spectrum of galaxy fluctuations provides a co-moving scale for measuring cosmological curvature. In shallow 3D surveys the peak is broad, but appears to be well resolved in 1D, at ∼ 130 h − 1 Mpc ( k = 0 . 048 h/ Mpc), comprising evenly spaced peaks and troughs. Surprisingly similar behaviour is evident at z ∼ 3 in the distribution of Lyman-break galaxies, for which we find a 5 σ excess of pairs separated by ∆ z ≃ 0 . 22 ± 0 . 02, equivalent to 85 h − 1 Mpc for Ω = 1, increasing to 170 h − 1 Mpc for Ω = 0, with a number density contrast of 30% averaged over 5 independent fields. The combination, 3 . 2Ω m − Ω Λ ≃ 0 . 7, matches the local scale of 130 h − 1 Mpc, i.e. Ω = 0 . 2 ± 0 . 1 or Ω flat m = 0 . 4 ± 0 . 1 for the matter-dominated and flat models respectively, with an uncertainty given by the width of the excess correlation. The consistency here of the flat model with SNIa based claims is encouraging, but overshadowed by the high degree of coherence observed in 1D compared with conventional Gaussian models of structure formation. The appearance of this scale at high redshift and its local prominence in the distribution of Abell clusters lends support to claims that the high- z ‘spikes’ represent young clusters. Finally we show that a spike in the primordial power spectrum of δρ/ρ ≃ 0 . 3 at k = 0 . 05 h/ Mpc has little effect on the CMB, except to exaggerate the first Doppler peak in flat matter-dominated models, consistent with recent observations.