Constraining Λ using cluster quadrupoles

We examine how the statistics of the quadrupoles of (projected) cluster masses can discriminate between flat cold dark matter (ΛCDM) universes with or without a cosmological constant term. Even in the era of high-precision cosmology that cosmic microwave background experiments should soon open, it is important to devise self-consistent tests of cosmogonic theories tuned at the matter radiation decoupling epoch using data from the nonlinear evolved universe. We build cluster catalogs from two large-volume simulations of a "tilted" cold dark matter (TCDM) model and a ΛCDM model with cosmic density parameter Ω_m = 0.35 and cosmological constant contribution Ω_Λ = 0.65. From the projected mass distribution of the clusters we work out the quadrupoles Q and examine their dependence on cluster mass and the cosmological model. We find that TCDM clusters have systematically larger quadrupoles than their ΛCDM counterpart. The effect is mass dependent: massive clusters (M ≳ 10 ¹⁵ h^-1 M_⊙) have quadrupoles differing by more than 30% in the two models, while for M ≲ 4 × 10¹⁴ h^-1 M_⊙ the difference rapidly drops to ∼1%. Performing a Kolmogorov-Smirnov D-statistic (K-S) test of the Q distributions, we estimate that using just the 15 most massive clusters in the simulation volume (360 h^-1 Mpc a side), we can discriminate between TCDM and ΛCDM at a confidence level better than 99.9%. In the volume probed by existing observations, there are potentially several hundred clusters with masses above the threshold for which the differences in the quadrupoles become relevant. Should weak lensing data become available for this whole set, a quadrupole analysis may be expected to discriminate among different values of Λ.