Evolution of the Cosmic Web Anisotropy Parameter and Its Cosmological Implication

We report a numerical finding of scaling relation among cosmic-web anisotropy parameter A, linear density rms fluctuation σ (r) and linear growth factor D(z). Using the tidal field derived from the Millennium Run simulations on 512^3 grids at z=0, 2, 5 and 124, we calculate the largest eigenvalues λ of the local tidal tensor at each grid and measure its two-point correlation, ξ_λ, averaged over distance as a function of the cosines of polar angles \cosθ in the local principal axis frame. It is shown that ξ_λ is quite anisotropic, increasing toward the directions of minimal matter compression and that the anisotropy of ξ_λ increases as the redshift z decreases and as the upper distance cutoff r_c decreases. Fitting the numerical results to an analytic fitting model ξ_λ(\cosθ)∝ (1+A\cos^nθ)^-1, it is found that the bestfit-value of A, dubbed the cosmic-web anisotropy parameter, varies systematically with σ(r_c) and D(z), which leads us to determine empirically a simple scaling relation A(r_c,z)=0.8D^0.76(z)σ (r_c). Finally we discuss the dependence of the cosmic web anisotropy parameter on the background cosmology.