IlkI_{lk} is the inertia tensor of the collapsing region.
In CDM, the density field is assumed to be Gaussian and statistically isotropic, resulting in random spin orientations at large scales.
However, if the initial density field exhibits fractal correlations, with long-range anisotropic fluctuations, the preferred axes for collapse and shear may align across large volumes, inducing measurable spin correlations.
3. Simulation Framework
We simulate a cosmological box (300 Mpc/h) using the following steps:
Generate fractal initial density fields (x)\delta(\vec{x}) using Fourier filtering with a power-law spectrum:
P(k)k(3DH)for DH[2.1,2.6]P(k) \sim k^{-(3 - D_H)} \quad \text{for } D_H \in [2.1, 2.6]
Compute tidal shear tensors from the potential field \Phi, derived via Poisson's equation,
Estimate inertia tensors from mass distribution within Lagrangian patches,
Calculate galaxy spin vectors L\vec{L} at protohalo locations via TTT,
Evaluate angular correlation functions:
2-point spin alignment cos2(ij)\langle \cos^2(\theta_{ij}) \rangle,
