Directional Signatures of Structural Commitment:Testing Late-Time Isotropy in a Non-Markovian Cosmology

The cosmological principle assumes statistical isotropy and homogeneity on large scales as an initial condition. Yet nonlinear structure formation does not proceed uniformly across directions inside any finite cosmic volume. If the effective expansion responds to accumulated nonlinear history, then uneven structural commitment may generate weak, late-time directional signatures without violating primordial isotropy.

The paper builds a computational pathway to test this idea. First, a two-region toy model demonstrates a baseline mechanism, anisotropy emerges transiently when collapse histories diverge, and the amplitude is regulated by the memory kernel, with longer memory horizons suppressing directional contrasts by temporal averaging. Second, the study moves to cosmological simulations, focusing on the TNG300-1 volume to calibrate the intrinsic structural dipole as a null baseline, verify that the preferred structural axis is coherent across late-time snapshots and strengthened by massive halos, and rule out a moving-box explanation via bulk-flow alignment tests. The study then measures a directional expansion response by fitting dipoles to the bulk-flow-subtracted radial velocity field, including shell tomography out to $\sim 200\,h^{-1}\mathrm{Mpc}$. In shell tomography, the outer shell shows a stable, structure aligned expansion dipole at the 1.1\% level in the peculiar velocity frame.

Finally, cross-checking of methodology in TNG50-1 and stress-test the structural dipole estimator on SDSS DR8, where survey geometry dominates the raw dipole and requires mask-aware null tests. Overall, these experiments establish that a coherent structural mode in a finite volume naturally induces a coherent directional expansion anomaly. This work provides the simulation benchmark that any observational dipole test of non-Markovian expansion must first clear.