Causal Shell Growth and Delayed Emergent Gravity: A 2D/1D Computational Exploration

Abstract. We extend the numerical Concentric Shell Theory (CST) program by introducing an explicitly causal picture in which shell structures are generated progressively at speed c rather than assumed to be fully developed from the outset. Starting from the previously published CST preprint and its 2D numerical reduction, we study five classes of simulations. First, we show that a pair of newborn neutral shell particles may exhibit a transient non-attractive or weakly repulsive stage before the long-range outer-shell attraction becomes dominant. Second, we show that when the interaction is coarse-grained from single particles to shell clusters, the strong microscopic phase sensitivity is smoothed while the attractive outer contribution becomes dominant and increasingly stable. Third, we compare causal and static cluster-cluster forces and define the maturation time t90 at which the causal force reaches 90% of the static value. Fourth, we fit t90(D) and find the simple numerical law t90 ≈ D/c, almost independent of cluster size. Finally, we introduce a one-dimensional toy cosmology calibrated on the cluster simulations. In that toy setting, a history-dependent pair-memory closure is required to avoid repeated resetting of the attractive channel; we therefore treat the cosmological exercise as exploratory rather than derived from the underlying field equations. The central result of the paper is thus the delayed-gravity law t90 ≈ D/c. Any qualitative connection to reduced early-time gravitational braking or Hubble-tension phenomenology should be understood as tentative and motivational, not as a quantitative cosmological claim.