The Holographic Arrow of Time: Objective Wavefunction Collapse and Topologically Filtered Baryogenesis via Modular Projection

Abstract

This paper explores the thermodynamic consequences of a bounded, non-Lipschitz primordial expansion. By abandoning the infinite-entropy initial singularity, we demonstrate that the non-equilibrium geometric expansion of the early cosmos natively generates the cosmological Arrow of Time and the observed matter-antimatter asymmetry. Key Breakthroughs: Emergent Entropy Gradients: Demonstrates that a finite, bounded initial state provides the necessary room for a strict macroscopic entropy gradient to form, mathematically deriving the unidirectional Arrow of Time as an artifact of spatial scaling rather than statistical chance. Geometric Baryogenesis: Evaluates the rapid non-Lipschitz phase transition of the early universe against the Sakharov conditions, demonstrating that the expansion natively provides the out-of-equilibrium environment required to drive matter-antimatter asymmetry. Elimination of CP-Violating Fields: Proves that baryogenesis operates as a direct thermodynamic consequence of chiral boundary reflection and geometric volume scaling, without requiring the postulation of undiscovered, ad-hoc CP-violating particles. This work connects the origin of time's directionality directly to the topology of the Big Bang, framing the predominance of matter as a strict geometric necessity of an expanding bounded space.