The Causal Accessibility Framework: An Interpretive Geometric Framework for Temporal Asymmetry, Causal Accessibility, and the Structure of the Block Universe

Key Points

• This research aims to redefine our understanding of temporal asymmetry and causality within a cosmological context.
• Introduced a geometric framework defining causal accessibility associated with cosmic event horizons.
• Developed a weighted accessibility scalar A(t) on a flat LCDM model.
• Demonstrated thermodynamic directionality using a numerical toy model.
• Identified the principal eigenvector of the causal connectivity kernel as a cosmological initial condition.
• The framework suggests that time's arrow arises from causal accessibility gradients.
• Regime-dependent thermodynamic directionality was validated through numerical simulations.
• The principal eigenvector could replace the Past Hypothesis in cosmological conditions without introducing new physics.

Abstract