Temporal Expansion as a Unified Framework for Computational Complexity: Implications for Post-Quantum Cryptography and Artificial Intelligence

The accelerated expansion of the universe, traditionally attributed to dark energy, may arisefrom inhomogeneous gravitational time dilation rather than an exotic energy component. Thisperspective—supported by timescape cosmology and recent analyses of cosmological timedilation in supernova data—views "dark energy" as an emergent effect of temporal flow acrosscosmic structures. Here, we unify this insight with the Fibonacci sequence's discreteapproximation of exponential growth (via Binet's formula and the golden ratio φ ≈ 1.618) andcognitive forward-backward simulation processes. We propose a Temporal ExpansionHypothesis (TEH): Computational complexity, particularly the P versus NP problem, mirrorscosmic expansion, where verification (NP) resembles rapid forward checks in an expandingtemporal landscape, while solution-finding (P) requires backward accumulation akin toFibonacci summation.This framework has groundbreaking applications in post-quantum cryptography and artificialintelligence. In blockchain systems, TEH-inspired defenses model quantum threats as "temporalexpansions" (dark energy-like acceleration of attacks), countered by Fibonacci-discretizedbackward iterations for resilient key management. In AI, it enables novel training paradigmswhere forward simulation yields intuitive insights, refined backward via fractalaccumulation—potentially bridging the efficiency gap in NP-hard optimization. We demonstratemathematical coherence, empirical grounding from cosmology and cognition, and practicalprototypes, revealing a WOW!-level interconnection: the universe's expansion may encode thevery complexity limits of computation and intelligence.Keywords: Temporal dilation, Fibonacci approximation, P vs NP, post-quantum cryptography,forward-backward cognition, blockchain security, AI optimization