A Unified Hypothesis_ Dark Energy as Temporal Expansion Modeled by Fibonacci Sequences – Implications for P vs NP and Cognitive Problem-Solving.

Abstract This paper proposes a novel interdisciplinary hypothesis positing that dark energy, the driving force behind the accelerated expansion of the universe, is equivalent to time itself, modeled through the Fibonacci sequence for parsimonious growth and scaling. Drawing from cosmology, computational complexity, and cognitive science, we argue that this equivalence provides an explanatory framework rather than a traditional solution for unresolved problems like P vs NP. In cognitive terms, human problem-solving mirrors this process via backward simulations: intuitive insights (forward expansion akin to dark energy) are iteratively refined backward using Fibonacci-like accumulation to bridge procedural understanding. We present a simple mathematical model integrating exponential cosmic expansion with discrete Fibonacci approximations, demonstrating convergence to the golden ratio (φ ≈ 1.618). Implications extend to P vs NP, where verification (NP) aligns with temporal "checking" and solution (P) with backward iteration under time constraints. This framework emphasizes understanding over resolution, akin to experiential phenomena like love, and calls for empirical validation through simulations in quantum cosmology and cognitive experiments. Keywords: Dark energy, Fibonacci sequence, P vs NP, backward simulation, temporal expansion, cognitive modeling