Quantum computational complexity, Einstein's equations and accelerated expansion of the Universe

TL;DR

This paper explores how quantum computational complexity relates to Einstein's equations and suggests that the universe's accelerated expansion might be driven by quantum complexity, offering a novel perspective on cosmology.

Contribution

It introduces a new approach linking quantum complexity to general relativity and proposes that cosmic acceleration can be explained through quantum complexity without fine-tuning.

Findings

Derived the full non-linear Einstein equation from complexity considerations

Linked quantum complexity to the accelerated expansion of the universe

Proposed complexity-driven cosmological model avoiding fine-tuning

Abstract

We study the relation between quantum computational complexity and general relativity. The quantum computational complexity is proposed to be quantified by the shortest length of geodesic quantum curves. We examine the complexity/volume duality in a geodesic causal ball in the framework of Fermi normal coordinates and derive the full non-linear Einstein equation. Using insights from the complexity/action duality, we argue that the accelerated expansion of the universe could be driven by the quantum complexity and free from coincidence and fine-tunning problems.