Fast optimization algorithms and the cosmological constant

TL;DR

This paper explores how advanced algorithms can efficiently find small cosmological constants in complex landscape models, overcoming NP-hardness limitations and demonstrating polynomial average-case complexity in high-dimensional problems.

Contribution

It introduces a method to solve the NP-hard problem of finding small cosmological constants using sophisticated algorithms with polynomial average-case complexity.

Findings

Successfully found a cosmological constant of order 10^{-120} in a 10^9-dimensional landscape.

Demonstrated that the problem's average-case complexity can be polynomial in certain regimes.

Showed that advanced algorithms outperform brute force search in this context.

Abstract

Denef and Douglas have observed that in certain landscape models the problem of finding small values of the cosmological constant is a large instance of an NP-hard problem. The number of elementary operations (quantum gates) needed to solve this problem by brute force search exceeds the estimated computational capacity of the observable universe. Here we describe a way out of this puzzling circumstance: despite being NP-hard, the problem of finding a small cosmological constant can be attacked by more sophisticated algorithms whose performance vastly exceeds brute force search. In fact, in some parameter regimes the average-case complexity is polynomial. We demonstrate this by explicitly finding a cosmological constant of order $10^{-120}$ in a randomly generated $10^9$-dimensional ADK landscape.