# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1706.08503