# Computational complexity of the landscape II - Cosmological considerations

## TL;DR

This paper introduces a novel multiverse analysis approach based on computational complexity, proposing a measure that avoids common paradoxes and is grounded in principles of limited and minimal computational complexity.

## Contribution

It develops a new framework for multiverse measure factors using computational complexity, offering solutions to longstanding problems like Boltzmann Brains and the youngness paradox.

## Key findings

- Proposes a supercomputer-based simulation for multiverse analysis.
- Defines a principle of limited computational complexity for early universe dynamics.
- Introduces a classification of natural complexity classes for cosmology.

## Abstract

We propose a new approach for multiverse analysis based on computational complexity, which leads to a new family of "computational" measure factors. By defining a cosmology as a space-time containing a vacuum with specified properties (for example small cosmological constant) together with rules for how time evolution will produce the vacuum, we can associate global time in a multiverse with clock time on a supercomputer which simulates it. We argue for a principle of "limited computational complexity" governing early universe dynamics as simulated by this supercomputer, which translates to a global measure for regulating the infinities of eternal inflation. The rules for time evolution can be thought of as a search algorithm, whose details should be constrained by a stronger principle of "minimal computational complexity." Unlike previously studied global measures, ours avoids standard equilibrium considerations and the well-known problems of Boltzmann Brains and the youngness paradox. We also give various definitions of the computational complexity of a cosmology, and argue that there are only a few natural complexity classes. (v2: version submitted for publication: clarified section 5.3; added references) (v3: added discussion of marginally hospitable vacua. Version to appear in Annals of Physics)