Axiomatic approach to the cosmological constant

TL;DR

This paper introduces an axiomatic framework for the cosmological constant, deriving a formula that aligns with observational data and provides a new perspective on its naturalness and underlying physical principles.

Contribution

It formulates axioms analogous to Khinchin's for information theory, leading to a novel formula for the cosmological constant based on fundamental constants.

Findings

Derived a formula for Lambda matching WMAP data

Provides physical interpretation for the Eddington-Dirac hypothesis

Suggests the cosmological constant's value is natural and not fine-tuned.

Abstract

A theory of the cosmological constant Lambda is currently out of reach. Still, one can start from a set of axioms that describe the most desirable properties a cosmological constant should have. This can be seen in certain analogy to the Khinchin axioms in information theory, which fix the most desirable properties an information measure should have and that ultimately lead to the Shannon entropy as the fundamental information measure on which statistical mechanics is based. Here we formulate a set of axioms for the cosmological constant in close analogy to the Khinchin axioms, formally replacing the dependency of the information measure on probabilities of events by a dependency of the cosmological constant on the fundamental constants of nature. Evaluating this set of axioms one finally arrives at a formula for the cosmological constant that is given by Lambda = (G^2/hbar^4) (m_e/alpha_el)^6, where G is the gravitational constant, m_e is the electron mass, and alpha_el is the low energy limit of the fine structure constant. This formula is in perfect agreement with current WMAP data. Our approach gives physical meaning to the Eddington-Dirac large number hypothesis and suggests that the observed value of the cosmological constant is not at all unnatural.