Misc,
Axiomatic approach to the cosmological constant
(2008)cite arxiv:0810.0752 Comment: 7 pages, no figures. Some further references added.
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.
