文档介绍：IL NUOVO CIMENTOVOL. 112 B, N. 9 Settembre 1997
Gravitational constant, cosmological constant and phases
of quantum gravity based on the Wheeler-DeWitt equation
T. HORIGUCHI
Kibi Institute of Fundamental Research - 1384 Tujita, Mabi-cho, Kibi-gun, Okayama-ken, Japan
(ricevuto il 20 Maggio 1996; revisionato il 2 Agosto 1996; approvato il 30 Agosto 1996)
Summary. — We re-examine the gravitational constant, cosmological constant and
phases of quantum gravity based on the Wheeler-DeWitt equation, considering
higher order contributions for the wave function in positive or negative (WKB)
power expansions in terms of the Planck mass. It is foundA that, in an unstable state,
the cosmological constant decreases with increasing a( m), and the gravitational
A A G A
constant increases with increasing a( m) for a( m) a ( m ) and decreases with
A A F A A * *
increasing a( m) for a( m) a ( m ), where a( m) is a renormalized cosmic-scale factor
A * *
and a ( m ) is a point in which the value of the gravitational constant es the
* *
maximum. This result may propose a new mechanism, in quantum gravity, which
explain the facts that the observed cosmological constant is very small and
gravitational forces are remarkably weak in atomic physics, by the old age of our
expanding universe. We also briefly discuss the relation between our results and
Dirac’s large-number hypothesis.
PACS – Quantum gravity.
PACS – Classical general relativity.
PACS – Self-gravitating systems; continuous media and classical fields in
curved spacetime.
PACS – Other topics in general relativity and gravitation.
PACS – Thermodynamics.
1. – Introduction
In a quantum theory of gravity, a wave function C is a function of the spatial metric
and matter fields. This wave function obeys the Wheeler DeWitt (WDW) equation
4
(HC 0) [1] which plays a central role in the theory. This equation is expected to be a
good framework of quantum