Does the gravitational “constant” increase?

Abstract

The possibility that the gravitational coupling “constant”G is an increasing function of the cosmic timet is discussed.

In Section 1 the Maximal Power Hypothesis (MPH) stating that no power in Nature can exceed the upper boundc ⁵/G (Gunn's luminosity) is advocated.

In Sections 2, 3, and 4 the MPH is employed on the cosmological scale to support the idea of an increasingG. In Section 2 the increasingG is obtained by two assumptions - the MPH and the energy conservation law - and by nothing else.

In Section 3 the increasingG follows naturally from the MPH in the Einstein-Cartan theory of gravity. The arguments proposed in Sections 2 and 3 lead todG(t)/dt > 0 but cannot specify the form ofG(t). In Section 4 the MPH is applied to the energy of the vacuum and leads to a relation betweenG and the cosmological term,G α ΛS ³, valid in a matter-dominated universe (S =S(t) is the expansion factor). This relation plus the time-dependence law (suggested by many authors) Λt ² = constant, plustH > 2/3 (suggested by observations on the age of globular clusters;H is the Hubble parameter) implies an increasingG. One finds also Λ αGU, whereU is the mass density of the universe, in agreement with other studies.