Weyl transformation: a dynamical degree of freedom in the light of Dirac's Large Number Hypothesis

Abstract

In Einstein's Field Equation(EFE) the geometry of the space-time is connected with the matter distribution. The geometry or the gravitational sector deals with classical macroscopic objects involving gravitational units while the matter sector can be better described by quantum theory involving atomic units. It has been argued by Bisabr that there exists an epoch-dependent conversion factor between these two unit systems present in two different conformal frames,i.e. the conformal factor is epoch dependent. We argue that the conformal transformation is a dynamical degree of freedom describing it's possible relevance in inflation in context to the graceful exit problem, dynamics of the cosmological constant {\Lambda} and justify the argument in the light of consequences of Dirac's Large Number hypothesis(LNH).