A gravitational constant and a cosmological constant in a spin-connection gravitational gauge field theory

Abstract

A spin-connection gravitational gauge theory with a spin-affine connection as its fundamental dynamical variable is suggested in the framework of vierbein formulation. The functional integral approach to the interaction between complex scalar matter fields and a heavy intermediate coupling field is considered, where the Einstein field equation appears as a first-integral solution to the low-energy spin-connection gauge field equation of Yang–Mills type. The most intriguing characteristics of the present scheme include: (i) the gravitational constant originates from the low-energy propagator of the heavy coupling field that mediates the gravitation between the matter fields and the spin-connection gauge field; (ii) the large cosmological constant resulting from the quantum vacuum energy actually makes no gravitational contribution since the spin-connection gauge field equation is a third-order differential equation of the metric, and an integration constant of the first-integral solution serves as an effective cosmological constant that would cause the cosmic accelerated expansion. The present mechanism for interpreting the nonzero but small cosmological constant provides a new insight into the cosmological constant problem.

Gravitational coupling, dynamical changes of units and the cosmological constant problem

“…In a slowly varying region, w »f 1 and V(f) mimics a cosmological term. In this approximation, (7) The cosmological constant receives strong contributions from various mass scales introduced by particle physics [20]. These mass scales accumulate in V(f) to make a large effective cosmological term.…”