Preinflation: Quantum nature of space–time to explain dark energy and the cosmological parameter

Abstract

In the framework of an extended theory of General Relativity that incorporates normalized relativistic velocities, where boundary terms in the varied action are treated as integral components of the physical system, I propose an unified nonperturbative formulation of physical and geometric quantum fields. This is illustrated through a recently proposed pre-inflationary model of the early universe. The approach involves introducing a novel canonical prescription for the scalar field $\hat{\phi }$, within the context of the quantum geometry of space–time, described by a quantum scalar field $\hat{\Omega }$, which satisfies a non-linear quantum algebra. In this framework, it is obtained the exact evolution of a time dependent cosmological parameter, which takes present-day values on the order of $4.1\times 10^{-52}$ m⁻², and will increase until it reaches an asymptotic value close to $4.23\times 10^{-52}$ m⁻², in the future.