Effective dimensionality of space-time in f(R)-general relativity with quantum boundary terms included

Abstract

I study an extended theory of General Relativity that incorporates normalized relativistic velocities, where the boundary terms in the varied $f(R)$-action are considered as a part of the physical system to be studied. Within this context, I investigate how the classical perturbations can be originated by quantum geometric perturbations, that alters the dynamics of the physical system without perturbations. To do it we use a modified nonlinear quantum algebra recently introduced. The quantum field perturbations of space-time also alter the geodesic equations that describe the dynamics of the relativistic velocities, the metric tensor and the Ricci tensor. But perhaps the mostintriguing of this phenomena is that these space-time alterations change the effective number of space-time dimensions of the system with perturbations included N(z), in a such manner that N(z) can take an irrational value N(z=2)=8/(1+sqrt{5})simeq 2.4721, when the nonlinear quantum perturbations of space-time are related to the relativistic velocities ar{U}^{mu}. To illustrate the theory, we calculate exactly the cosmological parameter in an early inflationary universe.