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

Mauricio Bellini

doi:10.1140/epjc/s10052-024-13635-3

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2024) 84: 1270
https://doi.org/10.1140/epjc/s10052-024-13635-3

Regular Article

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

Mauricio Bellini¹^,2^a

¹ Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata, Argentina
² Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350, C.P. 7600, Mar del Plata, Argentina

^a mbellini@mdp.edu.ar

Received: 29 August 2024
Accepted: 20 November 2024
Published online: 9 December 2024

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 most intriguing 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 $N (z = 2) = 8 / (1 + \sqrt{5}) ≃ 2.4721$ $N(z=2)=8/(1+\sqrt{5})\simeq 2.4721$ , when the nonlinear quantum perturbations of space-time are related to the relativistic velocities ${\bar{U}}^{μ}$ $\bar{U}^{\mu }$ . To illustrate the theory, we calculate exactly the cosmological parameter in an early inflationary universe.

© The Author(s) 2024

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