TITLE:
Cosmological Duality in Four Time and Four Space Dimensions
AUTHORS:
M. Medina, J. A. Nieto, P. A. Nieto-Marín
KEYWORDS:
Cosmology, (4 + 4)-Dimensional Gravitational Theory, Classical and Quantum Gravity
JOURNAL NAME:
Journal of Modern Physics,
Vol.12 No.7,
May
27,
2021
ABSTRACT: We describe a duality transformation in a cosmological model of four time and four space dimensions ((4 + 4)-dimensions). In particular, we show that via the Fourier transform, at the level of the zero-point energy of quantum mechanics and the de Sitter space, a Gaussian distribution in four dimensions leads to a dual Gaussian distribution also in four dimensions, with duality transformation , in the standard deviation σ. Moreover, we show that as a consequence of such a duality in σ a duality of the cosmological constant Λ can be obtained. Finally, we comment on the possibility that both the oriented matroid theory as well as the surreal number theory are related to the formalism presented in this work.