2013/10/02 by Patrick L. Nash, Nash, Patrick L.
Physics and Astronomy · #Cosmology and Gravitation Theories #Dark Matter and Cosmic Phenomena #FOS: Physical sciences #Galaxies: Formation, Evolution, Phenomena #General Physics (physics.gen-ph) #physics.gen-ph
paper · pdf · doi:10.48550/arxiv.1310.0697
This revision includes a THEOREM that guarantees the existence of stable solutions to the scalar field equation when the spacetime has extra time dimensions. Previous Changes=[1] included numerical solution examples; [2] extended derivations provided for several important results; [3] explained reheating
openalex publication_date 2013/10/02 · arxiv created 2014/06/06 · arxiv updated 2014/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Gravity cannot be quantized unless the quantized theory is cast on a manifold whose concomitant number of physical space dimensions and number of physical time dimensions correspond to physical reality, and not simply to the perception of reality. At present, the accepted number of physical time dimensions is dictated more by folklore than by science. In this paper we discuss a model of the early universe in which the number of physical time dimensions is four, and formulate Theorem[\reftj], which underlies an explanation of why the extra time dimensions do not source unphysical effects. In this paper we describe a new model of gravitational inflation that is driven by dark energy and "mediated" by a real massless scalar inflaton field φ whose potential is identically equal to zero. The coupled Einstein gravitational and inflaton field equations are formulated on an eight-dimensional spacetime manifold of four space dimensions and four time dimensions. We find explicit solutions to these field equations that exhibit temporal exponential deflation of three of the four time dimensions, and then study the dynamics of a massive complex scalar field ψ that propagates on the background ground state Einstein gravitational field to determine whether its quantum fluctuations δψ are stable or unstable. We compute explicit approximate solutions to the δψ field equations that are stable, meaning that the quantum fluctuations δψ of the field ψ do not grow exponentially with time. Instabilities driven by the momenta associated to the three extra time dimensions do not appear in the physical solutions of the field equations of this model.