On Some Accelerating Cosmological Kaluza-Klein Models

TL;DR

This paper develops a (4+D)-dimensional Kaluza-Klein cosmological model using real, p-adic, and adelic quantum mechanics, demonstrating dynamical compactification and accelerated expansion, with implications for early universe space-time structure.

Contribution

It introduces a p-adic and adelic quantum cosmological model with two scaling factors, extending standard quantum cosmology to explore space-time discreteness at early universe scales.

Findings

Existence of p-adic ground states in the model

Demonstration of dynamical compactification of extra dimensions

Potential for adelic generalization of cosmological evolution

Abstract

We consider (4+D)-dimensional Kaluza-Klein cosmological model with two scaling factors, as real, p-adic and adelic quantum mechanical one. One of the scaling factors corresponds to the D-dimensional internal space, and second one to the 4-dimensional universe. In standard quantum cosmology, i.e. over the field of real numbers R, it leads to dynamical compactification of additional dimensions and to the accelerating evolution of 4-dimensional universe. We construct corresponding $p$-adic quantum model and explore existence of its p-adic ground state. In addition, we explore evolution of this model and a possibility for its adelic generalization. It is necessary for the further investigation of space-time discreteness at very short distances, i.e. in a very early universe