Vanishing Dimensions in Four Dimensional Cosmology with Nonminimal Derivative Coupling of Scalar Field

TL;DR

This paper proposes a mechanism where the universe begins with fewer spatial dimensions and evolves to four dimensions, driven by a scalar field with nonminimal derivative coupling to curvature, with implications for unification theories.

Contribution

It introduces a novel dimensional evolution mechanism in four-dimensional cosmology using nonminimal derivative coupling of scalar fields.

Findings

Universe can start from lower dimensions and evolve to four dimensions.

Analytical solutions for Hubble parameter in specific limits.

Supports unification theories with lower-dimensional early universe.

Abstract

We discussed a mechanism that allows the universe to start from lower dimension ($d < 4$) in its very early era and evolves to four dimension at the end of the process. The mechanism is generated by a nonminimal derivative coupling of scalar field, where derivative terms of the scalar field coupled to curvature tensor. We solve the Einstein equations for a limit of large and nearly constant Hubble parameter and analyze the evolution of the Hubble parameter in this limit. The lower-dimensionality in early universe has advantages in the context of unification theory.