Cosmological models with one extra dimension

TL;DR

This paper explores cosmological models with a dynamic extra dimension, showing how gravitational self-interaction influences the universe's expansion by modifying the Friedmann equation.

Contribution

It introduces a model where the extra dimension's size varies with time and demonstrates its impact on cosmological dynamics through self-interaction energy.

Findings

Self-interaction energy dominates the Friedmann equation.

The size of the extra dimension depends on gravitational self-interaction.

The model links extra dimension size to energy dominance.

Abstract

We consider cosmological models in which a homogeneous isotropic universe is embedded as a 3+1 dimensional surface into a 4+1 dimensional manifold. The size of the extra dimension depends on time. It is small compared to the size of the universe only if the energy of gravitational self-interaction of the universe through the compact extra dimension dominates over all other kinds of energy. The self-interaction energy gives the main contribution into the Friedmann equation, which governs the dynamics of the scale factor of the universe.