# Inflationary limits on the size of compact extra space

## TL;DR

This paper investigates how inflationary models constrain the size and energy scale of extra dimensions in Kaluza-Klein theories, finding they must be extremely small and associated with high Planck masses.

## Contribution

It provides new bounds on the size of extra dimensions and the D-dimensional Planck mass based on inflationary model restrictions.

## Key findings

- Extra space size cannot exceed ~10^{-27} cm.
- D-dimensional Planck mass must be greater than ~10^{13} GeV.
- Stable scalar field excitations can form due to extra metric evolution.

## Abstract

We study restrictions imposed on the parameters of the Kaluza-Klein extra space supplied by the standard inflationary models. It is shown that the size of the extra space cannot be larger than $\sim 10^{-27}$cm and the $D$-dimensional Planck mass should be larger than $\sim 10^{13}$GeV. The validity of these estimates is discussed. We also study the creation of stable excitations of scalar field as the result of the extra metric evolution.