# Evolution of sub-spaces at high and low energies

## TL;DR

This paper investigates how sub-spaces evolve at different energies within higher-derivative gravity, using numerical solutions to understand the stability and size of our 3D space versus extra dimensions.

## Contribution

It provides numerical solutions to differential equations describing sub-space evolution and highlights the importance of initial conditions in space dynamics within higher-derivative gravity.

## Key findings

- Initial conditions crucially influence space evolution.
- Stable, large 3D space can coexist with small, stable extra dimensions.
- Parameter values at high energies are highly uncertain due to quantum corrections.

## Abstract

The evolution of sub-spaces in the framework of gravity with higher derivatives is studied. Numerical solutions to exact differential equations are found. It is shown that the initial conditions play crucial role in the space dynamic. Appropriate metrics describing an expanding and a stationary sub-space shed light on the well-known question: why our 3-dim space is large but extra space is small and stable (if exists)? It is assumed that the values of parameters at high energies strongly depend on uncontrolled quantum corrections and, hence, are not equal to their values at low energies. Therefore, there is no way to trace solutions throughout the energy range, and we restrict ourselves to the sub-Planckian and the inflationary energies.