Multi-scale hierarchy from multidimensional gravity

TL;DR

The paper proposes a novel approach to the hierarchy problem using $f(R)$ gravity and inhomogeneous extra dimensions, leading to a multiscale universe with stabilized parameters across domains.

Contribution

It introduces a mechanism involving slow domain evolution and extra dimensions to restore multiple energy scales from the Planck scale.

Findings

Formation of causally disconnected pocket universes

Quantum fluctuations produce diverse field and metric distributions

Distributions stabilize at low energy scales

Abstract

We discuss the way of solving the hierarchy problem. We show that starting at the Planck scale, the three energy scales -- inflationary, electroweak and the cosmological ones can be restored. The formation of small parameters is proposed that leads to a successful solution of the problem. The tools involved in the process are $f(R)$ gravity and inhomogeneous extra dimensions. Slow rolling of a space domain from the Planck scale down to the inflationary one gives rise to three consequences: an infinite set of causally disconnected domains (pocket universes) are nucleated; quantum fluctuations in each domain produce a variety of different fields and an extra-dimensional metric distribution; these distributions are stabilized at a sufficiently low energy scale.