Multi-scale hierarchy from multidimensional gravity

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. A mechanism for generating small parameters that leads to a successful solution of the problem is proposed. 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 fields and an extra-dimensional metric distribution; these distributions are stabilized at a sufficiently low energy scale. © 2023 Elsevier B.V.