# A scale at 10 MeV, gravitational topological vacuum, and large extra dimensions

## TL;DR

This paper explores a gravitational scale around 10 MeV linked to topological terms in gravity, extra dimensions, and early universe physics, suggesting a unified framework with implications for cosmology and quantum gravity.

## Contribution

It proposes a connection between a 10 MeV gravitational scale, topological Gauss-Bonnet terms, and large extra dimensions within the MacDowell-Mansouri formalism, offering new insights into quantum gravity and cosmology.

## Key findings

- A 10 MeV gravitational scale arises from topological terms in gravity.
- Six extra dimensions at the TeV scale relate to this gravitational scale.
- Implications for early universe physics and Big Bang Nucleosynthesis.

## Abstract

We discuss a possible scale of gravitational origin at around $10$ MeV, or $10^{-12}$ cm, which arises in the MacDowell-Mansouri formalism of gravity due to the topological Gauss-Bonnet term in the action, as pointed out by Bjorken several years ago. A length scale of the same size emerges also in the Kodama solution in gravity, which is known to be closely related to the MacDowell-Mansouri formulation. We particularly draw attention to the intriguing incident that existence of six compact extra dimensions originated from TeV-scale quantum gravity as well points to a length scale of $10^{-12}$ cm, as the compactification scale. The presence of six such extra dimensions is also in remarkable consistency with the MacDowell-Mansouri formalism; it provides a possible explanation for the factor of $\sim10^{120}$ multiplying the Gauss-Bonnet term in the action. We also comment on the relevant implications of such a scale regarding the thermal history of the universe motivated by the fact that it is considerably close to $1-2$ MeV below which the weak interactions freeze out, leading to Big Bang Nucleosynthesis.