On the relation between mass of pion, fundamental physical constants and cosmological parameters

TL;DR

This paper revisits the Dirac-Weinberg relation linking pion mass, fundamental constants, and cosmological parameters, proposing a form invariant to universe expansion that hints at virtual pions dominating the quantum vacuum.

Contribution

It reformulates the Dirac-Weinberg relation to be invariant under cosmic expansion without assuming a varying gravitational constant, suggesting a link to virtual pions in the quantum vacuum.

Findings

Reformulated the Dirac-Weinberg relation invariant to universe expansion.

Proposed virtual pions dominate the quantum vacuum content.

Connected fundamental constants with cosmological parameters.

Abstract

In this article we reconsider the old mysterious relation, advocated by Dirac and Weinberg, between the mass of the pion, the fundamental physical constants, and the Hubble parameter. By introducing the cosmological density parameters, we show how the corresponding equation may be written in a form that is invariant with respect to the expansion of the Universe and without invoking a varying gravitational "constant", as was originaly proposed by Dirac. It is suggest that, through this relation, Nature gives a hint that virtual pions dominante the "content" of the quantum vacuum.