Is there a connection between "dark" and "light" physics? (1707.07563v3)

Abstract: In the early-mid 20$^{\rm th}$ century Dirac and Zel'dovich were among the first scientists to suggest an intimate connection between cosmology and atomic physics. Though a revolutionary proposal for its time, Dirac's Large Number Hypothesis (1937) adopted a standard assumption of the day, namely, the non-existence of the cosmological constant term ($\Lambda = 0$). As a result, its implementation necessitated extreme violence to the theory of general relativity -- something few physicists were prepared to sacrifice in favour of numerology' -- requiring a time-dependent gravitational coupling of the form $G(t) \sim 1/t$. Zel'dovich's insight (1968) was to realise that a small but nonzero cosmological term ($\Lambda > 0$) allowed the present day radius of the Universe to be identified with the de Sitter radius, $r_{\rm U} \simeq l_{\rm dS} \simeq 1/{\sqrt{\Lambda}}$, which removed the need for time-dependence in the fundamental couplings. Thus, he obtained the formula $\Lambda \simeq m^6G^2/\hbar^4$, where $m$ is a mass scale characterising the relative strengths of the gravitational and electromagnetic interactions, which he identified with the proton mass $m_{\rm p}$. In this paper, we review a number of recent arguments which, instead, suggest the identification $m = m_{\rm e}/\alpha_{\rm e}$, where $m_{\rm e}$ is the electron mass and $\alpha_{\rm e} = e^2/\hbar c \simeq 1/137$ is the usual fine structure constant. We note that these are of a {\it physical} nature and, therefore, represent an attempt to lift previous arguments \emph{{\ a} la} Dirac from the realm of numerology into the realm of empirical science. If valid, such arguments suggest an intimate connection, not only between the macroscopic and microscopic worlds, but, perhaps even more surprisingly, between the very essence of "dark" and "light" physics.