In a recent preprint, we discuss the possibility that both the Planck mass and the dark energy scale are dynamically generated by stochastic effects during inflation.
Two of the energy scales involved in gravitation, the Planck mass \(M_\mathrm{Pl} \simeq 10^{18}\,\mathrm{GeV}\) and the cosmological constant energy scale \(\rho_{\Lambda}^{1/4} \simeq 10^{-3}\, \mathrm{eV}\) differ by many orders of magnitude.
Together with Teruaki Suyama and Masahide Yamaguchi from TiTech (Tokyo), we explore in Ref.[1] the possibility that both have been dynamically generated from a new and unique ultra light scalar field that would have experienced super-Hubble quantum fluctuations during primordial inflation.
The scenario is currently passing all cosmological and astrophysical constraints, and could be proven at work with future gravitational wave measurements of the non-minimal coupling.