Large mass hierarchy from a small nonminimal coupling

We propose a simple but novel cosmological scenario where both the Planck mass and the dark energy scale emerge from the same super-Hubble quantum fluctuations of a nonminimally coupled ultralight scalar field during primordial inflation. The current cosmic and Solar System observations constrain the nonminimal coupling to be small.

Figure 1

Time variation of $G$ at present day as a function of $\xi$. The bare mass of the field has been set to $m_0=\sqrt{6\xi {\mathrm{\Omega }}_{\mathrm{\Lambda }}}{H}_0$, the value explaining dark energy today. The orange region, which is obtained from improvements in the ephemeris of Mars [45], is the observationally allowed region.