Lightish but clumpy: scalar dark matter from inflationary fluctuations

It has recently been shown [1] that light vector particles produced from inflationary fluctuations can give rise to the dark matter in the Universe. A similar mechanism has been discussed in [2] for a non-minimally coupled scalar enjoying a Higgs portal interaction. We discuss in detail how such a generation of dark matter works in a minimal setup of a massive scalar non-minimally coupled to gravity. For suitable values of the non-minimal coupling any initial constant value of the field is suppressed during inflation. At the same time, the quantum fluctuations acquired during inflation give rise to a peaked energy density power spectrum. Isocurvature constraints can be avoided since nearly all of the energy is concentrated in fluctuations too small to be observed in the CMB. For masses $\gtrsim {\rm eV}$ and sufficiently high inflation scale the energy contained in these fluctuations is sufficient to account for the cold dark matter of the Universe. At small scales $\ell_{\rm today}\sim 10^{4}\,{\rm km}\sqrt{m/{\rm eV}}\sim 10^{-4}\,{\rm AU}\sqrt{m/{\rm eV}}$ fluctuations are large and we therefore expect a rather clumpy nature of this form of dark matter.