The paper proposes that the entirety of dark matter is a massive free (as in non-interacting and non-self-interacting) field that appeared at the end of inflation, but before big bang nucleosynthesis ("BBN"). In order to make this work with observations of the cosmic microwave background, the field has to have much lower mass earlier during inflation than at inflation's end. The mass-gaining mechanism is not elucidated.

There is only one known scalar field -- the Higgs -- and it is far from a free field.

Any non-gravitational interaction between this proposed field and the rest of the universe (including self-interactions) after the end of inflation is incompatible with this proposal. (One contrast this with other proposals such as WIMPs, which are not free fields, and typically also not scalars) and axions (which are scalars, but are not free); most of these are explicitly non-free because they also try to solve some problems in the Standard Model of Particle Physics via new interactions).

The phase between the end of inflation and before some of the dense matter (mostly the quark-gluon plasma, and ancestors thereof) condensed into nucleons and nuclei is far from the much hotter and much much denser phase in which quantum uncertainties and classical curvature do not obviously play well with one another. Barring very early black holes from direct collapse (perhaps seeded by overdensities in this massive proposed field), touched on in this paper only very briefly as "enhanced structure formation", the post-inflation/pre-BBN universe this paper describes is free from strong curvature requiring any sort of quantum gravity: one is safely in the land of quantum field theory on (classical) curved spacetime, and in practically any small spacetime region after the decay into the proposed massive free scalar, one can even ignore the (global) curvature.

The paper proposes constraints on the mass of the field and on its ancestor field(s) but otherwise does not contemplate the much earlier universe. The central feature of the paper is that it commits totally to minimal-coupling (i.e., the late time field is truly free, other than gravitation). The field contents generate and respond to curvature, and that's it.

The paper also features what appears to be one of the most confusing initial two sentences that science writers have latched onto in many many papers...

Finally, I think it is better to link the abs page than the PDF directly. Speaking only for myself, the abs page has puts significant and useful metadata front-and-centre and other metadata at the same reliable one-click distance from the PDF itself. Not all PDFs make it easy to go to the abs page in a click, and fewer still suggest that the PDF itself may have been superseded by a subsequent revision (or by publication somewhere in final form).

For this paper, the abs link is https://arxiv.org/abs/1905.01214