Higgs-dilaton model revisited: Can a dilaton act as a QCD axion?

The Standard Model Lagrangian has an approximate scale symmetry in the high-energy limit. This observation can be embedded into the fundamental principle of the ultimate theory of nature as the requirement of the exact quantum scale invariance. In this setup, all low-energy particle phenomenology can be obtained as a result of the spontaneous breaking of scale symmetry leading to the presence of the extra massless scalar field-the dilaton. We explore the scenario, in which this field is also capable of solving the strong CP problem in QCD in a similar way as in QCD axion models. The dilaton, playing the role of the axion, is coupled to the QCD sector and acquires a mass term due to nonperturbative breaking of scale symmetry. We show that the dilaton can form dark matter after the low-scale inflation. As a proof of concept, we construct a model of Higgs-driven inflation consistently realizing the axionlike dilaton dark matter production compatible with the cosmic microwave background (CMB) data.