In a recent letter we proposed a new nonthermal mechanism of dark matter production based on vacuum misalignment, where both the Higgs boson and a very light pseudoscalar η emerge from the dark sector. In this paper, we identify the parameter space in a composite scenario where the light pseudoscalar can be produced in the sun and explain the XENON1T excess in electron recoil data. The model's dark matter candidate has a mass around 50 TeV and out of range for direct detection. Testable predictions include gravitational waves at frequencies in the Hz range from a cosmological phase transition, an exotic decay Z→γ+inv with rates 4÷16×10-12 testable at a future Tera-Z collider, and an enhancement by 17÷40% of the branching ratio KL→π0+inv, not enough to explain the KOTO anomaly. All these predictions may be confirmed by future experiments.
Bibliografisk note6 pages, 2 figures