Alleviating the cosmological constant problem from particle production

We explore a toy model mechanism of geometric cancellation, alleviating the (classical) cosmological constant problem. To do so, we assume at primordial times that vacuum energy fuels an inflationary quadratic hilltop potential nonminimally coupled to gravity through a standard Yukawa-like interacting term, whose background lies on a perturbed Friedmann-Robertson-Walker metric. We demonstrate how vacuum energy release transforms into geometric particles, adopting a quasi-de Sitter phase where we compute the expected particle density and mass ranges. Perturbations are introduced by means of the usual external-field appproximation, so that the back-reaction of the created particles on the geometry is not considered here. We discuss the limitations of this approach and we also suggest possible refinements. We then propose the most suitable dark matter candidates, showing under which circumstances we can interpret dark matter as constituted by geometric quasiparticles. We confront our predictions with quantum particle production and constraints made using a Higgs portal. In addition, the role of the bare cosmological constant is reinterpreted to speed up the universe today. Thus, consequences on the standard $\Lambda$CDM paradigm are critically highlighted, showing how both coincidence and fine-tuning issues can be healed requiring the Israel-Darmois matching conditions between our involved inhomogeneous and homogeneous phases.