The Starobinsky inflation model is one of the simplest inflation models that is consistent with the cosmic microwave background observations. In order to explain dark matter of the universe, we consider a minimal extension of the Starobinsky inflation model with introducing the dark sector which communicates with the visible sector only via the gravitational interaction. In Starobinsky inflation model, a sizable amount of dark-sector particle may be produced by the inflaton decay. Thus, a scalar, a fermion or a vector boson in the dark sector may become dark matter. We pay particular attention to the case with dark non-Abelian gauge interaction to make a dark glueball a dark matter candidate. In the minimal setup, we show that it is difficult to explain the observed dark matter abundance without conflicting observational constraints on the coldness and the self-interaction of dark matter. We propose scenarios in which the dark glueball, as well as other dark-sector particles, from the inflaton decay become viable dark matter candidates. We also discuss possibilities to test such scenarios.
We study the stability of the electroweak vacuum during and after the Starobinky inflation, assuming the existence of the non-minimal Higgs coupling to the Ricci scalar. In the Starobinsky inflation, there exists R2 term (with R being the Ricci scalar), which modifies the evolution equation of the Higgs field. We consider the case that the non-minimal coupling is sizable so that the quantum fluctuation of the Higgs field is suppressed and that the Higgs amplitude is settled near the origin during the inflation. In such a case, the Higgs amplitude may be amplified in the preheating epoch after inflation because of the parametric resonance due to the non-minimal coupling. We perform a detailed analysis of the evolution of the Higgs field in the preheating epoch by a numerical lattice simulation and derive an upper bound on the non-minimal coupling constant ξ in order to realize the electroweak vacuum in the present universe. We find that the upper bound on ξ in the Starobinsky inflation model is more stringent than that in conventional inflation models without the R2 term.
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