We discuss the gravitational creation of superheavy particles $\chi$ in an inflationary scenario with a quartic potential and a non-minimal coupling between the inflaton $\varphi$ and the Ricci curvature: $\xi \varphi^2 R/2$. We show that for large constants $\xi >> 1$, there can be abundant production of particles $\chi$ with masses largely exceeding the inflationary Hubble rate $H_{infl}$, up to $(a~few) \times \xi H_{infl}$, even if they are conformally coupled to gravity. We discuss two scenarios involving these gravitationally produced particles $\chi$. In the first scenario, the inflaton has only gravitational interactions with the matter sector and the particles $\chi$ reheat the Universe. In this picture, the inflaton decays only due to the cosmic expansion, and effectively contributes to dark radiation, which can be of the observable size. The existing limits on dark radiation lead to an upper bound on the reheating temperature. In the second scenario, the particles $\chi$ constitute Dark Matter, if substantially stable. In this case, their typical masses should be in the ballpark of the Grand Unification scale.

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非最小耦合膨胀后的引力再加热和超重暗物质的产生

我们讨论了在具有四次势和暴胀子 $\varphi$ 和 Ricci 曲率之间的非最小耦合的暴胀情景中超重粒子 $\chi$ 的引力产生：$\xi \varphi^2 R/2$。我们表明，对于大常数 $\xi >> 1$，可以大量产生粒子 $\chi$，其质量大大超过了哈勃膨胀率 $H_{infl}$，最多 $(a~few) \times \xi H_{infl}$，即使它们与重力共形耦合。我们讨论了涉及这些引力产生的粒子 $\chi$ 的两种情况。在第一种情况下，暴胀子只与物质部门发生引力相互作用，粒子 $\chi$ 重新加热了宇宙。在这张图片中，暴胀子仅因宇宙膨胀而衰减，并有效地促成暗辐射，这可以是可观察的大小。暗辐射的现有限制导致了再加热温度的上限。在第二种情况下，粒子 $\chi$ 构成暗物质，如果基本稳定。在这种情况下，他们的典型群众应该在大统一规模的范围内。