We propose a minimal framework to address successful quartic inflation, dark matter (DM) production in the early universe and non-vanishing tiny Majorana neutrino mass from a common gravitational origin point of view. In this setup, the quartic inflation is revived successfully via non-minimal coupling of inflaton to gravity while the production of DM takes place from purely gravitational effects through a misalignment mechanism. The generation of light Majorana neutrino mass is aided by explicit breaking of global lepton number symmetry through Planck suppressed operators involving non-zero vacuum expectation value (VEV) of the inflaton field. We present a detailed study of the DM yield in presence of non-minimal inflation, considering both the metric and the Palatini formalisms of gravity wherever appropriate. We reach at some interesting and different results in the DM sector compared to the earlier works in the similar direction with minimal inflationary background. Restricting to the light DM regime ($\mathcal{O}\left(1\right)$ keV- $\mathcal{O}\left(100\right)\mathrm{MeV}$) where classical production is expected to dominate over the quantum production, we numerically predict the DM mass by varying the DM quartic and non-minimal coupling, to be consistent with relic density requirements. We also obtain some non-trivial dependence of DM phenomenology on some of the relevant parameters of the inflation sector e.g. non minimal coupling and inflaton VEV. To explore the dependence on inflationary parameters further, we also estimate the DM relic using the same mechanism for two other inflationary models consistent with latest data and observe that one of these models predicts different range of DM mass up to hundreds of TeV.

我们提出了一个最小框架来解决成功的四次膨胀、早期宇宙中暗物质 (DM) 的产生以及从共同引力起源的角度来看不消失的微小马约拉纳中微子质量。在这种设置中，四次膨胀是通过膨胀与重力的非最小耦合成功恢复的，而 DM 的产生是通过错位机制从纯粹的重力效应中产生的。通过涉及暴胀子场的非零真空期望值 (VEV) 的普朗克抑制算子显式破坏全局轻子数对称性，有助于产生轻质马约拉纳中微子质量。我们在存在非最小通货膨胀的情况下详细研究了 DM 收益率，并在适当的情况下考虑了重力的度量和帕拉蒂尼形式。与早期类似方向的研究相比，我们在 DM 部门得出了一些有趣且不同的结果，通胀背景最小。仅限于轻度 DM 制度（$\mathcal{哦}\left(1\right)$ keV- $\mathcal{哦}\left(100\right)\mathrm{电动汽车}$) 在预计经典生产将主导量子生产的情况下，我们通过改变 DM 四次和非最小耦合来数值预测 DM 质量，以符合遗物密度要求。我们还获得了 DM 现象学对通货膨胀部门的一些相关参数的一些非平凡的依赖，例如非最小耦合和膨胀 VEV。为了进一步探索对暴胀参数的依赖性，我们还使用与最新数据一致的其他两个暴胀模型的相同机制估计了 DM 遗迹，并观察到这些模型中的一个预测了不同范围的 DM 质量，最高可达数百 TeV。