Gravitational origin of dark matter and Majorana neutrino mass with
  non-minimal quartic inflation
  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 ($\mathcal{O}(1)$ keV- $\mathcal{O}(100)$
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 {\it 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 upto hundreds of TeV.
