Non-thermal leptogenesis and UV freeze-in of dark matter: impact of
  inflationary reheating
  We study a minimal scenario to realize non-thermal leptogenesis and UV
freeze-in of a Standard Model (SM) gauge singlet fermionic dark matter (DM)
simultaneously, with inflaton field playing a non-trivial role in their yields.
The renormalizable interactions are restricted to the SM fields, two right
handed neutrinos (RHN) and inflaton coupling exclusively to the RHNs, while the
DM couples to both the SM and the RHNs only via operators of dimension $d>4$.
Considering two separate cases of $d=\{5,6\}$, we show that for $d=5$, inflaton
decay into RHNs followed by their subsequent decay into SM particles lead to
both reheating as well as DM production from the SM bath. This requires a
cut-off scale as large as $\Lambda\sim 10^{17}~\rm GeV$ depending on the DM
mass. On the other hand, for $d=6$, DM production happens directly from
scattering of RHNs (for $\Lambda\gtrsim 10^{14}~\rm GeV$) that results in a
very non-trivial evolution of the DM yield. In both these cases, it is possible
to explain the observed baryon asymmetry through successful non-thermal
leptogenesis via the decay of the RHNs, together with the PLANCK observed relic
density of the DM via pure UV freeze-in mechanism. Taking into account both
instantaneous as well as non-instantaneous reheating separately, we constrain
the parameter space of this minimal scenario from relevant phenomenological
requirements including sub-eV scale active neutrino masses and their mixing.
