eV Hubble Scale Inflation with Radiative Plateau: Very light Inflaton,
  Reheating & Dark Matter in B-L Extensions
  We study radiative plateau-like inflation \& Z$_{BL}$-portal freeze-in
fermionic dark matter (DM) in minimal (B-L) extended model. The U(1)$_{B-L}$
Higgs, responsible for heavy neutrino masses, also drives inflation in early
universe, thanks to radiative corrections from the heavy neutrinos \& the
Z$_{BL}$ boson. The benchmark parameters (U(1)$_{B-L}$ gauge coupling
$g_{B-L}\sim10^{-4}$) makes it within the reach of current and future lifetime
frontier searches (FASER and FASER 2 at the LHC, SHiP, Belle II, LHCb, etc.) in
context to light Z$_{BL}$ candidates and freeze-in dark matter. For such
benchmark points, the Hubble scale of inflation ($H_{inf}$) is required to be
very low ($H_{inf} \sim \mathcal{O}(100)$ eV) \& the inflaton turns out to be
of very light mass ($\mathcal{O}(1)$ eV), and consequently the decay width of
inflaton is small. We investigate the \it{2-field-system} still find that
sufficient reheating occurs along the the Standard Model Higgs direction
component of the tangent along the trajectory in the field space, near the
water-fall of the potential. For our parameter choices, along with the chosen
DM mass $m_\chi\sim\mathcal{O}(10)$ GeV, we find the DM ($\chi$) is produced
via freeze-in.
