  We investigate for viable models of inflation that can successfully produce
dark matter (DM) from inflaton decay process, satisfying all the constraints
from Cosmic Microwave Background (CMB) and from some other observations. In
particular, we analyze near-inflection-point small field inflationary scenario
with non-thermal production of fermionic DM from the decaying inflaton field
during the reheating era. To this end, we propose two different models of
inflation with polynomial potential. The potential of Model I contains terms
proportional to linear, quadratic, and quartic in inflaton; whereas in Model
II, the potential contains only even power of inflaton and the highest term is
sextic in inflaton. For both the models, we find out possible constraints on
the model parameters which lead to proper inflationary parameters from CMB data
with a very small tensor-to-scalar ratio, as expected from a small-field model.
With the allowed parameter space from CMB, we then search for satisfactory
relic abundance for DM, that can be produced from inflaton via reheating, to
match with the present-day cold dark matter (CDM) relic density for the
parameter spaces of the DM $\chi$ mass and Yukawa couplings in the range
$10^{-9} \gtrsim y_{\chi} \gtrsim 10^{-15}$ and $10^3 \text{GeV} \lesssim
m_{\chi} \lesssim 10^9 \text{GeV}$. The DM relic is associated with the
inflection-points in each model via maximum temperature reached in the early
universe during its production. Finally, we find out allowed parameter space
coming out of combined constraints from stability analysis for both SM Higgs
and DM decays from inflaton as well as from BBN and Lyman-$\alpha$ bounds.

High Energy Physics - Phenomenology;Cosmology and Nongalactic Astrophysics