  A scalar field having the Coleman-Weinberg type effective potential arises in
various contexts of particle physics and serves as a useful framework for
discussing cosmic inflation. According to recent studies based on the Markov
chain Monte Carlo analysis, the coefficients of such an effective potential are
severely constrained by the cosmological data. We investigate the impact of
this observation on the physics beyond the Standard Model, focusing on an
inflationary model based on the $U(1)_X$-extended Standard Model as a
well-motivated example. We examine the parameter region that is not excluded by
the Large Hadron Collider (LHC) Run-2 at 139 fb${}^{-1}$ integrated luminosity,
and show that the model parameters can be further constrained by the
High-Luminosity LHC experiments in the near future. We also comment on the
possible reheating mechanism and the dark matter candidates of this scenario.
