  We explore a possibility that an inflaton, which drives the cosmological
inflation in the early Universe, can be detected by the recently approved FASER
at the High-Luminosity LHC (HL-LHC). We consider nonminimal quartic inflation
scenario in the minimal U(1)$_X$ extension of the Standard Model (SM) with the
classical conformal invariance, where the inflaton is identified with the
U(1)$_X$ Higgs field ($\phi$). By virtue of the classical conformal invariance
and the radiative U(1)$_X$ symmetry breaking via the Coleman-Weinberg
mechanism, the inflationary predictions (in particular, the tensor-to-scaler
ratio ($r$)), the U(1)$_X$ coupling ($g_X$) and the U(1)$_X$ gauge boson mass
($m_{Z^\prime}$), are all determined by only two free parameters, the inflaton
mass ($m_\phi$) and its mixing angle ($\theta$) with the SM Higgs field. The
FASER can search for the inflaton for the parameter ranges of $0.1 \lesssim
m_\phi[{\rm GeV}] \lesssim 4$ and $10^{-5} \lesssim \theta \lesssim 10^{-3}$.
Because of the direct connection among $r$, $g_X$ and $m_{Z^\prime}$, the
$Z^\prime$ boson resonance search at the HL-LHC and the future measurement of
the primordial gravitational wave are complementary to the inflaton search at
the FASER.
