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 ($ϕ$). 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 ($m_ϕ$) and its mixing angle ($θ$) with the SM Higgs field. The FASER can search for the inflaton for the parameter ranges of $0.1 \lesssim m_ϕ[{\rm GeV}] \lesssim 4$ and $10^{-5} \lesssim θ\lesssim 10^{-3}$. 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.

8 pages, 4 figures, (updated) version to be published in PRD