Hunting Inflaton at FASER

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 ($\varphi$). 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 ($m_{Z^{\mathrm{\prime }}}$), are all determined by only two free parameters, the inflaton mass ($m_{\varphi }$) 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 $m_{Z^{\mathrm{\prime }}}$, the $Z^{\mathrm{\prime }}$ 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.