### Abstract:

We consider a nonminimal quartic inflation scenario in the minimal \({U\left(1\right)}_{X}\) extension of the Standard Model (SM) with the classical conformal invariance, where the inflaton is identified with the \({U\left(1\right)}_{X}\) Higgs field (\(\varphi \)). By virtue of the classically conformal invariance and the radiative \({U\left(1\right)}_{X}\) symmetry breaking via the Coleman-Weinberg mechanism, the inflationary predictions (in particular, the tensor-to-scaler ratio \(r\)), the \({U\left(1\right)}_{X}\) coupling \({g}_{X}\), and the \({U\left(1\right)}_{X}\) gauge boson mass \({m}_{{Z}^{\prime }}\) are all determined by only two free parameters: the inflaton mass \({m}_{\varphi }\) and its mixing angle \(\theta \) with the SM Higgs field. FASER can search for a long-lived scalar, which is the inflaton in our scenario, for the parameter ranges \(0.1\lesssim {m}_{\varphi }\left[\mathrm{GeV}\right]\lesssim 4\) and \({10}^{-5}\lesssim \theta \lesssim {10}^{-3}\). Therefore, if such a scalar is discovered at FASER, both \({m}_{\varphi }\) and \(\theta \) would be fixed, leading to the predictions for \(r\), \({g}_{X}\), and \({m}_{{Z}^{\prime }}\) in our model. These predictions can be tested by future cosmological observations and LHC searches for the \({Z}^{\prime }\) boson resonance.