Hunting for Inflaton at FASER

We consider the nonminimal quartic inflation driven by the U(1)_X Higgs field Φ in classically conformal U(1)_X extended Standard Model (SM). Since the conformal symmetry is broken radiatively, the U(1)_X gauge boson mass m_Z', the U(1)_X gauge coupling g_X, and the inflationary predictions for tensor-to-scaler ratio (r) are determined by only two free parameters, the inflaton mass m_Φ and its mixing angle (Θ) with the SM Higgs field. We show that the new FASER experiment at the High-Luminosity LHC (HL-LHC) can detect the inflaton in both cases if the mass is in the range 0.1 ≲ m_Φ [GeV] ≲ 4. By performing a comparative study of the metric and Palatini formulations of gravity we show that the complementarity between the searches for the primordial gravitational wave, collider searches for Z' at the LHC, and the inflaton search at FASER can distinguish between the two formulations.