  We propose quartic inflation with non-minimal gravitational coupling in the
context of the classically conformal U(1)_X extension of the SM. In this model,
the U(1)_X gauge symmetry is radiatively broken through the Coleman-Weinberg
(CW) mechanism, by which the U(1)_X gauge boson (Z' boson) and the right-handed
neutrinos (RHNs) acquire their masses. We consider their masses in the range of
O(10 GeV)-O(10 TeV), which are accessible to high energy collider experiments.
The radiative U(1)_X gauge symmetry breaking also generates a negative mass
squared for the SM Higgs doublet, and the electroweak symmetry breaking occurs
subsequently. We identify the U(1)_X Higgs field with inflaton and calculate
the inflationary predictions. Due to the CW mechanism, the inflaton quartic
coupling during inflation, which determines the inflationary predictions, is
correlated to the U(1)_X gauge coupling. With this correlation, we investigate
complementarities between the inflationary predictions and the current
constraint from the Z' boson resonance search at the LHC Run-2 as well as the
prospect of the search for the Z' boson and the RHNs at the future collider
experiments. The radiative U(1)_X gauge symmetry breaking also generates a
negative mass squared for the SM Higgs doublet, and the electroweak symmetry
breaking occurs subsequently. We identify the U(1)_X Higgs field with inflaton
and calculate the inflationary predictions. Due to the Coleman-Weinberg
mechanism, the inflaton quartic coupling during inflation, which determines the
inflationary predictions, is correlated to the U(1)_X gauge coupling. With this
correlation, we investigate complementarities between the inflationary
predictions and the current constraint from the Z' boson resonance search at
the LHC Run-2 as well as the prospect of the search for the Z' boson and the
RHNs at the future collider experiments.
