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We revisit a cosmological scenario based on the classically conformal$U(1)_{B-L}$-extension of the Standard Model. Our focus is on the mechanism ofreheating after inflation and the constraints on the model parameters. In thisscenario, the inflationary dynamics is driven by the $U(1)_{B-L}$ Higgs fieldthat is nonminimally coupled to gravity and breaks the $U(1)_{B-L}$ symmetryspontaneously as it acquires a vacuum expectation value through theColeman-Weinberg mechanism. It is found that the reheating process proceedsstepwise, and as the decay channels of the $U(1)_{B-L}$ Higgs field are known,the reheating temperature is evaluated. The relation between the e-foldingnumber of inflation and the reheating temperature provides a strong consistencycondition on the model parameters, and we find that the recent cosmologicaldata gives an upper bound on the $U(1)_{B-L}$ breaking scale $v_{BL}\lesssim10^{12}$ GeV. The lower bound is $v_{BL}\gtrsim 10^6$ GeV, obtained as thecondition for successful reheating in this model. The prediction for the cosmicmicrowave background (CMB) spectrum of this model fits extremely well withtoday's cosmological data. The model can be tested and is falsifiable by nearfuture CMB observations, including the LiteBIRD and CMB-S4.

Reheating consistency condition on the classically conformal $U(1)_{B-L}$ Higgs inflation model