Inflation in the Scale Symmetric Standard Model and Weyl geometry

This work explores the possibility of inflation in a scale-symmetric extension of the Standard Model Higgs sector, where the Higgs field $\phi_1$ is coupled to a singlet scalar, the dilaton $\phi_0$. The two-scalar theory is formulated within Weyl geometry, which modifies the Einstein frame form of the resulting single-field inflationary potential. We extend the analysis to include quantum corrections, incorporating curvature effects in the one-loop effective potential. We find that the resulting spectral index $n_s$ and tensor-to-scalar ratio $r_{0.002}$ can be consistent with the Planck 2018 observational constraints. The predicted value $r_{0.002} \lesssim 10^{-6}$ remains too small to yield a detectable gravitational wave signal. In the regime with a strong hierarchy between the non-minimal couplings, $\xi_1\ll\xi_0$, the unitarity cutoff in the large-field background, $\Lambda_{UV}\sim M_P/\sqrt{\xi_1}$, lies below the energy scales relevant during inflation.