Inflation in the Scale Symmetric Standard Model and Weyl geometry

Abstract

This work explores the possibility of inflation in a scale-symmetric extension of the Standard Model Higgs sector, where the Higgs field $φ_1$ is coupled to a singlet scalar, the dilaton $φ_0$. 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, $ξ_1\llξ_0$, the unitarity cutoff in the large-field background, $Λ_{UV}\sim M_P/\sqrt{ξ_1}$, lies below the energy scales relevant during inflation.

Figures (21)

• Figure 1: Plots of $\delta$ for different values of $\xi_i$ and $\tau$, where $\xi_1=p\cdot\xi_0$. The exclusion of certain regions in the $\xi_i$ parameter space follows from subsequent argumentation, as illustrated in Figure \ref{['Vmax_fulfilled']}. The right plot is evaluated for $p=10^{14.4}$.
• Figure 2: Plots of the potential $V(\tau)$ from equation (\ref{['Vtau_infl']}) for $\xi_0=10^{15}$ and $\xi_1=10^{10}$. For small $\tau$, two degenerate non-zero minima are visible, while for large $\tau$, the potential becomes nearly flat, allowing for the possibility of slow-roll inflation.
• Figure 3: (a): Region plot of the parameter space for which $V_{\infty}\leq V_*$. The constraint can be approximated by the inequality $\log_{10}p\geq -\log_{10}\xi_0+4.4$. (b): Plot illustrating the constraint $\eta_V(\infty) > -0.0095-0.0030$, resulting from (\ref{['etainf_definition']}), limiting $\xi_0$ to $\log_{10}\xi_0 \lesssim -1.727$.
• Figure 4: Plots of the parameter space satisfying the slow-roll conditions from Table \ref{['tab:inflation_params']}. The minimum $p$ values correspond to the boundary values determined by inequality (\ref{['p_x0_inequality']}).
• Figure 5: Left: Parameter space points used to generate the corresponding $r_{0.002}(n_s)$ plot on the right. The dark gray dotted line marks the constraint $\log_{10}p=-\log_{10}\xi_0+4.4$. Right: Tensor-to-scalar ratio $r_{0.002}$ as a function of the scalar spectral index $n_s$ in the model with the inflaton field $\tau$. The black dashed line corresponds to the experimental value, $n_s=0.974$, and the gray dashed line to $n_s=0.974+0.003$. Variations in $\xi_0$ and $p$ lead to small differences in $n_s$, as illustrated in Figure \ref{['ns_r_contours']}.