Insights into the highest natural scale: Finite naturalness challenges inflationary dynamics

Abstract

We apply the criterion of finite naturalness to the limiting case of a generic heavy sector decoupled from the Standard Model. The sole and unavoidable exception to this decoupling arises from gravitational interactions. We demonstrate that gravity can couple the Higgs to the heavy scale significantly earlier than the well-known three-loop top-quark-mediated diagrams discussed in previous literature. As an application, we show that finite naturalness disfavors large-field inflationary models involving super-Planckian field excursions. In contrast, in the small-field regime, achieving successful inflation requires substantial fine-tuning of the initial conditions, in agreement with previous results. Recent data from the Atacama Cosmology Telescope further amplify the tension between naturalness and fine-tuning, challenging the theoretical robustness of single-field inflation as a compelling explanation for the origin of the universe.

Figures (8)

• Figure 1: Finite naturalness limits for new physics scenarios. Thick blue lines show heavy states with mass ${M}$ coupled to Standard Model particles (thin black lines in loops).
• Figure 2: Prediction in the $(n_s,r)$ plane for the model given in Eq. \ref{['eq:quasi_inflection_point']}. We fix two characteristic values $\beta = 0, 10^{-2}$ while varying the parameter $x_0$. We keep track of the latter in the color bar, treating it as the mass of the inflaton $m_{\phi}$. We require $N=55$$e$-folds of inflation after CMB modes exited the horizon. Experimental constraints are shown using the Planck 2018 baseline analysis (green regions) and including BICEP/Keck and baryon acoustic oscillation (BAO) data (blue regions), cf. Ref. BICEP:2021xfz. We also show (purple regions) the recent results from the Atacama Cosmology Telescope (ACT), cf. Ref. ACT:2025tim. We show the 65% and 95% confidence contours. When the inflection point is exact ($\beta = 0$) the model is in tension with BK18+BAO and ACT data.
• Figure 3: Phase-space portrait of the classical inflationary dynamics for $x_0 = 15$ ($\beta = 0$). The slow-roll trajectory associated to observable inflation is indicated in solid bold black. The trajectories marked in red are disconnected from the rest of the phase space.
• Figure 4: Phase-space portrait of the classical inflationary dynamics for $x_0 = 6$ and $\beta = 10^{-3}$. Varying $\beta$ does not qualitatively change the behaviors of the dynamics. The point along the slow-roll trajectory that marks the transition between the continuous and dashed part corresponds to $x_*$, i.e. the field value at which the CMB modes exited the horizon during inflation.
• Figure 5: Phase-space portrait of the classical inflationary dynamics for $x_0 = 1$ and $\beta = 1.85 \times 10^{-6}$. Varying $\beta$ does not qualitatively change the behaviors of the dynamics. There are two distinct trajectories that contains a phase of slow-roll inflation, marked in blue and in orange. The red point along the blue trajectory corresponds to $x_* \approx 0.9992$, i.e. the field value at which the CMB modes exited the horizon during inflation. The resulting observables are $n_s = 0.965$ and $r = 2 \times 10^{-8}$.