Higgs pole inflation with loop corrections in light of ACT results

TL;DR

This work investigates Higgs and PQ pole inflation with loop-induced Coleman-Weinberg corrections, treating the loop effects as a running inflaton quartic coupling up to two loops. The authors derive RG-improved inflaton potentials for both Higgs- and PQ-driven pole inflation, incorporating spectator-field contributions (e.g., SM gauge bosons, top quark, singlets, KSVZ/DFSZ content) and clarifying how the beta-function coefficients b_1 and b_2 shape inflationary observables. They show that positive one-loop beta-function (b_1>0) can raise the spectral index n_s toward ACT’s preferred values while keeping r within observational bounds, whereas negative b_1 may require sizable two-loop corrections to achieve the same. Overall, the study provides a model-dependent but framework-wide approach to reconcile pole-inflation predictions with ACT data, linking inflationary signals to the high-scale particle content and their couplings through the running of the inflaton quartic coupling $\lambda_H(h)$ or $\lambda_\Phi(\rho)$.

Abstract

We present the Coleman-Weinberg potential for the inflaton in the pole inflation scenarios such as the Higgs pole inflation and the Peccei-Quinn (PQ) pole inflation. The loop corrections stem from the Standard Model particles and extra singlet scalar fields in the former case, making the quartic coupling for the Higgs inflaton modified by the inflaton-dependent power corrections during inflation. We also obtain similar power corrections to the quartic coupling for the PQ inflaton, depending on the realizations of the PQ symmetry in KSVZ and DFSZ models. We show that the loop corrections can shift the spectral index in the pole inflation to a larger value in favor of the ACT results, while being compatible with the bound on the tensor-to-scalar ratio. For a positive one-loop beta function for the inflaton quartic coupling (namely, $b_1>0$), a sub-dominant contribution from the two-loop corrections can be accommodated. On the other hand, if the one-loop beta function for the inflaton coupling is negative (namely, $b_1<0$), we need sizable contributions from two-loops that are larger than the one-loop corrections due to the ACT results.

Figures (5)

• Figure 1: (Left) The full two-loop running Higgs quartic coupling $\lambda_H$ for the SM in black dashed line and for the SM plus the singlet scalar in blue solid line. (Right) The running Higgs $\lambda_H$ and its beta function in blue and black lines, respectively. The beta function remains negative all the way to $\mu\sim M_P$.
• Figure 2: The same as in Fig. \ref{['fig:RG1']}, except for relatively larger couplings for the singlet scalar. The beta function becomes a positive value near $\mu\sim M_P$.
• Figure 3: Parameter space for $b_1/\lambda_{H_*}$ vs $b_2/\lambda_{H_*}$ being consistent with Planck$+$ACT$+$LB data ACT. The range of the spectral index within $1\sigma$ and $2\sigma$ errors are shown in yellow and green. We took $N=50$ on left and $N=60$ on right. The gray region is not consistent with perturbativity and the purple region shows the two-loop dominance.
• Figure 4: The same as in Fig. \ref{['fig:ns']}, except that $b_1$ takes negative values.
• Figure 5: The spectral index vs the tensor-to-scalar ratio. The range of the spectral index allowed by Planck$+$ACT$+$LB data ACT are shown in yellow and green colors within $1\sigma$ and $2\sigma$ errors, respectively. We chose $b_1/\lambda_{H_*}=0.02(-0.01)$ and $b_2/\lambda_{H_*}=0.001(0.005)$ on left and right, respectively.