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arxiv: 2506.21189 · v3 · submitted 2025-06-26 · ✦ hep-ph · gr-qc

Higgs pole inflation with loop corrections in light of ACT results

Jeonghak Han , Hyun Min Lee , Jun-Ho Song This is my paper

Pith reviewed 2026-05-19 07:52 UTC · model grok-4.3

classification ✦ hep-ph gr-qc
keywords pole inflationHiggs inflationColeman-Weinberg potentialloop correctionsspectral indextensor-to-scalar ratioACT resultsbeta function
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The pith

Loop corrections in pole inflation can increase the spectral index to align with ACT results while compatible with tensor-to-scalar ratio bounds.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper investigates the impact of quantum loop corrections on the effective potential in pole inflation scenarios, focusing on the Higgs and Peccei-Quinn models. These corrections arise from the Coleman-Weinberg mechanism and introduce inflaton-dependent modifications to the quartic coupling of the inflaton field. By incorporating one-loop and two-loop contributions to the beta function of this coupling, the predicted spectral index of density perturbations can be increased. This adjustment aligns the model predictions more closely with the results from the Atacama Cosmology Telescope while respecting the upper limits on the tensor-to-scalar ratio. The analysis covers cases where the one-loop beta function is positive or negative, requiring different levels of two-loop support.

Core claim

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 be

What carries the argument

The Coleman-Weinberg loop corrections that generate inflaton-dependent power corrections to the quartic coupling of the inflaton during inflation.

If this is right

  • The spectral index can be shifted higher to values preferred by ACT data.
  • The tensor-to-scalar ratio remains compatible with existing upper bounds.
  • When the one-loop beta function b1 is positive, sub-dominant two-loop terms suffice for the adjustment.
  • When b1 is negative, two-loop contributions must exceed the one-loop terms to reach the desired spectral index.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If ACT results hold under further scrutiny, these loop effects could keep pole inflation viable against tightening constraints from other probes.
  • Varying the number or couplings of extra singlet scalars offers a way to tune the size of the corrections for different observational targets.
  • The same inflaton-dependent correction structure might be tested in related models such as Starobinsky inflation or other non-minimal couplings.

Load-bearing premise

The inflaton-dependent power corrections from loops can be reliably computed with appropriate choices for the sign and magnitude of the one-loop beta function and two-loop terms to achieve the required spectral index shift.

What would settle it

A future precise measurement of the scalar spectral index falling outside the adjustable range from varying one- and two-loop beta function contributions while the tensor-to-scalar ratio stays below current bounds would falsify the proposed shift mechanism.

Figures

Figures reproduced from arXiv: 2506.21189 by Hyun Min Lee, Jeonghak Han, Jun-Ho Song.

Figure 1
Figure 1. Figure 1: Parameter space for b1/λH∗ vs b2/λH∗ being consistent with Planck+ACT+LB data [3]. The range of the spectral index within 1σ and 2σ 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. 10-4 10-3 10-2 10-1 1 10-4 10-3 10-2 10-1 -b1/λH b2/λH N=50 10-4 10-3 10-2 10-1 1 10-4 10… view at source ↗
Figure 2
Figure 2. Figure 2: The same as in Fig. 3, except that [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The spectral index vs the tensor-to-scalar ratio. The range of the spectral index allowed [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript computes the Coleman-Weinberg effective potential for the inflaton in pole-inflation scenarios (Higgs pole inflation and Peccei-Quinn pole inflation). Loop corrections from SM particles and extra singlets generate inflaton-dependent power corrections to the quartic coupling. The authors show that these corrections raise the spectral index ns to values preferred by ACT data while remaining compatible with the upper bound on the tensor-to-scalar ratio r. Separate cases are treated for positive and negative one-loop beta-function coefficient b1; for b1<0 sizable two-loop terms larger than the one-loop piece are required.

Significance. If the perturbative expansion remains under control, the explicit derivation of inflaton-dependent power corrections supplies a concrete mechanism to reconcile pole inflation with the latest ACT constraints on ns without additional free parameters. The compatibility with r bounds and the distinction between KSVZ/DFSZ realizations for the PQ case are useful. The paper supplies machine-readable expressions for the beta functions and the resulting ns(r) trajectories, which strengthens its utility for model comparison.

major comments (1)
  1. [§4.2] §4.2 (discussion of the b1<0 regime): the requirement that two-loop contributions exceed the one-loop term in magnitude to produce the ACT-favored ns shift violates the ordering assumed in the Coleman-Weinberg truncation. Because the effective potential is expanded to two loops, a hierarchy in which the two-loop piece dominates the one-loop piece for the relevant field values during inflation renders the quoted ns shift unreliable; this directly undermines the central claim for the negative-b1 branch.
minor comments (2)
  1. [abstract and §3] The abstract and §3 should state the precise range of b1 and the matching procedure from inflationary to post-inflationary scales; currently these steps are only sketched.
  2. [Eq. (12)] Eq. (12) for the two-loop correction: the numerical prefactor multiplying the b2 term should be written explicitly rather than absorbed into a generic coefficient.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their thorough review and insightful comments on our work. We address the major comment below and will revise the manuscript to strengthen the discussion of perturbative control.

read point-by-point responses

  1. Referee: [§4.2] §4.2 (discussion of the b1<0 regime): the requirement that two-loop contributions exceed the one-loop term in magnitude to produce the ACT-favored ns shift violates the ordering assumed in the Coleman-Weinberg truncation. Because the effective potential is expanded to two loops, a hierarchy in which the two-loop piece dominates the one-loop piece for the relevant field values during inflation renders the quoted ns shift unreliable; this directly undermines the central claim for the negative-b1 branch.

    Authors: We acknowledge the referee's concern that in the b1<0 regime, achieving the ACT-preferred spectral index requires the two-loop contributions to be larger than the one-loop ones, which challenges the perturbative ordering in the two-loop truncation of the effective potential. This is a valid point regarding the reliability of the approximation in that specific case. In response, we will revise the discussion in §4.2 to include an explicit analysis of the relative magnitude of the loop terms during inflation. We will add text clarifying that while the full two-loop potential is used, for b1<0 the results should be interpreted with caution and may indicate the need for resummation or higher-loop contributions. For the b1>0 case, the sub-dominant two-loop terms remain consistent with the expansion. These changes will be incorporated in the revised version to address the validity of the ns shift in the negative-b1 branch. revision: yes

Circularity Check

0 steps flagged

No significant circularity; spectral index shift follows from explicit Coleman-Weinberg loop corrections applied to pole inflation potential.

full rationale

The paper derives the modified inflaton potential by adding standard one- and two-loop Coleman-Weinberg corrections (parameterized by the beta-function coefficient b1 and higher terms) to the tree-level quartic term in Higgs or PQ pole inflation. The shift in ns is then obtained by recomputing the slow-roll parameters on this corrected potential, which is a direct calculation rather than a redefinition or fit. No step equates the output ns shift to the input loop coefficients by construction, and no load-bearing claim rests on a self-citation chain or imported uniqueness theorem. The discussion of b1 sign and relative two-loop size is an exploration of parameter regimes needed to match ACT data, not a forced prediction. The derivation remains self-contained against external benchmarks such as the standard Coleman-Weinberg formula and slow-roll formulas.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The analysis rests on the standard Coleman-Weinberg effective potential in quantum field theory, the assumption that extra singlet scalars can be added without altering the pole structure, and the validity of the slow-roll approximation during inflation. No new free parameters beyond the usual couplings and the sign of b1 are introduced in the abstract.

free parameters (1)
  • b1 (one-loop beta function for inflaton quartic)
    Its sign determines whether two-loop terms must dominate; value is not numerically fitted but chosen to satisfy ACT data.
axioms (2)
  • standard math Coleman-Weinberg potential provides the leading quantum correction to the tree-level quartic potential for the inflaton.
    Invoked in the opening sentence of the abstract as the starting point for loop corrections.
  • domain assumption Slow-roll inflation remains valid when the effective quartic coupling receives inflaton-dependent power corrections.
    Required for the spectral index and tensor-to-scalar ratio formulas to apply.

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Forward citations

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Reference graph

Works this paper leans on

21 extracted references · 21 canonical work pages · cited by 5 Pith papers · 7 internal anchors

  1. [1]

    Kallosh and A

    R. Kallosh and A. Linde, [arXiv:2505.13646 [hep-th]]

    work page arXiv

  2. [2]

    Planck 2018 results. X. Constraints on inflation

    Y. Akrami et al. [Planck], Astron. Astrophys. 641 (2020), A10 doi:10.1051/0004- 6361/201833887 [arXiv:1807.06211 [astro-ph.CO]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004- 2020

  3. [3]

    The Atacama Cosmology Telescope: DR6 Power Spectra, Likelihoods and $\Lambda$CDM Parameters

    T. Louis et al. [ACT], [arXiv:2503.14452 [astro-ph.CO]]

    work page internal anchor Pith review Pith/arXiv arXiv

  4. [4]

    F. L. Bezrukov and M. Shaposhnikov, Phys. Lett. B 659 (2008), 703-706 doi:10.1016/j.physletb.2007.11.072 [arXiv:0710.3755 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.physletb.2007.11.072 2008

  5. [5]

    A. A. Starobinsky, Phys. Lett. B 91 (1980), 99-102 doi:10.1016/0370-2693(80)90670-X

    work page doi:10.1016/0370-2693(80)90670-x 1980

  6. [6]

    P. A. R. Ade et al. [BICEP and Keck], Phys. Rev. Lett. 127 (2021) no.15, 151301 doi:10.1103/PhysRevLett.127.151301 [arXiv:2110.00483 [astro-ph.CO]]

    work page doi:10.1103/physrevlett.127.151301 2021

  7. [7]

    I. D. Gialamas, A. Karam, A. Racioppi and M. Raidal, [arXiv:2504.06002 [astro- ph.CO]]; W. J. Wolf, [arXiv:2506.12436 [astro-ph.CO]]; W. Ahmed and M. U. Rehman, [arXiv:2506.18077 [astro-ph.CO]]

    work page arXiv

  8. [8]

    Antoniadis, J

    I. Antoniadis, J. Ellis, W. Ke, D. V. Nanopoulos and K. A. Olive, [arXiv:2504.12283 [hep-ph]]; D. S. Zharov, O. O. Sobol and S. I. Vilchinskii, [arXiv:2505.01129 [astro- ph.CO]]

    work page arXiv

  9. [9]

    Kallosh, A

    R. Kallosh, A. Linde and D. Roest, [arXiv:2503.21030 [hep-th]]; A. Salvio, [arXiv:2504.10488 [hep-ph]]; M. He, M. Hong and K. Mukaida, [arXiv:2504.16069 [astro-ph.CO]]; S. Aoki, H. Otsuka and R. Yanagita, [arXiv:2504.01622 [hep-ph]]; J. McDonald, [arXiv:2506.12916 [hep-ph]]; S. Choudhury, B. Gulnur, S. K. Singh and K. Yerzanov, [arXiv:2506.15407 [astro-ph...

    work page arXiv

  10. [10]

    Superconformal Inflationary $\alpha$-Attractors

    R. Kallosh, A. Linde and D. Roest, JHEP 11 (2013), 198 doi:10.1007/JHEP11(2013)198 [arXiv:1311.0472 [hep-th]]; M. Galante, R. Kallosh, A. Linde and D. Roest, Phys. Rev. Lett. 114 (2015) no.14, 141302 doi:10.1103/PhysRevLett.114.141302 [arXiv:1412.3797 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/jhep11(2013)198 2013

  11. [11]

    H. M. Lee and A. G. Menkara, JHEP 09 (2021), 018 doi:10.1007/JHEP09(2021)018 [arXiv:2104.10390 [hep-ph]]

    work page doi:10.1007/jhep09(2021)018 2021

  12. [12]

    S. Aoki, H. M. Lee, A. G. Menkara and K. Yamashita, JHEP 05 (2022), 121 doi:10.1007/JHEP05(2022)121 [arXiv:2202.13063 [hep-ph]]

    work page doi:10.1007/jhep05(2022)121 2022

  13. [13]

    Cl´ ery, H

    S. Cl´ ery, H. M. Lee and A. G. Menkara, JHEP 10 (2023), 144 doi:10.1007/JHEP10(2023)144 [arXiv:2306.07767 [hep-ph]]

    work page doi:10.1007/jhep10(2023)144 2023

  14. [14]

    H. M. Lee, A. G. Menkara, M. J. Seong and J. H. Song, JHEP 05 (2024), 295 doi:10.1007/JHEP05(2024)295 [arXiv:2310.17710 [hep-ph]]

    work page doi:10.1007/jhep05(2024)295 2024

  15. [15]

    H. M. Lee, A. G. Menkara, M. J. Seong and J. H. Song, Eur. Phys. J. C 84 (2024) no.12, 1260 doi:10.1140/epjc/s10052-024-13648-y [arXiv:2408.17013 [hep-ph]]

    work page doi:10.1140/epjc/s10052-024-13648-y 2024

  16. [16]

    H. M. Lee, Phys. Rev. Lett. 134 (2025) no.21, 211001 doi:10.1103/skhx-yc43 [arXiv:2411.16944 [hep-ph]]

    work page doi:10.1103/skhx-yc43 2025

  17. [17]

    D. M. Ghilencea and H. M. Lee, Phys. Rev. D 99 (2019) no.11, 115007 doi:10.1103/PhysRevD.99.115007 [arXiv:1809.09174 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.99.115007 2019

  18. [18]

    H. M. Lee, Phys. Lett. B 722 (2013), 198-206 doi:10.1016/j.physletb.2013.04.024 [arXiv:1301.1787 [hep-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.physletb.2013.04.024 2013

  19. [19]

    Stabilization of the Electroweak Vacuum by a Scalar Threshold Effect

    J. Elias-Miro, J. R. Espinosa, G. F. Giudice, H. M. Lee and A. Strumia, JHEP 06 (2012), 031 doi:10.1007/JHEP06(2012)031 [arXiv:1203.0237 [hep-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/jhep06(2012)031 2012

  20. [20]

    J. E. Kim, Phys. Rev. Lett. 43 (1979) 103. doi:10.1103/PhysRevLett.43.103 M. A. Shif- man, A. I. Vainshtein and V. I. Zakharov, Nucl. Phys. B 166 (1980) 493. doi:10.1016/0550-3213(80)90209-6

    work page doi:10.1103/physrevlett.43.103 1979

  21. [21]

    M. Dine, W. Fischler and M. Srednicki, Phys. Lett.104B (1981) 199. doi:10.1016/0370- 2693(81)90590-6; A. P. Zhitnitskii, Sov. J. Nucl. Phys. 31, 260 (1980). 17

    work page doi:10.1016/0370- 1981