Constraining Inflation via FIMP dark matter using the $\beta$-function with collider implications

Ananya Tapadar; Sarif Khan; Sourov Roy

REVIEW 3 major objections 4 minor 53 references

Constraining Inflation via FIMP dark matter using the $\beta$-function with collider implications

T0 review · 3 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Inflation and freeze-in dark matter together force the Standard Model Higgs quartic coupling into the narrow window 0.18–0.25, with collider-visible consequences.

desk verdict The inflation-DM connection is plausible and worth a referee, but the headline λ_H∈[0.18,0.25] window is a scan artifact of the ξ_H cap, not a physical prediction. read the letter →

arxiv 2506.23770 v1 pith:BNWHB3HD submitted 2025-06-30 hep-ph

Sarif Khan , Sourov Roy , Ananya Tapadar This is my paper

classification hep-ph

keywords Higgsinflationfreeze-indarkmatterFIMPU(1)_DgaugesymmetryrenormalisationgrouprunningPlanckconstraintsself-couplingsvector

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper tries to show that inflation and feebly interacting dark matter (FIMP) can be treated as one connected system even though the observables sit at vastly different energy scales, with the connection made by running the couplings from the top-quark mass to the Planck scale. The model extends the Standard Model by a dark U(1) gauge symmetry and a dark singlet scalar; the SM Higgs doubles as the inflaton through a non-minimal coupling to gravity, and the new gauge boson is produced as freeze-in dark matter. After Planck inflation bounds and the dark-matter relic-density upper bound are imposed, the parameters are so tightly correlated that the SM Higgs quartic at the top mass is forced into 0.18–0.25, and the allowed region in the Higgs mixing angle and second Higgs mass plane shrinks dramatically. The same constraints push the predicted Higgs trilinear and quartic self-couplings away from their Standard Model values, which is why a future measurement of these couplings can test the whole construction.

What carries the argument

The machinery is the renormalisation-group-improved effective action for Higgs inflation, with the non-minimal coupling $\xi_H h^2 R$ (where $R$ is the Ricci scalar) making the SM Higgs the inflaton, evolved by two-loop $\beta$ functions from the top-quark pole mass to the Planck scale. The identity that carries the connection between the two sectors is $\lambda_H=[M_{h_2}^2+M_{h_1}^2-(M_{h_2}^2-M_{h_1}^2)\cos 2\theta]/(4v^2)$, which ties the low-scale Higgs quartic to the second Higgs mass and mixing angle; requiring this coupling to stay positive on the way up selects the $\lambda_H\ge 0.18$ band. On the dark matter side the load-bearing mechanism is freeze-in production described by the Boltzmann equation with decay and annihilation sources, including one-loop gluon and photon channels, evaluated with a starting temperature $T_{\rm ini}=1.5$ TeV; the inflation-side stability condition $\lambda_{HD}-2\lambda_H\,\xi_D/\xi_H>0$ is what forces $\xi_D=0$ at the top mass.

What would settle it

Measure the Higgs trilinear and quartic couplings at a future collider: if the measured pair $(\kappa_3,\kappa_4)$ is consistent with the Standard Model values $(1,1)$ within the projected uncertainties, the paper's central claim that inflation forces deviations is false.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central claim is that freeze-in vector dark matter and Higgs inflation cannot be treated independently. Imposing the Planck constraints on $A_s$, $n_s$, and $r$ at horizon exit, together with the positivity of the Higgs quartic up to the Planck scale, fixes $\lambda_H$ at the top-quark pole mass to the narrow range $0.18\le \lambda_H\le 0.25$; lower values run negative and higher values are cut off by the collider bound on the mixing angle. In the allowed $M_{h_2}$–$\sin\theta$ plane the paper finds a sharp anti-correlation, and imposing the relic-density upper bound further reduces the allowed $(g_D,\lambda_{HD})$ region to a narrow band. To keep inflation on the SM Higgs direction, the dark Higgs non-minimal coupling $\xi_D$ must vanish at the top mass even though it is regenerated by running. The resulting $\kappa_3$ and $\kappa_4$ Higgs self-coupling ratios deviate from the Standard Model point $(1,1)$, so a future collider measurement that finds the Standard Model values would directly rule out the Higgs-inflation scenario.

Load-bearing premise

The freeze-in calculation assumes dark matter production from SM gauge-boson annihilation starts only at $T_{\rm ini}=1.5$ TeV, so the relic-density bound that shrinks the allowed parameter space depends on this chosen starting temperature.

Editorial extensions

If this is right

If the measured Higgs self-coupling ratios stay at the Standard Model values $(1,1)$, the Higgs-inflation scenario in this setup is ruled out.
The narrow window $\lambda_H\in[0.18,0.25]$ at the top mass is a sharp quantitative prediction that future precision on the Higgs potential can check.
Demanding that the vector boson supply all of the observed dark matter leaves a much smaller allowed region than allowing a multi-component dark sector.
Because the dark-sector couplings are feeble, the model escapes current direct-detection and collider searches, which is consistent with long-running null results.
The HL-LHC projection with $3\,{\rm ab}^{-1}$ can reach part of the inflation-allowed $\kappa_3$ region for negative mixing angle, making the scenario testable in the near term.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A consequence the authors leave implicit is that the $g_D$–$\lambda_{HD}$ correlation is structural: once the second Higgs mass, mixing angle, and $M_{W_D}$ are set, the portal coupling is fixed, so future measurements of any one of these dark-sector quantities would pin down the others.
If electroweak symmetry breaking happened at a higher temperature, as in the reference the paper cites for this issue, the $T_{\rm ini}$ dependence would drop out and gluon- and photon-annihilation channels would dominate production, shifting the allowed dark-matter region; carrying out that scan quantitatively is a direct extension of the present work.
The same running machinery can be pointed at dark Higgs inflation, where $\lambda_D$ is not pinned by collider data and smaller $\xi$ values suffice; in that case the freeze-in constraints found here would likely look different (the authors flag this as future work).
A precision determination of the electroweak vacuum-stability bound could cross-check the predicted $\lambda_H$ window, because a measured quartic outside $[0.18,0.25]$ at the top mass would be in tension with the combined inflation-plus-DM picture.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

What you should know: this paper connects Higgs inflation with FIMP vector DM through RG running, and that combination is new relative to the earlier WIMP treatment in Ref [21]. The authors do a real numerical study with micrOMEGAs, including loop-induced gluon/photon annihilation for freeze-in, and they are transparent about many model choices. The broad idea—that inflation plus DM relic density can shrink the Higgs-sector parameter space—is reasonable and likely robust.

The genuine new content is the correlated constraint on (M_h2, sinθ) from inflation observables and the κ3/κ4 projections that follow. That is a fair phenomenological contribution.

But the central quantitative claim does not hold as stated. The abstract and Section 7 say Planck inflation plus DM force λ_H(M_t) into [0.18,0.25]. The lower edge is a stability boundary, fine. The upper edge is a scan artifact. From Eq. (2.6), λ_H ≈ 0.54 is allowed by the stated scan limits (sinθ=0.2, M_h2≈1125 GeV). The only thing excluding λ_H>0.25 is the explicit cap ξ_H≤1.5×10^4 in Eq. (5.1). No physical upper bound on ξ_H is given. Extend the ξ_H scan and λ_H moves up; A_s is fixed by adjusting ξ_H. So the 'window' is conditional on an arbitrary boundary, and the κ3/κ4 predictions derived from it are not as robust as claimed.

Two other soft spots. First, the appendix labels the beta functions 'two-loop' but displays one-loop forms with the s_H, s_D suppression factors; the two-loop claim is unsupported as written. Second, the freeze-in gauge-boson production depends on the assumed Tini=1.5 TeV. The authors acknowledge this in footnote 6, but it does mean the shrinking of the g_D-λ_HD region is not model-derived.

I would push back on the circularity critique: fitting A_s and Ω_DM and then projecting κ3/κ4 is what parameter scans do; the issue is not circularity per se, it is that the upper edge of the fit is an artifact. If the constraints were physical, the projection would be fine.

This paper deserves serious refereeing. The framework is standard, the numerics are apparently careful, and the idea is worth airing. With the ξ_H boundary explained or extended, and the two-loop claim fixed, it would be publishable as a phenomenological study. As it stands, I would not rely on the 0.18–0.25 interval as a prediction.

Recommendation: send to peer review, but insist the authors either extend the ξ_H scan to show the λ_H upper edge, or present the bound as a choice of prior, not a result.

Referee Report

3 major / 4 minor

Summary. The paper extends the Standard Model with a U(1)_D dark gauge symmetry and a dark singlet scalar. The SM Higgs doublet is treated as the inflaton with a non-minimal coupling to gravity, and the dark gauge boson is a FIMP dark matter candidate stabilized by a Z2 remnant of charge conjugation. The authors run the scalar, gauge, Yukawa, and non-minimal couplings from the top-quark pole mass to the Planck scale using RG equations, impose Planck constraints on the inflationary observables n_s, r, and A_s, and impose an upper bound on the dark matter relic density. They report a tightly correlated allowed region in the (M_h2, sin θ) plane that fixes the SM Higgs quartic coupling at the top mass scale to λ_H ∈ [0.18, 0.25], correlations in the (g_D, λ_HD) plane, and deviations of the Higgs trilinear and quartic self-couplings κ_3 and κ_4 from their SM values. The paper argues that future measurements of κ_3, κ_4 could validate or rule out the Higgs-inflation scenario in this model.

Significance. If the tight interval λ_H ∈ [0.18, 0.25] and the resulting κ_3/κ_4 deviations were robust, the paper would provide a novel, testable connection between Higgs inflation, freeze-in dark matter, and future collider measurements. The framework is reasonable: the use of RG-improved inflationary observables, the inclusion of loop-induced gluon and photon annihilation channels in freeze-in, and the explicit scan over the dark-sector parameters are all sensible. The paper also gives a clear discussion of the stabilization of the dark matter candidate and of the need for a negligibly small ξ_D. However, the central quantitative claim is currently not established because the upper edge of the λ_H interval is controlled by a scan boundary on ξ_H rather than by a derived physical constraint, and because the RG equations shown in the appendix are one-loop rather than the advertised two-loop forms. As a result, the headline collider prediction in Section 6 is conditional on the same unstated cut.

major comments (3)

[§5, Fig. 2 and Eq. (2.6)] The text states that λ_H > 0.25 is excluded by the collider bound sin θ < 0.23 and the chosen M_h2 range, but this is numerically incorrect. Using the scan extrema of Eq. (5.1), sin θ = 0.2 and M_h2 ≈ 1125 GeV, Eq. (2.6) gives λ_H ≈ 0.54, a factor of two above 0.25. The actual exclusion of such points must come from the As normalization combined with the scan range 10^4 ≤ ξ_H ≤ 1.5 × 10^4 in Eq. (5.1). Since no physical upper bound on ξ_H is stated in the paper, the upper edge of the claimed λ_H ∈ [0.18, 0.25] interval is a scan artifact. The abstract and Section 6 inherit this artifact because the predicted κ_3/κ_4 deviations are computed over this restricted region. Please rescan with a wider ξ_H range, or identify and justify a physical upper bound on ξ_H, and then revisit the abstract and the collider conclusions.
[Appendix A.1, Eqs. (A.1)–(A.13)] The Introduction and Section 4.2 advertise the use of two-loop RG running, but the beta functions displayed in Appendix A.1 are one-loop expressions. There are no two-loop contributions from gauge, Yukawa, or scalar quartic terms. This matters because the lower edge of the λ_H interval is obtained from the requirement that λ_H remains positive up to the Planck scale, and that boundary is quantitatively sensitive to the loop order of the running. Either provide the actual two-loop beta functions used in the numerical code, or revise the text to say one-loop running is used.
[§5, footnote 6 and Fig. 5] The dark matter production from SM gauge-boson annihilation, which is important in the sharp rise of the allowed g_D for M_WD > 500 GeV, is computed with an assumed initial temperature T_ini = 1.5 TeV. This value is an input, not a derived quantity, and Eq. (3.8) shows that the UV part of the yield scales as T_ini^3. While the κ_3/κ_4 prediction is not affected by this choice because the DM bound does not shrink that region, the combined 'inflation + DM' allowed region in the g_D–λ_HD plane is conditional on T_ini. Please quantify the dependence of the relic-density bound on T_ini or discuss the range of T_ini consistent with the electroweak symmetry breaking history assumed in the paper.

minor comments (4)

[Eq. (5.2)] The coefficient in the integrated RGE for g_D, 1/(6π^2), is inconsistent with the beta function in Eq. (A.4). With (4π)^2β_gD = s_D/3 g_D^3, the integrated form gives 1/(24π^2) (for s_D = 1). The final conclusion that g_D remains essentially constant for feeble couplings is unchanged, but the displayed equation should be corrected.
[General presentation] There are several typographical issues, including 'scalar-to-tensor ratio' in the caption of Fig. 3, 'no as such restrictions' in Section 6, and inconsistent pluralization of 'Higgs'. These should be corrected in a final pass.
[Section 7] The concluding statement that a future SM-like measurement of κ_3 and κ_4 would directly rule out the Higgs-inflation scenario is too strong, because the predicted deviations are calculated within the specific scan range of Eq. (5.1); outside that prior the scenario remains viable. The claim should be qualified to the parameter region studied here.
[§5, lower bound on λ_H] The lower bound λ_H > 0.18 is presented as a stability boundary, but no discussion is given of the sensitivity of this boundary to uncertainties in the top-quark Yukawa coupling or to the two-loop threshold corrections. A short estimate of this uncertainty would make the quoted interval more robust.

Circularity Check

1 steps flagged · score 6.0 of 10

The claimed λ_H∈[0.18,0.25] window is partly a projection of the scan's ξ_H cutoff; the κ_3,κ_4 'predictions' inherit this input-dependent window, although the lower stability bound and negative-θ κ deviations retain independent content.

fitted input called prediction [Section 5, Fig. 2 discussion; Eqs. (2.6), (4.16), (5.1); Abstract/Introduction.]
"On the other hand, λH > 0.25 is also not allowed because of the bound on the mixing angle from collider sin θ <0.23 and the choice of Mh2 mass range."

Eq. (2.6) makes λ_H a function of M_h2 and sinθ: at the scan maxima from Eq. (5.1), sinθ=0.2 and M_h2=1125 GeV, λ_H≈0.54, so the quoted collider mixing-angle bound and M_h2 range do not exclude λ_H>0.25. The actual exclusion comes from the imposed input interval 10^4≤ξ_H≤1.5×10^4 combined with the fit to As≈2.1×10^-9 (As∝λ_H/ξ_H^2, Eq. 4.16). Since ξ_H has no stated physical upper bound, λ_H>0.25 points are removed by an arbitrary scan boundary, not by inflation or DM physics. The κ_3,κ_4 'deviations' in Section 6 are computed from this scan-limited λ_H window, so the collider 'test' is partly a projection of input boundaries rather than an independent prediction.

full rationale

The derivation chain is largely a conventional two-scale scan: choose couplings at Mt, run two-loop β-functions, impose Planck As, ns, r and a freeze-in relic bound, then evaluate κ3,κ4. That loop is not circular because κ3,κ4 are not used as inputs. Self-citations (Refs. [18]–[22], [30]) are background/technical and are not load-bearing; the inflation condition Eq. (4.11) is derived in the paper, and the freeze-in Tini=1.5 TeV choice is an explicit modeling assumption rather than a circular reuse of the output. The one substantive circular step is the upper edge of the headline λ_H window: Eq. (2.6) with the scan ranges in Eq. (5.1) permits λ_H≈0.54, so the text's explanation for λ_H<0.25 is not supported by those inputs; the actual exclusion comes from the imposed 10^4≤ξ_H≤1.5×10^4 interval plus the As normalization. Consequently the quoted κ3,κ4 region is partly a projection of input boundaries. The lower bound from vacuum stability and the resulting departure of κ3,κ4 from (1,1) are genuine, so the circularity is partial (score 6) rather than total.

Assumptions & free parameters 7 free parameters · 6 assumptions · 2 invented entities

The central scan is driven by seven free parameters, most with broad hand-chosen ranges. The core assumptions are the dark sector construction, the Higgs-inflation single-field approximation, the freeze-in mechanism, and the specific RGEs used. Two new scalar/gauge entities are introduced; neither has independent falsifiable handles beyond the model-specific kappa3/kappa4 deviations.

free parameters (7)

gD = scanned in [1e-14, 1e-9]
Dark gauge coupling; controls freeze-in production rate and lambda_HD via v_D = M_WD/gD.
M_WD = scanned in [1, 1000] GeV
Dark gauge boson mass, i.e., the DM mass; enters decay and annihilation cross-sections.
sin theta = scanned in [1e-3, 0.2]
Higgs mixing angle; sets lambda_H, lambda_D, lambda_HD through Eq. 2.6.
M_h2 - M_h1 = scanned in [1, 1000] GeV
Mass splitting between BSM and SM-like Higgses; also enters quartic couplings via Eq. 2.6.
xi_H = scanned in [1e4, 1.5e4]
Non-minimal Higgs-curvature coupling; tuned so that the curvature power spectrum A_s matches Planck observation.
xi_D = set to 0 at top mass scale
Dark Higgs-curvature coupling set to zero to satisfy the Higgs inflation condition Eq. 4.11; generated at high scale by RG running.
Tini = 1.5 TeV
Initial temperature for freeze-in production from gauge-boson annihilation; UV contribution depends on it and the choice is not derived from the model.

assumptions (6)

domain assumption The model Lagrangian (Eq. 2.1) with U(1)D and charge conjugation symmetry forbidding kinetic mixing.
The new dark sector and the discrete symmetry are postulated; absence of kinetic mixing is built in by the Z2 symmetry.
standard math The non-minimal gravity action (Eq. 4.1) and the Weyl rescaling procedure to the Einstein frame.
This is a standard conformal transformation used in Higgs inflation, following Ref. [21].
domain assumption Inflation proceeds along the SM Higgs direction chi=0, stable when lambda_HD - 2 lambda_H xi_D/xi_H > 0 at the horizon exit scale (Eq. 4.11).
The paper restricts to SM Higgs inflation and uses this minimum condition to select parameter points.
domain assumption The background-dependent cutoff argument of Ref [14] is accepted, so Higgs inflation is valid despite unitarity concerns.
The paper relies on this cited resolution of the unitarity issue to legitimize the inflationary analysis.
domain assumption Freeze-in assumes zero initial DM abundance and uses the Boltzmann equation Eq. 3.1.
The FIMP mechanism is an input; the initial abundance is assumed negligible.
domain assumption The beta functions in Appendix A.1 (claimed two-loop in the text, but shown one-loop) are correct for the RG running from Mt to Mpl.
The numerical results depend entirely on these RGEs; the appendix lists only one-loop forms, so the two-loop claim is unverified.

invented entities (2)

Dark gauge boson W_D (U(1)D gauge boson)
purpose: Dark matter candidate; mass M_WD = g_D v_D, stabilized by the Z2 remnant of charge conjugation.
It couples feebly (g_D <= 1e-9), so direct production or detection is unrealistic; the only testable consequences are indirect Higgs self-coupling deviations, which are not specific to this particle.
Dark singlet scalar phi_D (dark Higgs)
purpose: Breaks U(1)D, gives mass to W_D, and mixes with the SM Higgs via lambda_HD.
No direct production at colliders due to tiny couplings; its existence is inferred from the structure of the model.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Constraining Inflation via FIMP dark matter using the $\beta$-function with collider implications." pith.science (2026). https://pith.science/paper/BNWHB3HD

@misc{pith2026250623770,
  author       = {Pith},
  title        = {Pith review of: Constraining Inflation via FIMP dark matter using the $\beta$-function with collider implications},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BNWHB3HD}},
  note         = {Machine review of arXiv:2506.23770}
}

abstract

The present study connects inflation and freeze-in type dark matter (DM) within the same setup. Although the observables in these two phenomena lie at vastly different energy scales, they have been properly handled using the RG running of couplings. For studying DM and inflation, the SM has been minimally extended by introducing an abelian dark gauge symmetry and a dark singlet scalar. In studying inflation, the SM Higgs doublet has been considered as the inflaton, which has a non-minimal coupling with the Ricci scalar. All inflationary observables have been computed at the horizon exit scale and constrained using the Planck data. Moreover, inflationary constraints have revealed strong correlations among model parameters, significantly reducing the allowed parameter space. In particular, in the Higgs mixing angle and BSM Higgs mass plane, only those values that ensure the Higgs quartic coupling remains above 0.18 are allowed. The additional gauge boson serves as a suitable DM candidate, produced via the freeze-in mechanism and stabilised by charge conjugation symmetry. The upper bound on the DM relic density further shrinks the parameter space allowed from inflationary constraints, becoming even narrower if we assume that the present vector DM constitutes the total DM density. Since DM interactions are feeble, it remains safe from all terrestrial experimental constraints. Additionally, the feeble dark matter coupling requires the dark Higgs-Ricci scalar non-minimal coupling to be negligible to satisfy Higgs inflation conditions. Finally, we have explored collider aspects and found that the trilinear and quartic Higgs vertices deviate from their SM values after incorporating inflation and DM constraints. Therefore, once we measure $\kappa_{3,4}$ at the future collider, we can establish the robustness of the Higgs inflation scenario.

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

53 extracted references · 3 canonical work pages

[21]

S. Khan, J. Kim and P. Ko, JHEP 05, 250 (2024) doi:10.1007/JHEP05(2024)250 [arXiv:2309.07839 [hep-ph]]

arXiv 2024
[1]

L. J. Hall, K. Jedamzik, J. March-Russell and S. M. West, JHEP 03, 080 (2010) doi:10.1007/JHEP03(2010)080 [arXiv:0911.1120 [hep-ph]]. – 22 –

arXiv 2010
[2]

Biswas, S

A. Biswas, S. Ganguly, D. Nanda and S. K. Sahoo, [arXiv:2505.13624 [hep-ph]]

arXiv
[3]

Lebedev, JCAP 02, 032 (2023) doi:10.1088/1475-7516/2023/02/032 [arXiv:2210.02293 [hep-ph]]

O. Lebedev, JCAP 02, 032 (2023) doi:10.1088/1475-7516/2023/02/032 [arXiv:2210.02293 [hep-ph]]

arXiv 2023
[4]

A. H. Guth, Phys. Rev. D 23, 347-356 (1981) doi:10.1103/PhysRevD.23.347

doi:10.1103/physrevd.23.347 1981
[5]

A. D. Linde, Phys. Lett. B 108, 389-393 (1982) doi:10.1016/0370-2693(82)91219-9

doi:10.1016/0370-2693(82)91219-9 1982
[6]

Albrecht and P

A. Albrecht and P. J. Steinhardt, Phys. Rev. Lett. 48, 1220-1223 (1982) doi:10.1103/PhysRevLett.48.1220

doi:10.1103/physrevlett.48.1220 1982
[7]

Aghanim et al

N. Aghanim et al. [Planck], Astron. Astrophys. 641, A6 (2020) [erratum: Astron. Astrophys. 652, C4 (2021)] doi:10.1051/0004-6361/201833910 [arXiv:1807.06209 [astro-ph.CO]]

arXiv 2020

Show all 53 references

[8]

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

1980 doi
[9]

Kallosh, A

R. Kallosh, A. Linde and D. Roest, JHEP 11, 198 (2013) doi:10.1007/JHEP11(2013)198 [arXiv:1311.0472 [hep-th]]

2013 arXiv
[10]

J. L. Cervantes-Cota and H. Dehnen, Nucl. Phys. B 442, 391-412 (1995) doi:10.1016/0550-3213(95)00128-X [arXiv:astro-ph/9505069 [astro-ph]]

1995 arXiv
[11]

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

2008 arXiv
[12]

F. L. Bezrukov, A. Magnin and M. Shaposhnikov, Phys. Lett. B 675, 88-92 (2009) doi:10.1016/j.physletb.2009.03.035 [arXiv:0812.4950 [hep-ph]]

2009 arXiv
[13]

Bezrukov, D

F. Bezrukov, D. Gorbunov and M. Shaposhnikov, JCAP 06, 029 (2009) doi:10.1088/1475-7516/2009/06/029 [arXiv:0812.3622 [hep-ph]]

2009 arXiv
[14]

Bezrukov, A

F. Bezrukov, A. Magnin, M. Shaposhnikov and S. Sibiryakov, JHEP 01, 016 (2011) doi:10.1007/JHEP01(2011)016 [arXiv:1008.5157 [hep-ph]]

2011 arXiv
[15]

Gondolo and G

P. Gondolo and G. Gelmini, Nucl. Phys. B 360, 145-179 (1991) doi:10.1016/0550-3213(91)90438-4

1991 doi
[16]

Aalbers et al

J. Aalbers et al. [LZ], [arXiv:2410.17036 [hep-ex]]

arXiv
[17]

McDonald, Phys

J. McDonald, Phys. Rev. Lett. 88, 091304 (2002) doi:10.1103/PhysRevLett.88.091304 [arXiv:hep-ph/0106249 [hep-ph]]

2002 arXiv
[18]

Costa, S

F. Costa, S. Khan and J. Kim, JHEP 06, 026 (2022) doi:10.1007/JHEP06(2022)026 [arXiv:2202.13126 [hep-ph]]

2022 arXiv
[19]

B´ elanger, S

G. B´ elanger, S. Choubey, R. M. Godbole, S. Khan, M. Mitra and A. Roy, JHEP 11, 133 (2022) doi:10.1007/JHEP11(2022)133 [arXiv:2208.00849 [hep-ph]]

2022 arXiv
[20]

Costa, S

F. Costa, S. Khan and J. Kim, JHEP 12, 165 (2022) doi:10.1007/JHEP12(2022)165 [arXiv:2209.13653 [hep-ph]]

2022 arXiv
[22]

S. Khan, J. Kim, J. Kim and P. Ko, [arXiv:2409.07851 [hep-ph]]

arXiv
[23]

A. D. Linde, Phys. Lett. B 129, 177-181 (1983) doi:10.1016/0370-2693(83)90837-7

1983 doi
[24]

Alloul, N

A. Alloul, N. D. Christensen, C. Degrande, C. Duhr and B. Fuks, Comput. Phys. Commun. 185, 2250-2300 (2014) doi:10.1016/j.cpc.2014.04.012 [arXiv:1310.1921 [hep-ph]]. – 23 –

2014 arXiv
[25]

Belyaev, N

A. Belyaev, N. D. Christensen and A. Pukhov, Comput. Phys. Commun. 184, 1729-1769 (2013) doi:10.1016/j.cpc.2013.01.014 [arXiv:1207.6082 [hep-ph]]

2013 arXiv
[26]

B´ elanger, F

G. B´ elanger, F. Boudjema, A. Goudelis, A. Pukhov and B. Zaldivar, Comput. Phys. Commun. 231, 173-186 (2018) doi:10.1016/j.cpc.2018.04.027 [arXiv:1801.03509 [hep-ph]]

2018 arXiv
[27]

Aad et al

G. Aad et al. [ATLAS], Nature 607, no.7917, 52-59 (2022) [erratum: Nature 612, no.7941, E24 (2022)] doi:10.1038/s41586-022-04893-w [arXiv:2207.00092 [hep-ex]]

2022 arXiv
[28]

Aad et al

G. Aad et al. [ATLAS and CMS], JHEP 08, 045 (2016) doi:10.1007/JHEP08(2016)045 [arXiv:1606.02266 [hep-ex]]

2016 arXiv
[29]

Y. Heo, D. W. Jung and J. S. Lee, Phys. Rev. D 110, no.1, 013003 (2024) doi:10.1103/PhysRevD.110.013003 [arXiv:2402.02822 [hep-ph]]

2024 arXiv
[30]

Khan and H

S. Khan and H. M. Lee, [arXiv:2503.02635 [hep-ph]]

arXiv
[31]

Edsjo and P

J. Edsjo and P. Gondolo, Phys. Rev. D 56, 1879-1894 (1997) doi:10.1103/PhysRevD.56.1879 [arXiv:hep-ph/9704361 [hep-ph]]

1997 arXiv
[32]

Catani, D

S. Catani, D. de Florian and M. Grazzini, JHEP 05, 025 (2001) doi:10.1088/1126-6708/2001/05/025 [arXiv:hep-ph/0102227 [hep-ph]]

2001 arXiv
[33]

R. V. Harlander and W. B. Kilgore, Phys. Rev. Lett. 88, 201801 (2002) doi:10.1103/PhysRevLett.88.201801 [arXiv:hep-ph/0201206 [hep-ph]]

2002 arXiv
[34]

Djouadi, Phys

A. Djouadi, Phys. Rept. 457, 1-216 (2008) doi:10.1016/j.physrep.2007.10.004 [arXiv:hep-ph/0503172 [hep-ph]]

2008 arXiv
[35]

Lebedev and H

O. Lebedev and H. M. Lee, Eur. Phys. J. C 71, 1821 (2011) doi:10.1140/epjc/s10052-011-1821-0 [arXiv:1105.2284 [hep-ph]]

2011 arXiv
[36]

E. D. Stewart and D. H. Lyth, Phys. Lett. B 302, 171-175 (1993) doi:10.1016/0370-2693(93)90379-V [arXiv:gr-qc/9302019 [gr-qc]]

1993 arXiv
[37]

A. R. Liddle, P. Parsons and J. D. Barrow, Phys. Rev. D 50, 7222-7232 (1994) doi:10.1103/PhysRevD.50.7222 [arXiv:astro-ph/9408015 [astro-ph]]

1994 arXiv
[38]

S. M. Leach, A. R. Liddle, J. Martin and D. J. Schwarz, Phys. Rev. D 66, 023515 (2002) doi:10.1103/PhysRevD.66.023515 [arXiv:astro-ph/0202094 [astro-ph]]

2002 arXiv
[39]

J. Kim, P. Ko and W. I. Park, JCAP 02, 003 (2017) doi:10.1088/1475-7516/2017/02/003 [arXiv:1405.1635 [hep-ph]]

2017 arXiv
[40]

R. L. Workman et al. [Particle Data Group], PTEP 2022, 083C01 (2022) doi:10.1093/ptep/ptac097

2022 doi
[41]

Buttazzo, G

D. Buttazzo, G. Degrassi, P. P. Giardino, G. F. Giudice, F. Sala, A. Salvio and A. Strumia, JHEP 12, 089 (2013) doi:10.1007/JHEP12(2013)089 [arXiv:1307.3536 [hep-ph]]

2013 arXiv
[42]

C. P. Burgess, H. M. Lee and M. Trott, JHEP 09, 103 (2009) doi:10.1088/1126-6708/2009/09/103 [arXiv:0902.4465 [hep-ph]]

2009 arXiv
[43]

J. L. F. Barbon and J. R. Espinosa, Phys. Rev. D 79, 081302 (2009) doi:10.1103/PhysRevD.79.081302 [arXiv:0903.0355 [hep-ph]]

2009 arXiv
[44]

R. N. Lerner and J. McDonald, JCAP 04, 015 (2010) doi:10.1088/1475-7516/2010/04/015 [arXiv:0912.5463 [hep-ph]]

2010 arXiv
[45]

C. P. Burgess, H. M. Lee and M. Trott, JHEP 07, 007 (2010) doi:10.1007/JHEP07(2010)007 [arXiv:1002.2730 [hep-ph]]. – 24 –

2010 arXiv
[46]

M. P. Hertzberg, JHEP 11, 023 (2010) doi:10.1007/JHEP11(2010)023 [arXiv:1002.2995 [hep-ph]]

2010 arXiv
[47]

Baldes and G

I. Baldes and G. Servant, JHEP 10, 053 (2018) doi:10.1007/JHEP10(2018)053 [arXiv:1807.08770 [hep-ph]]

2018 arXiv
[48]

Cepeda, S

M. Cepeda, S. Gori, P. Ilten, M. Kado, F. Riva, R. Abdul Khalek, A. Aboubrahim, J. Alimena, S. Alioli and A. Alves, et al. CERN Yellow Rep. Monogr. 7, 221-584 (2019) doi:10.23731/CYRM-2019-007.221 [arXiv:1902.00134 [hep-ph]]

2019 arXiv
[49]

D. M. Asner, T. Barklow, C. Calancha, K. Fujii, N. Graf, H. E. Haber, A. Ishikawa, S. Kanemura, S. Kawada and M. Kurata, et al. [arXiv:1310.0763 [hep-ph]]

arXiv
[50]

T. Liu, K. F. Lyu, J. Ren and H. X. Zhu, Phys. Rev. D 98, no.9, 093004 (2018) doi:10.1103/PhysRevD.98.093004 [arXiv:1803.04359 [hep-ph]]

2018 arXiv
[51]

[ATLAS], ATLAS-CONF-2022-050

2022
[52]

[ATLAS], ATLAS-CONF-2021-030

2021
[53]

Aad et al

G. Aad et al. [ATLAS], Phys. Lett. B 843, 137745 (2023) doi:10.1016/j.physletb.2023.137745 [arXiv:2211.01216 [hep-ex]]. – 25 –

2023

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [21]

S. Khan, J. Kim and P. Ko, JHEP 05, 250 (2024) doi:10.1007/JHEP05(2024)250 [arXiv:2309.07839 [hep-ph]]

arXiv 2024

[2] [1]

L. J. Hall, K. Jedamzik, J. March-Russell and S. M. West, JHEP 03, 080 (2010) doi:10.1007/JHEP03(2010)080 [arXiv:0911.1120 [hep-ph]]. – 22 –

arXiv 2010

[3] [2]

Biswas, S

A. Biswas, S. Ganguly, D. Nanda and S. K. Sahoo, [arXiv:2505.13624 [hep-ph]]

arXiv

[4] [3]

Lebedev, JCAP 02, 032 (2023) doi:10.1088/1475-7516/2023/02/032 [arXiv:2210.02293 [hep-ph]]

O. Lebedev, JCAP 02, 032 (2023) doi:10.1088/1475-7516/2023/02/032 [arXiv:2210.02293 [hep-ph]]

arXiv 2023

[5] [4]

A. H. Guth, Phys. Rev. D 23, 347-356 (1981) doi:10.1103/PhysRevD.23.347

doi:10.1103/physrevd.23.347 1981

[6] [5]

A. D. Linde, Phys. Lett. B 108, 389-393 (1982) doi:10.1016/0370-2693(82)91219-9

doi:10.1016/0370-2693(82)91219-9 1982

[7] [6]

Albrecht and P

A. Albrecht and P. J. Steinhardt, Phys. Rev. Lett. 48, 1220-1223 (1982) doi:10.1103/PhysRevLett.48.1220

doi:10.1103/physrevlett.48.1220 1982

[8] [7]

Aghanim et al

N. Aghanim et al. [Planck], Astron. Astrophys. 641, A6 (2020) [erratum: Astron. Astrophys. 652, C4 (2021)] doi:10.1051/0004-6361/201833910 [arXiv:1807.06209 [astro-ph.CO]]

arXiv 2020