Pith. sign in

REVIEW 4 major objections 5 minor 79 references

Gravitational Waves dynamics with Higgs portal and U(1) X SU(2) interactions

T0 review · 4 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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

Pith's one-line read This paper claims that Higgs portal interactions during inflation amplify sourced gravitational waves so that the tensor-to-scalar ratio reaches about 0.04, ten times the vacuum prediction and detectable by LiteBird.

desk verdict Plausible new combination of Higgs-singlet inflation with axion-SU(2) sourced GWs, but the central r* numbers rely on an equation missing a factor of H^2 and on lambda_s values the paper itself excludes. read the letter →

arxiv 2501.08000 v1 pith:47IQ5NLQ submitted 2025-01-14 hep-ph

Lucia A.Popa This is my paper · ORCID
classification hep-ph PACS 98.80.Cq04.30.-w12.60.Fr
keywords primordialgravitationalwavestensor-to-scalarratioHiggsportalHiggs-singletinflationaxion-gaugefieldspectatorCMBB-modepolarizationLiteBirdelectroweakvacuumstability
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

This paper tries to establish that a Standard-Model extension in which the Higgs boson mixes with a heavy singlet scalar can do two things at once: drive inflation consistently with Planck data, and boost the gravitational-wave signal generated by a spectator axion--SU(2) gauge-field sector. The portal interaction between the Higgs and the singlet raises the Hubble rate during inflation, which shifts the mass parameter of the gauge-field fluctuations and thereby amplifies the sourced tensor modes. If the argument is right, the model predicts a detectable B-mode signal with tensor-to-scalar ratio $r_* \approx 0.039$--$0.047$ at $k_p = 5 \times 10^{-3}\,\mathrm{Mpc}^{-1}$, about an order of magnitude above the vacuum prediction and far above the LiteBird threshold. The same mechanism avoids electroweak vacuum metastability and leaves a Higgs-singlet mixing angle large enough to be probed at the LHC, so the paper connects inflationary gravitational waves to collider-accessible particle physics.

What carries the argument

The load-bearing object is the time-dependent mass parameter of the gauge-field fluctuations, $m_Q(t) = gQ/H$, evaluated at its maximum $m_* = m_Q(\chi_* = 0.5\pi f)$ during the transient roll of the spectator axion. The sourced tensor power spectrum is $P_t^{(s)}(k_p) = (\epsilon_{QB} H^2/\pi^2) F^2(m_*)$, with $F(m) \simeq \exp(2.4308\,m - 0.0218\,m^2 - 0.0064\,m^3 - 0.86)$ for $3 \leq m \leq 7$, so the signal is exponentially sensitive to $m_*$. Higgs portal interactions enter because the tree-level threshold correction $\delta\lambda_h = \lambda_{hs}^2/(4\lambda_s)$ changes the inflationary Hubble rate $H_{\rm inf}$, which changes $\beta_* = \lambda\mu^4/(f^2 H^2)$ and hence the value of $m_*$; the paper's parameter choices place $m_*$ in the window 3.09--3.21 where $F^2$ is strongly amplifying. The two analytic stable slow-roll solutions $m_*^A \simeq (\kappa\beta/3)^{1/3}$ for $\kappa \ll 1$ and $m_*^B \simeq [\beta + \sqrt{\beta^2 - 144}]/12$ for $\kappa \gg 1$ provide the two trajectories studied, with $\kappa = (gf/\lambda H)^2$.

What would settle it

Measure the CMB B-mode polarization around $k_p \approx 5 \times 10^{-3}\,\mathrm{Mpc}^{-1}$: if LiteBird or a successor finds no scale-dependent bump and places $r_*$ below about 0.01, the predicted sourced signal $r_* \approx 0.039$--$0.047$ is excluded. A full numerical lattice or backreaction computation of the axion--SU(2) system that yields $m_* \approx 2.5$ would likewise falsify the parameter choice on which the enhancement depends.

Watch

Extended reading notes

Core claim

Working in the Higgs-singlet inflation model with a spectator $U(1)$ axion and $SU(2)$ gauge field, the paper shows that the positive tree-level threshold correction $\delta\lambda_h = \lambda_{hs}^2/(4\lambda_s)$ to the SM Higgs quartic coupling raises the Hubble expansion rate $H_{\rm inf}$ during inflation. Because the axion-gauge sector is coupled only gravitationally, this change in $H_{\rm inf}$ propagates into the spectator dynamics through $\beta_* = \lambda\mu^4/(f^2 H^2)$, shifting the maximum value $m_*$ of the time-dependent gauge-field mass parameter $m_Q(t)$. The sourced tensor power spectrum $P_t^{(s)} = (\epsilon_{QB} H^2/\pi^2) F^2(m_*)$ depends exponentially on $m_*$ through $F^2$, so a modest shift in $m_*$ produces a large change in the sourced gravitational-wave signal. After imposing the consistency bound $P_\zeta = P_\zeta^{\rm obs}$, the loop bound $R_{\delta\phi} < 0.1$, and the backreaction bounds of Ref. [62], the MCMC analysis for the two stable slow-roll solutions $m_*^A$ and $m_*^B$ yields best-fit values $r_* = 0.039 \pm 0.0027$ and $r_* = 0.047 \pm 0.0031$ at $k_p = 5 \times 10^{-3}\,\mathrm{Mpc}^{-1}$, with $m_* = 3.091 \pm 0.035$ and $m_* = 3.201 \pm 0.036$. The paper concludes that the sourced tensor-to-scalar ratio therefore exceeds the vacuum ratio $r_v = 3.44 \times 10^{-3}$ by an order of magnitude, putting the signal above the detection threshold of the LiteBird B-mode experiment while remaining consistent with Planck curvature-perturbation data.

Load-bearing premise

The central claim collapses if the gauge-field mass parameter $m_*$ does not actually sit in the narrow window near 3.1--3.2 where the exponential amplification factor $F^2$ is large; the paper's parameter ranges are chosen, through consistency and backreaction bounds together with $\beta_* = \lambda\mu^4/(f^2 H^2)$, to put it there, and a full numerical treatment including backreaction could instead yield $m_* \approx 2.5$, erasing the tenfold boost.

Editorial extensions

If this is right

  • LiteBird should see a scale-dependent, chiral B-mode bump at $k_p \approx 5 \times 10^{-3}\,\mathrm{Mpc}^{-1}$ with $r_* \approx 0.039$--$0.047$, well above its sensitivity $\delta r < 10^{-3}$.
  • The sourced gravitational-wave energy-density spectrum $h^2\Omega_{\rm GW}$ is potentially detectable by pulsar timing arrays and by LISA/DECIGO/BBO-class interferometers in the $10^{-2}$--$1$ Hz band after rescaling to 15 e-folds before the end of inflation.
  • The model's vacuum tensor-to-scalar ratio $r_v = 3.44 \times 10^{-3}$ stays below the current bound $r < 0.036$, so the vacuum contribution alone does not rule the model out.
  • The required Higgs-singlet mixing angle $|\sin\theta| \approx 0.12$ and threshold correction $\delta\lambda_h \approx (0.7\text{--}1.2)\times 10^{-2}$ are in principle measurable at the LHC, providing a particle-physics cross-check.
  • Both stable solutions $m_*^A$ and $m_*^B$ give the same qualitative result, an order-of-magnitude enhancement, so the conclusion does not depend on which slow-roll branch is chosen.

Reading between the lines

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

  • Beyond the paper, the enhancement lives in a narrow $m_*$ window near 3.1--3.2, so a full numerical treatment of the axion-gauge-field dynamics with backreaction could shift $m_*$ toward 2.5 and erase the claimed order-of-magnitude factor; the use of analytic stable solutions is the main fragility.
  • Beyond the paper, the sourced gravitational waves are chiral, so measuring parity-violating CMB correlations (TB/EB cross-spectra) would provide an independent test distinguishing this mechanism from vacuum tensor modes; the paper analyses only the BB power spectrum.
  • Beyond the paper, the same spectator sector should generate non-Gaussianity, so an estimate of the sourced $f_{\rm NL}$ in the Higgs-portal parameter region would let current and future surveys cross-check the model without waiting for B-mode data.
  • Beyond the paper, the inferred $\lambda_{hs}$ interval $(4.7\text{--}5.2) \times 10^{-2}$ is narrow enough that a precise measurement of singlet-like Higgs production at the LHC could confirm or exclude the specific portal coupling needed for the enhancement.
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.

Referee Report

4 major / 5 minor

Summary. The paper studies Higgs-singlet inflation with a spectator U(1) axion and SU(2) gauge field, and claims that Higgs-portal threshold corrections modify the inflationary Hubble rate, shifting the gauge-field mass parameter m_* into a range where sourced gravitational waves are exponentially enhanced. The central claim is that the sourced tensor-to-scalar ratio is r_* ≈ 0.039–0.047 at k_p = 5×10^-3 Mpc^-1, about an order of magnitude above the Higgs-singlet vacuum ratio, and detectable by LiteBIRD. The paper presents an MCMC parameter scan and forecasts for CMB B-modes, pulsar timing arrays, and laser interferometers. The main results are stated to be in agreement with current CMB constraints and with the allowed Higgs-portal parameter space.

Significance. If correct, the paper would establish a nontrivial connection between BSM Higgs physics and a detectable sourced CMB B-mode signal, and would extend the known spectator axion-SU(2) mechanism to a concrete inflationary model. The paper is explicit about its assumptions and includes a broad parameter scan, which is useful. However, the central numerical claim fails internal consistency checks with the equations as written, and the adopted Higgs-sector parameters are inconsistent with the paper's own quoted confidence interval. These issues are load-bearing rather than cosmetic, so the headline result is not currently supported.

major comments (4)
  1. [Section 3, Eqs. (31), (33), (35), (36), (39), (44), and Table 1] The sourced-ratio formulas are internally inconsistent. From Eq. (31) and Eq. (33), ε_QB = g^2 Q^4/H^2 and m_Q = gQ/H, so ε_QB = m_Q^4 H^2/g^2. Substituting this into Eq. (35) gives P_t^(s) = m_*^4 H^4/(π^2 g^2) F^2(m_*), meaning Eq. (39) is missing one factor of H^2 relative to the expression obtained from Eqs. (35)–(36). The problem is not merely notational: with the Table 1 values (g ≈ 8.3×10^-3, m_* ≈ 3.09) and H_inf ≈ 3×10^-6 M_pl, one obtains ε_QB ≈ 1.2×10^-5 and r_* ≈ 10^-5, not 0.039. Furthermore, the lower bound in Eq. (44) makes this unavoidable: at g = g_min, ε_QB = H^2/(32π^2 P_ζ^obs), so the sourced ratio is at most r_* ≈ H^4/(32π^4 (P_ζ^obs)^2) F^2 ≈ 10^-6–10^-4 for the H_inf range in Eq. (21). The reported r_* ≈ 0.039–0.047, and all quantities derived from it, are therefore not supported by the equations as written.
  2. [Section 2, Eq. (21), Figure 4, and Table 1] The adopted values of λ_s are inconsistent with the paper's own 99% CL interval. Eq. (21) states λ_s ∈ [1.5×10^-2, 1.9×10^-2], yet the text adopts (λ_s, λ_hs) = (0.1, 0.05) as "best fit values", Figure 4 uses λ_s = 0.01, and Table 1 reports MCMC means λ_s = 0.084±0.011 and 0.071±0.022 — several standard deviations outside the quoted interval. Because m_* is driven into the 3.1–3.2 enhancement window through H_inf and β_* = λμ^4/(f^2 H^2), which depend on the Higgs-singlet couplings, the r_* values in Table 1 are not obtained within the paper's own allowed parameter space. The abstract's claim of agreement with the allowed Higgs-portal parameter space is therefore unsupported.
  3. [Section 4, Eq. (38), and Introduction] The paper does not translate the peak ratio r_* at k_p = 5×10^-3 Mpc^-1 into the tensor-to-scalar ratio constrained by BICEP/Keck at k_0 = 0.05 Mpc^-1. The log-normal bump in Eq. (38) has σ ≈ 3, so the suppression from k_p to k_0 is only exp[−ln^2(10)/(2σ^2)] ≈ 0.7. The total r at k_0 is therefore approximately r_vac + 0.7 r_*, which for the B solution is about 0.038, exceeding the r < 0.036 bound quoted in the Introduction. The manuscript must perform this check before claiming agreement with the observational tensor constraints.
  4. [Section 4 and Figure 5] The detectability analysis adopts a target model with r_vac = 0.05, despite the Higgs-singlet model's own vacuum ratio being r_vac = 3.44×10^-3 and the cited observational bound being r < 0.036. The black ΛCDM curve in Figure 5 is therefore not a valid fiducial for this model. The "factor O(10)" in the abstract refers to the ratio r_*/3.44×10^-3, so comparing against r = 0.05 is misleading; the claim of being "much above the detection threshold of LiteBird" must be recomputed with the model's actual vacuum spectrum plus the sourced bump.
minor comments (5)
  1. [Section 3, Eq. (37)] Eq. (37) should read r = (P_t^(v)+P_t^(s))/P_ζ^(v), not r = P_t^(v)+P_t^(s)/P_ζ^(v); the missing parentheses make the ratio ambiguous.
  2. [Throughout] There are numerous typographical errors, including "ploarization" in the abstract, "reprezented" in the abstract, "beackreaction" near Eq. (26), and "effective" throughout. These should be corrected.
  3. [Section 4, MCMC analysis] The MCMC likelihood, the data vector, and the prior ranges are not specified, so the posterior distributions in Figures 7–9 and the means in Table 1 cannot be reproduced or checked.
  4. [Section 4, Figure 4 caption] The caption states that the calculation uses λ_s = 0.01, which is below the lower bound of the 99% CL interval in Eq. (21); this choice needs to be justified or reconciled with the stated interval.
  5. [Section 2.1] The sentence "the upper bound of the invisible Higgs boson branching ratio is BRH→hh inv < 0.11" uses an unusual notation; the invisible branching ratio should be denoted BR_inv, not BRH→hh.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular reduction found; the sourced-GW prediction is a direct evaluation of external axion-gauge formulas, though an internal parameter-space inconsistency is noted as a correctness concern.

full rationale

The claimed enhancement r* ≈ 0.039–0.047 is obtained by evaluating the cited axion–SU(2) sourced-tensor formula (Eqs. 35–39) with parameter ranges fixed by the consistency/backreaction bounds and the Planck normalization. The chain is: the Higgs-singlet model fixes H_inf from λs and λhs; β* = λμ^4/(f^2H^2) determines m*; Eq. (39) then gives r* = (m*^4 H^2)/(π^2 g^2 P_ζ) F^2(m*). This is a genuine model-to-observable mapping, not a fit of the observable back into a parameter: no sourced-GW or B-mode data are used as a likelihood to set the reported r* values, and no parameter is defined in terms of r*. The analytical m* solutions and backreaction bounds are imported from external papers (Refs. [54], [62], [72]), not from a self-citation chain, and the exponential F^2(m*) factor is a prior published result rather than an ansatz invented here. A serious internal-consistency caveat exists: Table 1 lists λs means (0.084, 0.071) that lie outside the paper's own 99% CL interval (0.015–0.019) from Eq. (21), and the text does not reconcile this. That is a correctness/reproducibility concern about which parameters are truly 'allowed,' but it is not a circular reduction: the quoted r* is still computed from the model equations rather than being equivalent to a chosen input by construction.

Assumptions & free parameters 8 free parameters · 8 assumptions · 0 invented entities

The model relies heavily on imported results: the Higgs-singlet inflation potential and threshold corrections, the stable axion-gauge slow-roll solutions, the backreaction bounds, and the log-normal sourced tensor template. These are used as axioms rather than re-derived. No new particle or force is introduced beyond the singlet scalar and the axion-gauge spectator fields already present in the cited literature.

free parameters (8)
  • lambda_s (singlet quartic coupling) = Table 1: 0.084 (A), 0.071 (B); Eq(21): 0.015-0.019
    MCMC posterior constrained by Planck normalization; inconsistent between Eq(21) and Table 1.
  • lambda_hs (Higgs portal coupling) = 0.049 (A), 0.051 (B)
    MCMC posterior constrained by Planck normalization and perturbativity.
  • xi_h (non-minimal coupling of Higgs) = 1.469e4 to 1.473e4
    Constrained by Planck normalization in Eq(21).
  • xi_s (non-minimal coupling of singlet) = 2.39e3 to 2.83e3
    Constrained by Eq(8) and Planck normalization in Eq(21).
  • g (SU(2) gauge coupling) = 8.32e-3 (A), 1.01e-2 (B)
    MCMC posterior in Table 1, priors from consistency bounds in Eq(47).
  • lambda (axion-gauge Chern-Simons coupling) = 50.85 (A), 49.46 (B)
    MCMC posterior in Table 1, prior range lambda = 30 to 100.
  • mu (axion modulation amplitude) = 6.21e-4 (A), 2.15e-4 (B)
    MCMC posterior in Table 1, prior from beta_* relation and H_inf range.
  • f (axion decay constant) = 4.37e-2 (A), 2.15e-2 (B)
    MCMC posterior in Table 1, prior from kappa < or > 1 condition.
assumptions (8)
  • domain assumption The Z2-symmetric Higgs-singlet potential and the large-field regime with xi_h >> xi_s and xi_h h^2 + xi_s s^2 >> 1.
    Used throughout Section 2 to derive the single-field effective potential Eq(9).
  • ad hoc to paper There is no coupling, up to gravitational interactions, between the inflation sector and the spectator sector.
    Stated in the abstract and Section 3; this decoupling is essential for treating the axion-gauge field as a spectator.
  • domain assumption The Hubble expansion rate H is constant during inflation, evaluated at phi_* = 5.26 Mpl.
    Section 3 and Section 4 use H_inf from the Higgs-singlet model to set the spectator dynamics.
  • domain assumption The axion potential has the form V(chi) = mu^4[1 + cos(chi/f)] with transient rolling.
    Imported from Refs. [55,56,57]; used to define beta(chi) and the stable solutions m_Q^A and m_Q^B.
  • domain assumption The SU(2) gauge field obeys the isotropic ansatz A_i^a = delta_i^a a(t) Q(t).
    Standard chromo-natural inflation ansatz from Refs. [51,58,59]; used in the equations of motion.
  • domain assumption The analytical stable solutions m_Q^A and m_Q^B from Ref. [62] remain valid when H is changed by Higgs portal corrections.
    Section 4 uses these solutions without re-deriving them in the Higgs-modified background.
  • domain assumption The sourced tensor power spectrum is a log-normal bump as in Eq(38), imported from Refs. [72,75].
    Central to the computation of r_* and the CMB B-mode power spectra.
  • domain assumption Perturbativity requires lambda_i < 1 and the Planck normalization P_zeta^obs = 2.1e-9.
    Used to constrain the Higgs-singlet parameter space in Section 2.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Gravitational Waves dynamics with Higgs portal and U(1) X SU(2) interactions." pith.science (2026). https://pith.science/paper/47IQ5NLQ

@misc{pith2026250108000,
  author       = {Pith},
  title        = {Pith review of: Gravitational Waves dynamics with Higgs portal and U(1) X SU(2) interactions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/47IQ5NLQ}},
  note         = {Machine review of arXiv:2501.08000}
}
read the original abstract

We show that a mixture of Higgs boson with a heavy scalar singlet with large vacuum expectation value ( vev) is a viable model of inflation that satisfy the existing observational data, the perturbativity constraints, avoiding in the same time the EW vacuum metastability as long as the Higgs portal interactions lead to positive tree-level threshold corrections for SM Higgs quartic coupling. The tree-level threshold corrections lead to the change of Hubble expansion rate during inflation with impact on the evolution of the axion-gauge field spectator sector, modifying the time-dependent mass parameter of the gauge field fluctuation. We evaluate this effect on the GW sourced tensor modes while accounting for the consistency and backreaction constraints and show that the Higgs portal interactions enhance the GW signal sourced by the gauge field fluctuations in the CMB B-mode ploarization power spectra. We address the detectability of the GW sourced by the gauge field fluctuations in presence of Higgs portal interactions for the experimental configuration of the future CMB polarization LiteBird space mission. We find that the sourced GW tensor-to-scalar ratio in presence of Higgs portal interactions is enhanced to a level that overcomes the vacuum tensor-to-scalar ratio by a factor of 10, much above the detection threshold of the LiteBird experiment, in agreement with the existing observational constraints on the curvature fluctuations and the allowed parameter space of Higgs portal interactions. We also show that a large enhancement of the sourced GW can be also detected by experiments such as pulsar timing arrays and laser/atomic interferometers. Moreover, a significant Higgs-singlet mixing can be probed by the LHC Higgs searchers.

Figures

Figures reproduced from arXiv: 2501.08000 by the authors.

Figure 1
Figure 1. Left: The marginalised likelihood probability distributions obtained for Higgs-singlet inflation model parameters. Right: Evolution of the Hubble expansion rate during inflation Hin f with λhs for different values of λs . Here Hin f is evaluated at φ∗ = 5.26 Mpl corresponding to the Hubble crossing of the largest observable CMB scale at N ≃ 55 e-folds before the end of inflation [7]. m s [ GeV] 150 200 250 300 350 4… view at source ↗
Figure 2
Figure 2. Maximal allowed values for |sin(θ)| in the scalar-singlet high mass region ms ∈ [125 − 600] GeV from the direct LHC Higgs searchers [36] (blue) compared with ms and |sin(θ)| values obtained in Higgs-scalar singlet model for λs=0.1 (red) and λs=0.2 (green) when λhs is allowed to vary in the confidence interval given in Eq. (21). Some particular values (λs , λhs) are also indicated. The figure shows that the Higgs-sin… view at source ↗
Figure 3
Figure 3. Consistency and backreaction constraints: Lower [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: The evolution of {m∗ , ǫ∗ B , σ ,r∗} with the Higgs portal quartic coupling λhs obtained for the stable solutions of mQ given in Eq. (40) at their maximum values m A ∗ (blue) and m B ∗ (red). The sourced tensor-to-scalar ratio r∗ is obtained at kp = 5 × 10−3Mpc−1 . We …
Figure 5
Figure 5. Figure 5: Left: The best fit of sourced GW power spectra P (s) t for m A ∗ (blue line) and m B ∗ (red line) solutions. The best fit parameters of P (s) t are also indicated. Right: The corresponding best fit B-mode polarization power spectra for m A ∗ (blue line) and m B ∗ (red …
Figure 6
Figure 6. Figure 6: Left: Evolution with frequency of the energy density parameter h 2ΩGW (f) of the sourced primordial GW for m A ∗ (blue line) and m B ∗ (red line) best fit solutions obtained for the LiteBird observing strategy. The solid green line shows the vacuum energy contribution …
Figure 7
Figure 7. Figure 7: The marginalised probability distributions obta [PITH_FULL_IMAGE:figures/full_fig_p015_7.png]
Figure 8
Figure 8. Figure 8: The marginalised probability distributions obta [PITH_FULL_IMAGE:figures/full_fig_p016_8.png]
Figure 9
Figure 9. Figure 9: The 2D marginalised probability distributions ob [PITH_FULL_IMAGE:figures/full_fig_p016_9.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

79 extracted references · 35 canonical work pages

  1. [1]

    A. H. Guth, Inflationary universe: A possible solution to the horizon and flatness problems, Phys. Rev. D 23 (1981) 347

    work page 1981

  2. [2]

    A. D. Linde, A new inflationary universe scenario: A possi ble solution of the horizon, flatness, homogeneity, isotrop y and primordial monopole problems, Phys. Lett. B 108 (1982) 389-393

    work page 1982

  3. [3]

    Albrecht and P

    A. Albrecht and P . J. Steinhardt, Cosmology for Grand Uni fied Theories with Radiatively Induced Symmetry Breaking, P hys. Rev. Lett. 48 (1982) 1220

    work page 1982

  4. [4]

    V . F. Mukhanov and G. V . Chibisov, Quantum Fluctuations and a Nonsingular Universe, JETP Lett. 33 (1981) 532

    work page 1981

  5. [5]

    A. A. Starobinsky, Dynamics of phase transition in the ne w inflationary universe scenario and generation of perturba tions, Phys. Lett. B 117 (1982) 175

    work page 1982

  6. [6]

    J. M. Bardeen, P . J. Steinhardt and M. S. Turner, Spontane ous creation of almost scale-free density perturbations in an inflationary universe, Phys. Rev. D 28 (1983) 679

    work page 1983

  7. [7]

    Akrami et al., Planck 2018 resu lts X

    Planck Collaboration: Y . Akrami et al., Planck 2018 resu lts X. Constraints on inflation, Astron. Astrophys. 641 (202 0) A10 [1807.06211]. 17

    arXiv 2018

  8. [8]

    Aghanim et al., Planck 2018 res ults

    Planck Collaboration: N. Aghanim et al., Planck 2018 res ults. VI. Cosmological parameters, Astron. Astrophys. 641 (2020) A6 [1807.06209]

    arXiv 2020

Show all 79 references
  1. [9]

    P . A. R Ade et al., Improved Constraints on Primordial Gra vitational Waves using Planck, WMAP , and BICEP/Keck Observations through the 2018 Observing Season, PRL 127 (2021) 15, 151301 [2110.0 0483]

    2021

  2. [10]

    Hazumi et al., LiteBIRD: A Satellite for the Studies o f B-Mode Polarization and Inflation from Cosmic Background R adiation Detection, J

    M. Hazumi et al., LiteBIRD: A Satellite for the Studies o f B-Mode Polarization and Inflation from Cosmic Background R adiation Detection, J. Low Temp. Phys. 194 (2019) 443

    2019

  3. [11]

    Allys et al., E

    LiteBIRD Collaboration ; E. Allys et al., E. Probing cos mic inflation with the LiteBIRD cosmic microwave background polarization survey, Progress of Theoretical and Experimental Physics 4 (2023) 1 43 [2202.02773]

    2023 arXiv

  4. [12]

    Abazajian et al., CMB-S4 Scie nce Book, First Edition [1610.02743]

    CMB-S4 collaboration, K. Abazajian et al., CMB-S4 Scie nce Book, First Edition [1610.02743]

    arXiv

  5. [13]

    Grishchuk, Amplification of gravitational waves i n an istropic universe, Zh

    L.P . Grishchuk, Amplification of gravitational waves i n an istropic universe, Zh. Eksp. Teor. Fiz. 67 (1974) 825

    1974

  6. [14]

    Starobinsky, Spectrum of relict gravitational ra diation and the early state of the universe, JETP Lett

    A.A. Starobinsky, Spectrum of relict gravitational ra diation and the early state of the universe, JETP Lett. 30 (19 79) 682

  7. [15]

    Lyth, What would we learn by detecting a gravitatio nal wave signal in the cosmic microwave background anisotro py?, Phys

    D.H. Lyth, What would we learn by detecting a gravitatio nal wave signal in the cosmic microwave background anisotro py?, Phys. Rev. Lett. 78 (1997) 1861 [9606387]

    1997

  8. [17]

    Adshead and M

    P . Adshead and M. Wyman, Gauge-inflation trajectories i n chromo-natural inflation, Phys. Rev. D 86 (2012) 043530 [12 03.2264]

    2012

  9. [18]

    Barnaby and M

    N. Barnaby and M. Peloso, Large Nongaussianity in Axion Inflation, Phys. Rev. Lett. 106 (2011) 181301 [1011.1500]

    2011 arXiv

  10. [19]

    Cook and L

    J.L. Cook and L. Sorbo, An inflationary model with small s calar and large tensor nongaussianities, JCAP 11 (2013) 047 [1307.7077]

    2013 arXiv

  11. [20]

    Ozsoy, Parity violating non-Gaussianity from axion -gauge field dynamics, Phys

    O. Ozsoy, Parity violating non-Gaussianity from axion -gauge field dynamics, Phys. Rev. D 104 (2021) 123523 [2106.1 4895]

    2021

  12. [21]

    Agrawal, T

    A. Agrawal, T. Fujita and E. Komatsu, Large tensor non-G aussianity from axion-gauge field dynamics, Phys. Rev. D 97 ( 2018) 103526 [1707.03023]

    2018 arXiv

  13. [22]

    Agrawal, T

    A. Agrawal, T. Fujita and E. Komatsu, Tensor Non-Gaussi anity from Axion-Gauge-Fields Dynamics : Parameter Search , JCAP 06 (2018) 027 [1802.09284]

    2018 arXiv

  14. [23]

    Shiraishi, C

    M. Shiraishi, C. Hikage, R. Namba, T. Namikawa and M. Haz umi, Testing statistics of the CMB B -mode polarization toward unambiguously establishing quantum fluctuation of the vacuum, Phys. Rev. D 94 (2016) 043506 [1606.06082]

    2016 arXiv

  15. [24]

    Lue, L.-M

    A. Lue, L.-M. Wang and M. Kamionkowski, Cosmological si gnature of new parity violating interactions, Phys. Rev. Le tt. 83 (1999) 1506 [astro-ph/9812088]

    1999 arXiv

  16. [25]

    Namba, E

    R. Namba, E. Dimastrogiovanni and M. Peloso, Gauge-flat ion confronted with Planck, JCAP 11, 045 (2013) [arXiv:1308 .1366]

    2013

  17. [26]

    Pajer and Marco Peloso, A review of axion inflation in t he era of Planck, Class

    E. Pajer and Marco Peloso, A review of axion inflation in t he era of Planck, Class. Quantum Grav. 30 (2013) 214002 [1305 .3557]

    2013

  18. [27]

    Aad et al., Obse rvation of a new particle in the search for the Standard Model Higgs boson with the A TLAS detector at the LHC, Phys.Lett

    A TLAS Collaboration Collaboration, G. Aad et al., Obse rvation of a new particle in the search for the Standard Model Higgs boson with the A TLAS detector at the LHC, Phys.Lett. B716 (2012) 1 [1207.72 14]

    2012

  19. [28]

    Chatrchyan et al

    CMS Collaboration Collaboration, S. Chatrchyan et al. , Observation of a new boson at a mass of 125 GeV with the CMS exp eriment at the LHC, Phys.Lett. B 716 (2012) 30 [207.7235]

    2012

  20. [29]

    Beacham, et al., Physics Beyond Colliders at CERN Bey ond the Standard Model Working Group Report, J

    J. Beacham, et al., Physics Beyond Colliders at CERN Bey ond the Standard Model Working Group Report, J. Phys. G 47 (20 20) 1, 010501 [arXiv:1901.09966]

    1901 arXiv

  21. [30]

    F. L. Bezrukov and M. Shaposhnikov, Phys. Lett. B 659, 70 3 (2008)

    2008

  22. [31]

    Bezrukov, A

    F. Bezrukov, A. Magnin, M. Shaposhnikov and S. Sibiryak ov, Higgs inflation: consistency and generalisations, JHEP 1101 (2011) 016 [1008.5157]

    2011 arXiv

  23. [32]

    Bezrukov, J

    F. Bezrukov, J. Rubio and M. Shaposhnikov, Living beyon d the edge: Higgs inflation and vacuum metastability Phys. Re v. D 92 (2015) 083512 [1412.3811]

    2015 arXiv

  24. [33]

    Degrassi, S

    G. Degrassi, S. Di Vita, J. Elias-Miro, J. R. Espinosa, G . F. Giudice, G. Isidori and A. Strumia, Higgs mass and vacuum stability in the Standard Model at NNLO, JHEP 1208 (2012) 098 [1205.6497 ]

    2012 arXiv

  25. [34]

    Lebedev and H

    O. Lebedev and H. M. Lee, The Higgs portal interactions, Eur. Phys. J. C 71 (2011) 1821

    2011

  26. [35]

    Elias, J

    J. Elias, J. R. Espinosa, G. F. Giudice, H. M. Lee, A. Stru mia, Stabilization of the Electroweak V acuum by a Scalar Thr eshold Effect, JHEP 2012 (2012) 31 [1203.0237]

    2012 arXiv

  27. [36]

    Robens, T

    T. Robens, T. Stefaniak, LHC benchmark scenarios for th e real Higgs singlet extension of the standard model, Eur. Ph ys. Jour. C76 (2016) 268 [1601.07880]

    2016 arXiv

  28. [37]

    Navas et al

    S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 0 30001 (2024)

    2024

  29. [38]

    Lebedev,The Higgs Portal to Cosmology, Progress in P article and Nuclear Physics 120 (2021) 103881 [ arXiv:2104

    O. Lebedev,The Higgs Portal to Cosmology, Progress in P article and Nuclear Physics 120 (2021) 103881 [ arXiv:2104. 03342]

    2021

  30. [39]

    Caprini, M

    C. Caprini, M. Hindmarsh, S. Huber et al, Science with th e space-based interferometer eLISA. II: gravitational wav es from cosmological phase transitions, JCAP 04 (2016) 001 [1512.06239]

    2016 arXiv

  31. [40]

    V . K. Oikonomou, A. Giovanakis, Electroweak phase tran sition in singlet extensions of the standard model with dime nsion-six operators, Phys. Rev. D109 (2024) 055044 [ arXiv:2403.01591]

    2024 arXiv

  32. [41]

    Alanne, T

    T. Alanne, T. Hugle, M. Platscher, K. Schmitz, A fresh lo ok at the gravitational-wave signal from cosmological phas e transitions, JHEP 03 (2020) 4 [1909.11356]

    2020 arXiv

  33. [42]

    Schmitz, New Sensitivity Curves for Gravitational- Wave Signals from Cosmological Phase Transitions, JHEP 01 ( 2021) 097 [2002.04615]

    K. Schmitz, New Sensitivity Curves for Gravitational- Wave Signals from Cosmological Phase Transitions, JHEP 01 ( 2021) 097 [2002.04615]

    2021 arXiv

  34. [43]

    V . K. Oikonomou, E ffects of the axion through the Higgs portal on primordial grav itational waves during the electroweak breaking, Phys. Rev. D110 (2023) 075003 [2303.05889]

    2023 arXiv

  35. [44]

    V . K. Oikonomou, Theoretical probes of Higgs boson-axi on nonperturbative couplings, Phys. Rev. D110 (2024) 07500 3 [2409.10709]

    2024 arXiv

  36. [45]

    Gross, O

    A.Falkowski, C. Gross, O. Lebedev, A second Higgs from t he Higgs portal, JHEP 2015 (2015) 57 [1502.01361]

    2015 arXiv

  37. [46]

    Ema, Higgs scalaron mixed inflation, Phys

    Y . Ema, Higgs scalaron mixed inflation, Phys. Lett. B, (2 017) 770, 403 [1701.07665]

    arXiv

  38. [47]

    Y . Ema, M. Karciauskas, O. Lebedev, S. Rusak and M. Zatta , Higgs inflaton mixing and vacuum stability, Phys. Lett. B 78 9 (2019) 373 [1711.10554]

    2019 arXiv

  39. [48]

    J. Kim, P . Ko, W. Park, Higgs-portal assisted Higgs infla tion with a sizeable tensor-to-scalar ratio, JCAP 02 (2017) 003 (2017) [1405.1635]. 18

    2017 arXiv

  40. [49]

    R. N. Lerner and J. McDonald, Gauge singlet scalar as infl aton and thermal relic dark matter, Phys. Rev. D 80 (2009) 123 507 [0909.0520]

    2009 arXiv

  41. [50]

    Lewis, A

    A. Lewis, A. Challinor, A. Lasenby, E fficient computation of CMB anisotropies in closed FRW models, ApJ 538 (2000) 473

    2000

  42. [51]

    Adshead and M

    P . Adshead and M. Wyman, Chromo-Natural Inflation: Natu ral inflation on a steep potential with classical non-Abelia n gauge fields, Phys. Rev. Lett. 108 (2012) 261302 [1202.2366]

    2012 arXiv

  43. [52]

    Adshead, E

    P . Adshead, E. Martinec and M. Wyman, Gauge fields and infl ation: Chiral gravitational waves, fluctuations, and the Ly th bound, Phys. Rev. D 88 (2013) 021302 [1301.2598]

    2013 arXiv

  44. [53]

    Adshead, E

    P . Adshead, E. Martinec, E.I. Sfakianakis and M. Wyman, Higgsed Chromo-Natural Inflation, JHEP 12 (2016) 137 [1609. 04025]

    2016

  45. [54]

    Dimastrogiovanni, M

    E. Dimastrogiovanni, M. Fasiello and T. Fujita, Primor dial Gravitational Waves from Axion-Gauge Fields Dynamics , JCAP 01 (2017) 019 [1608.04216]

    2017 arXiv

  46. [55]

    Barnaby, J

    N. Barnaby, J. Moxon, R. Namba, M. Peloso, G. Shiu et al., Gravity waves and non-Gaussian features from particle prod uction in a sector gravitationally coupled to the inflaton, Phys.Rev. D 86 (201 2) 103508 [1206.6117]

    arXiv

  47. [56]

    Namba, M

    R. Namba, M. Peloso, M. Shiraishi, L. Sorbo and C. Unal, S cale-dependent gravitational waves from a rolling axion, J CAP 1601 (2016) 041 [1509.07521]

    2016 arXiv

  48. [57]

    Ozsoy, Synthetic Gravitational Waves from a Rolling Axion Monodromy, JCAP 04 (2021) 040 [2005.10280]

    O. Ozsoy, Synthetic Gravitational Waves from a Rolling Axion Monodromy, JCAP 04 (2021) 040 [2005.10280]

    2021 arXiv

  49. [58]

    Maleknejad and M.M

    A. Maleknejad and M.M. Sheikh-Jabbari, Gauge-flation: Inflation From Non-Abelian Gauge Fields, (2011) [arXiv:110 2.1513]

    2011

  50. [59]

    Maleknejad and M.M

    A. Maleknejad and M.M. Sheikh-Jabbari, Non-Abelian ga uge field inflation, Phys. Rev. D 84 (2011) 043515 [1102.1932]

    2011 arXiv

  51. [60]

    D. I. Kaiser, Conformal Transformations with Multiple Scalar Fields, Phys. Rev. D, 81 (2010) 084044 [1003.1159]

    2010 arXiv

  52. [61]

    Iarygina, E

    O. Iarygina, E. Sfakianakis, R. Sharma, A. Brandenburg , Backreaction of axion-SU(2) dynamics during inflation, JC AP 04 (2024) 18, 28 [2311.07557]

    2024 arXiv

  53. [62]

    Ishiwata, E

    K. Ishiwata, E. Komatsu, I. Obata, Axion-gauge field dyn amics with backreaction, JCAP 03 (2022) 03, 10 [2111.14429]

    2022 arXiv

  54. [63]

    Caprini and D.G

    C. Caprini and D.G. Figueroa, Cosmological Background s of Gravitational Waves, Class. Quant. Grav. 35 (2018) 1630 01 [1801.04268]

    2018 arXiv

  55. [64]

    P . F. de Salas, S. Pastor, Relic neutrino decoupling wit h flavour oscillations revisited, JCAP 07 (2016) 051 [1606.0 6986 ]

    2016

  56. [65]

    Audley et al., Laser Interferom eter Space Antenna, [1702.00786]

    LISA Collaboration, H. Audley et al., Laser Interferom eter Space Antenna, [1702.00786]

    arXiv

  57. [66]

    Isoyama, H

    S. Isoyama, H. Nakano, and T. Nakamura, Multiband Gravi tational-Wave Astronomy: Observing binary inspirals with a decihertz detector, B-DECIGO, PTEP 2018 (2018) 073E01 [1802.06977]

    2018 arXiv

  58. [67]

    Corbin and N

    V . Corbin and N. J. Cornish, Detecting the cosmic gravit ational wave background with the big bang observer, Class. Q uant. Grav. 23 (2006) 2435 [0512039]

    2006

  59. [68]

    Schmitz, New Sensitivity Curves for Gravitational- Wave Experiments, https://zendo.org/records/368958 (2020)

    K. Schmitz, New Sensitivity Curves for Gravitational- Wave Experiments, https://zendo.org/records/368958 (2020)

    2020

  60. [69]

    Campeti, E

    P . Campeti, E. Komatsu, D. Poletti, C. Baccigalupi, Mea suring the spectrum of primordial gravitational waves with CMB, PTA and Laser Interferometers. JCAP 01 (2021) 012 [2007.04241]

    2021 arXiv

  61. [70]

    Papageorgiou, M

    A. Papageorgiou, M. Peloso and C. Unal, Nonlinear pertu rbations from axion-gauge fields dynamics during inflation, JCAP 07 (2019) 004, [1904.01488]

    2019 arXiv

  62. [71]

    Fujita, R

    T. Fujita, R. Namba, Y . Tada, Does the detection of primo rdial gravitational waves exclude low energy inflation?, Ph ysics Lett B, 778 (2018) 17 [1705.01533]

    2018 arXiv

  63. [72]

    Thorne, T

    B. Thorne, T. Fujita, M. Hazumi, N. Katayama, E. Komatsu , M. Maresuke, Finding the chiral gravitational wave backgr ound of an axion-S U (2 ) inflationary model using CMB observations and laser int erferometers, Phys. Rev. D 97 (2018) 043506 [1707.03240]

    2018 arXiv

  64. [73]

    Komatsu, C

    P ., Campeti, E. Komatsu, C. Baccigalupi et al., LiteBIR D science goals and forecasts. A case study of the origin of pr imordial gravitational waves using large-scale CMB polarization, JCAP 06, (2024) 0 08

    2024

  65. [74]

    Dimastrogiovanni and M

    E. Dimastrogiovanni and M. Peloso, Stability analysis of chromo-natural inflation and possible evasion of Lyth bou nd, Phys. Rev. D 87 (2013) 103501 [1212.5184]

    2013 arXiv

  66. [75]

    Fujita, E

    T. Fujita, E. Sfakianakis, M. Shiraishi,Tensor Spectr a Templates for Axion-Gauge Fields Dynamics during Inflatio n, JCAP 05 (2019) 057 [1812.03667]

    2019 arXiv

  67. [76]

    Campeti, E

    P . Campeti, E. Komatsu, C. Baccigalupi et al., LiteBIRD science goals and forecasts. A case study of the origin of pri mordial gravitational waves using large-scale CMB polarization, JCAP 06 (2024) 00 8 [2312.00717]

    2024 arXiv

  68. [77]

    Papageorgiou, M

    A. Papageorgiou, M. Peloso, C. Unal, Nonlinear perturb ations from the coupling of the inflaton to a non-Abelian gaug e ?field, with a focus on Chromo-Natural Inflation, JCAP 09 (2018) 030 [ arXiv:1806 .08313

    2018

  69. [78]

    Fujita, R

    T. Fujita, R. Namba, I. Obata, Mixed non-gaussianity fr om axion-gauge field dynamics, JCAP 04 (2019) 044 [1811.1237 1]

    2019

  70. [79]

    Maleknejad and E

    A. Maleknejad and E. Komatsu, Production and Backreact ion of Spin-2 Particles of SU(2) Gauge Field during Inflation , JHEP 05 (2019) 174 [1808.09076]

    2019 arXiv

  71. [80]

    Mirzagholi, A

    L. Mirzagholi, A. Maleknejad and K.D. Lozanov, Product ion and backreaction of fermions from axion-SU(2) gauge fiel ds during inflation, Phys. Rev. D 101 (2020) 083528 [1905.09258]. 19

    2020 arXiv

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.