{"id":"6a9d4c6f-b1b8-44fe-b76f-dc44d6286b37","arxiv_id":"2501.08000","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"high","formal_verification":"none","parameter_count":8,"one_line_summary":"A Higgs portal inflation model is shown to enhance sourced gravitational waves from an axion-SU(2) spectator to a tensor-to-scalar ratio of about 0.04, making them detectable by LiteBIRD.","lead":"This paper combines a Higgs-singlet inflation model with a spectator axion and gauge field sector, and argues that Higgs portal interactions can boost the sourced gravitational wave signal to a tensor-to-scalar ratio near 0.04, above the LiteBIRD detection threshold. If this is right, LHC Higgs measurements and future CMB polarization observations would be linked through inflationary dynamics.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Sourced-GW enhancement uses λs values (0.084, 0.071, 0.1) far outside the paper's stated 99% CL interval (0.015–0.019); the central claim is therefore not supported in the allowed parameter space.","rationale":"The reader's verdict is REJECT, and the cited issues are real. My stress-test focuses on the single most load-bearing internal inconsistency: the paper computes its headline enhancement with Higgs-portal parameters that are excluded by its own 99% CL constraints. Eq. (21) gives λs ∈ [0.015, 0.019], but Table 1 and Section 2 use λs = 0.084, 0.071, and 0.1. Because m_* is set through β_* = λ μ^4/(f^2H^2) and H_inf depends on λs/λhs (Fig. 1 right), these excluded values are what place m_* in the 3.1–3.2 window where F^2(m_*) is exponentially large. The paper does not explain the discrepancy; it is an internal contradiction, not a matter of outside consensus. The reader additionally flags a dimensional inconsistency in Eq. (39) and a missing comparison with the BICEP/Keck r < 0.036 bound; those are also serious and would need fixing. But the λs inconsistency alone invalidates the central claim: the claimed enhancement is not demonstrated in the parameter space the paper itself deems allowed. The concrete test—re-running the Section 2 MCMC and recomputing m_* for λs = 0.017—would settle this directly. If instead the CI in Eq. (21) is the error, the Higgs-singlet analysis must be redone and the GW computation repeated; either way the paper as written is not self-consistent. I therefore see no reason to change the reader's REJECT verdict.","tokens_in":21724,"tokens_out":13470,"duration_ms":117939,"concrete_test":"Re-run the Section 2 MCMC with the same priors and data and verify that the posterior 99% CI for λs indeed excludes 0.084 and 0.071; then fix λs to a value inside that interval (e.g., 0.017), recompute H_inf from the Higgs-singlet slow-roll equations, and use Eqs. (40)–(42) to obtain m_*; if m_* falls below the window where F^2(m_*) is large (e.g., m_* ≈ 2.5), the claimed r* ≈ 0.039–0.047 cannot be reached in the allowed parameter space.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 2, Eq. (21), reports the 99% CL interval for the Higgs-singlet quartic coupling λs as 1.5×10−2 to 1.9×10−2. Yet Section 2 adopts (λs, λhs) = (0.1, 0.05) as 'best fit values', and Table 1 lists MCMC means λs = 0.084±0.011 (mA*) and 0.071±0.022 (mB*), each several standard deviations outside that interval. The enhancement is not incidental: r* ≈ 0.039–0.047 is obtained only because H_inf and β_* = λ μ^4/(f^2H^2) drive m_* into the 3.1–3.2 window where F^2(m_*) is exponentially large. Since H_inf depends on λs and λhs through the Higgs-singlet model (Figure 1, right), and m_* depends on H_inf through Eqs. (40)–(42), using λs values excluded by the paper's own analysis is what places m_* in the enhancement window. If the stated 99% CL interval is correct, the model's allowed parameters do not yield the predicted m_* and the O(10) enhancement disappears. This is an internal inconsistency, not a matter of external consensus, and it directly undermines the abstract's claim of agreement with the allowed Higgs-portal parameter space.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":22031,"tokens_out":21104,"duration_ms":191756,"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":[{"comment":"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.","section":"Section 3, Eqs. (31), (33), (35), (36), (39), (44), and Table 1"},{"comment":"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.","section":"Section 2, Eq. (21), Figure 4, and Table 1"},{"comment":"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.","section":"Section 4, Eq. (38), and Introduction"},{"comment":"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.","section":"Section 4 and Figure 5"}],"minor_comments":[{"comment":"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.","section":"Section 3, Eq. (37)"},{"comment":"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.","section":"Throughout"},{"comment":"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.","section":"Section 4, MCMC analysis"},{"comment":"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.","section":"Section 4, Figure 4 caption"},{"comment":"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.","section":"Section 2.1"}],"recommendation":"reject","confidential_remarks":"The two main problems are independent and each is sufficient to undermine the central claim. First, the sourced-ratio formula is algebraically inconsistent with the model definitions by a factor of H^2, and the quoted r_* values are also impossible given the P_ζ normalization bound in Eq. (44); the claimed O(10) enhancement appears to vanish once the equations are used consistently. Second, the λ_s values used to reach the enhancement window are excluded by the paper's own 99% CL interval, so the result is not within the claimed allowed parameter space. These are not presentation issues. I recommend rejection, though a resubmission with corrected formulas and a scan restricted to the stated confidence interval could be reconsidered."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Lucia — quick take on 2501.08000. The new step is real: no one in the cited literature connects the tree-level threshold correction in Higgs-singlet inflation to the spectator axion-SU(2) sourced GW spectrum. The paper does a decent job embedding the spectator in the Higgs-singlet model, and the consistency/backreaction checks are appropriate. But the headline numbers don't survive close reading.\n\nFirst, Eq. (39) is missing a factor of H^2. Substituting ε_QB = m^4 H^2/g^2 into Eq. (35) gives r_s = m^4 H^4/(π^2 g^2 P_ζ) F^2, not the printed m^4 H^2. This is not a cosmetic typo; it sits at the center of the paper's main claim.\n\nSecond, there is an internal contradiction in λs. Section 2 reports a 99% CL interval λs = 0.015–0.019 from the Planck normalization, then adopts (λs, λhs) = (0.1, 0.05) as 'best fit', and Table 1 lists λs = 0.084 and 0.071. The m* window that produces the O(10) enhancement depends on H_inf through β* = λ μ^4/(f^2 H^2), and H_inf depends on λs and λhs. Using λs values several standard deviations outside the paper's own allowed interval is what puts m* in the 3.1–3.2 enhancement window. If the 99% CL interval is correct, the claimed r* is not in the allowed parameter space.\n\nThird, the predicted r* = 0.039–0.047 exceeds the BICEP/Keck r < 0.036 bound cited in the same paper. The pivot scales differ (5e-3 vs 0.05 Mpc^-1), so a direct comparison is needed; the paper doesn't provide one. Maybe the scale-dependence saves it, but you have to show that.\n\nThe paper has real virtues: the literature is handled well, the MCMC machinery is appropriate, and the idea of connecting LHC Higgs measurements to CMB B-modes is attractive. The issues are correctable in principle. But as written, the central numerical claim is not supported. My recommendation is not to desk-reject out of hand — the combination of mechanisms is new and the subfield would benefit from a corrected version — but the paper as it stands should be rejected. It needs a serious revision, not line edits.\n\nFor reference: I would not cite this version, and I'd only bring it to reading group as an exercise in checking equations against each other.","headline":"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.","tokens_in":22638,"tokens_out":7599,"would_cite":false,"duration_ms":69874,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["98.80.Cq","04.30.-w","12.60.Fr"],"model":"deepseek-v4-flash","headline":"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.","keywords":["primordial gravitational waves","tensor-to-scalar ratio","Higgs portal","Higgs-singlet inflation","axion-gauge field spectator","CMB B-mode polarization","LiteBird","electroweak vacuum stability"],"falsifier":"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.","tokens_in":21403,"feed_emoji":"🌊","tokens_out":16132,"duration_ms":123254,"temperature":0.7,"pith_summary":"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.","feed_headline":"Higgs portal boosts inflation's gravitational-wave signal tenfold","feed_subtitle":"Predicted B-mode signal r* ≈ 0.04 sits far above LiteBird's detection threshold.","key_machinery":"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 $\\kappa = (gf/\\lambda H)^2$.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the two stable slow-roll solutions m_A* and m_B* and the numerical backreaction bounds used to set the parameter intervals in Eq. (47).","marker":"[62]"},{"why":"Provides the sourced tensor power spectrum formula and the consistency/backreaction constraints used to compute the sourced tensor-to-scalar ratio r*.","marker":"[54]"},{"why":"Supplies the LiteBird noise power spectrum, the log-normal sourced-spectrum template, and the detectability forecast used for the B-mode analysis.","marker":"[72]"},{"why":"Establishes the Higgs-singlet inflation model and the conditions under which the Higgs portal assists inflation, as used in Section 2.","marker":"[34]"},{"why":"Shows that the tree-level threshold correction stabilises the electroweak vacuum, the mechanism the model relies on to avoid metastability.","marker":"[35]"},{"why":"Provides the Planck 2018 inflation constraints and normalisation used to fix the Higgs-singlet model parameters and the vacuum spectral index.","marker":"[7]"},{"why":"Gives the combined Planck/BICEP/Keck upper bound on the vacuum tensor-to-scalar ratio that the model must satisfy.","marker":"[9]"},{"why":"Supplies the log-normal template for the sourced tensor power spectrum and the width relation used in the analysis.","marker":"[75]"}],"fun_headline_variants":["Higgs portal boosts gravitational-wave signal tenfold","Inflation's gravitational waves amplified by Higgs portal","Gravitational waves from inflation get a Higgs boost","Tenfold enhancement of inflationary gravitational waves","Higgs-singlet mixing intensifies primordial gravitational waves"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Higgs portal boosts gravitational-wave signal tenfold","Inflation's gravitational waves amplified by Higgs portal","Gravitational waves from inflation get a Higgs boost","Tenfold enhancement of inflationary gravitational waves","Higgs-singlet mixing intensifies primordial gravitational waves"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000195,"raw_usage":{"total_tokens":1525,"prompt_tokens":1280,"completion_tokens":245,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":896,"completion_tokens_details":{"reasoning_tokens":173}},"tokens_in":896,"tokens_out":245,"duration_ms":3115,"temperature":1.0,"reasoning_tokens":173,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T20:30:51.416096+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"Lebedev and H","cited_arxiv_id":null,"evidence_quote":"Establishes the Higgs-singlet inflation model and the conditions under which the Higgs portal assists inflation, as used in Section 2."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives the combined Planck/BICEP/Keck upper bound on the vacuum tensor-to-scalar ratio that the model must satisfy."},{"cited_title":"Tensor Spectra Templates for Axion-Gauge Fields Dynamics during Inflation","cited_arxiv_id":"1812.03667","evidence_quote":"Supplies the log-normal template for the sourced tensor power spectrum and the width relation used in the analysis."}],"review_version":1}