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Axion USR Inflation

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read An axion inflation model with an intermediate ultra slow-roll phase produces two peaks in the primordial curvature power spectrum, because the USR onset shuts off gauge-field production.

desk verdict Plausible new mechanism with a defensible qualitative picture, but the quantitative claims rest on an unchecked source truncation and unreported auxiliary functions; worth refereeing after the draft is finished. read the letter →

arxiv 2507.02685 v1 pith:4PW5DXML submitted 2025-07-03 astro-ph.CO gr-qchep-phhep-th

Alireza Talebian , Hassan Firouzjahi This is my paper
classification astro-ph.COgr-qchep-phhep-th PACS 98.80.Cq
keywords axioninflationultraslow-rollChern-Simonscouplinginversedecayinstabilityparameterprimordialpowerspectrumbispectrumblackholes
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 claims that inserting an ultra slow-roll (USR) phase into axion inflation terminates the inflationary production of gauge-field particles at the moment the USR phase begins. Because the instability parameter $\xi \equiv |\tilde{\alpha}|\sqrt{\epsilon/2}$ is proportional to the square root of the first slow-roll parameter and $\epsilon$ falls off exponentially during USR, the Chern-Simons sourced inverse-decay contribution to curvature perturbations stops effectively at that point. The total curvature power spectrum therefore has two separate peaks, one from gauge-field production at the scale leaving the horizon when USR starts and one from the standard USR enhancement. Between these peaks the spectrum rises steeply as $\mathcal{P}_{\mathcal{R}} \propto k^m$ with $m>4$, reaching $m \simeq 8.6$ in the plotted example with $\tilde{\alpha}=25$, and the bispectrum develops multiple non-trivial peaks. If correct, the model gives a concrete mechanism for a double-peaked, steeply rising curvature spectrum relevant to primordial black hole formation and induced gravitational waves while staying in the perturbative regime.

What carries the argument

The load-bearing object is the instability parameter $\xi \equiv |\tilde{\alpha}|\sqrt{\epsilon/2}$, which controls the tachyonic growth of one polarization of the gauge field and hence the strength of the inverse-decay source. During the USR phase $\epsilon$ falls off so quickly that $\xi$ decays exponentially, which effectively truncates the source integral at the onset of USR and shifts the lower bounds of the integrals $I_1$ and $I_2$ entering the effective function $f_2(\xi_k)$. The second essential piece is the gluing of perturbation mode functions across the two instantaneous transitions, controlled by the sharpness parameter $h$; this fixes the coefficients $\alpha_k^{(3)}$ and $\beta_k^{(3)}$ that appear in both the vacuum and sourced power spectra and determines the dip location and the relaxation to the final slow-roll attractor. The power spectrum formula combines the USR-amplified vacuum contribution with the gauge-sourced term proportional to $e^{4\pi\xi_k}f_2(\xi_k)$, while the bispectrum is built from a convolution integral $f_3$ over the same sourced mode functions.

What would settle it

Recompute the curvature power spectrum of the same model with a full numerical evolution of the gauge mode functions through the USR and second slow-roll phases instead of imposing the $\Theta(\tau_i-\tau')$ cutoff; if the first peak's amplitude or the extracted index $m$ at $\tilde{\alpha}=25$ changes appreciably, the central claim is refuted. A lattice simulation of axion-$U(1)$ inflation with an inflection-point potential could provide that check directly.

Watch

Extended reading notes

Core claim

The paper's central claim is that the gauge-field source for curvature perturbations in the three-stage SR-USR-SR axion setup is active only during the first slow-roll stage. When USR begins, $\epsilon(\tau) \propto \tau^6$ drives $\xi \propto \sqrt{\epsilon} \propto e^{-3\Delta N}$ down rapidly, so tachyonic gauge-field production and the inverse-decay process $A+A\to\delta\phi$ are effectively switched off, and the source can be parametrized as $J_k(\tau') \propto \Theta(\tau_i-\tau')$. The total power spectrum is then $\mathcal{P}_{\mathcal{R}}(k) = \mathcal{P}_{\rm CMB}(\xi_{\rm CMB}/\xi_i)^2 e^{6\Delta N}(36/h^2)|\alpha_k^{(3)}+\beta_k^{(3)}|^2 + \mathcal{P}_{\rm CMB} f_2(\xi_k) e^{4\pi\xi_k}$, with the gauge-field piece peaking at the wavenumber that exits around the USR onset. The paper shows that this spectrum has a dip at $-k_d\tau_i = \sqrt{5h/(4(h-6))}\,e^{-3\Delta N/2}$, followed by the universal $k^4$ growth, then a steeper $k^m$ growth with $m>4$ before the first peak, and a second USR-induced peak after it. It also computes the bispectrum and finds a non-Gaussianity parameter that peaks near the dip and can develop multiple peaks, with the local USR contribution $f_{\rm NL}^{\rm USR}=5h^2/(h-6)^2$ adding incoherently to the gauge-field contribution.

Load-bearing premise

The quantitative two-peak shape and the steep slope $m$ rest on the assumption that once the ultra slow-roll phase begins, the gauge field stops sourcing inflaton perturbations immediately, with no remaining production during the later slow-roll stage.

Editorial extensions

If this is right

  • The power spectrum in this model has two separate peaks: the gauge-induced peak at $\kappa=1$, the scale exiting at the USR onset, and the standard USR peak at $\kappa>1$; for couplings $20<\tilde{\alpha}<27$ the first peak can be larger than the second.
  • Between the dip and the first peak, the spectrum scales as $\mathcal{P}_{\mathcal{R}}\propto k^m$ with $m>4$, reaching $m\simeq 8.6$ in the plotted example and increasing with $\tilde{\alpha}$, which is steeper than the universal $k^4$ growth of ordinary USR models.
  • Because $\xi$ decays during USR, the backreaction parameters $\Omega_{\rm em}$ and $S_{\rm em}$ remain small, so this setup avoids the strong-backreaction and oscillatory regime that limits conventional axion inflation.
  • The total bispectrum is the sum of a local USR contribution and a gauge-induced contribution with non-trivial shape; the effective $f_{\rm NL}$ peaks near the dip in the power spectrum and can have multiple peaks as $\tilde{\alpha}$ increases.
  • The double-peaked, steeply rising spectrum is a candidate source for primordial black hole formation and induced gravitational waves, with an additional chiral gravitational wave component coming from the gauge sector.

Reading between the lines

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

  • Extension: relaxing the instantaneous SR1-to-USR and USR-to-SR2 transitions to smooth ones would likely smooth the first peak and reduce the slope $m$, since the sharpness parameter $h$ already controls the dip and post-USR relaxation.
  • Extension: the location of the first peak at $\kappa=1$ ties the peak scale to the position of the USR episode, so detecting a primordial black hole or gravitational wave signal from this model would directly probe the inflection-point scale of the axion potential.
  • Extension: the steep index $m>4$ makes the primordial black hole abundance extremely sensitive to the coupling $\tilde{\alpha}$, a sensitivity the paper does not quantify.
  • Extension: the gauge-induced $f_{\rm NL}$ near the dip implies that primordial black hole formation in this model proceeds under strongly non-Gaussian, scale-dependent statistics; whether that enhances or suppresses the abundance relative to Gaussian estimates is not computed here.
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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 a three-stage SR-USR-SR axion-inflation model with a Chern-Simons coupling to a U(1) gauge field. During the first slow-roll stage the instability parameter xi grows and tachyonic gauge-field production enhances curvature perturbations through inverse decay; once the USR phase starts, epsilon and hence xi ~ sqrt(epsilon) fall sharply, so gauge production is claimed to terminate efficiently. The authors compute the vacuum and sourced contributions to the curvature perturbation by piecing together mode functions across instantaneous transitions, and obtain a power spectrum with two peaks: a sourced peak near the start of USR and a standard USR peak, separated by a dip, with an intermediate steep scaling P_R ~ k^m with m > 4. They also present a bispectrum calculation and plots of the effective f_NL for the equilateral configuration.

Significance. If the central quantitative claims are confirmed, the model is interesting phenomenologically: it provides a concrete mechanism in which the USR phase not only enhances the vacuum curvature perturbation but also cuts off axion-gauge production, yielding a double-peaked power spectrum with a steep k^m region relevant for primordial black hole and induced gravitational wave studies. The qualitative two-peak picture follows cleanly from xi ~ sqrt(epsilon) falling during USR, and the background construction, backreaction checks, and mode-matching strategy are standard. The paper gives explicit parameter choices and analytic mode functions, and the claims are genuine consequences rather than being forced by construction. However, the quantitative results—m ~ 8.6, the first-peak amplitude, and the f_NL peaks—depend on matching coefficients and auxiliary functions that the manuscript does not report, so these numbers cannot currently be verified from the text.

major comments (4)
  1. [Section 4.2, Eqs. (4.27)-(4.30)] The central quantitative claim rests on the source truncation J_k(tau') proportional to Theta(tau_i - tau') introduced in Eq. (4.29). The justification given is qualitative: xi falls exponentially during USR and previously produced gauge fields dilute. But gauge modes amplified before tau_i have non-vanishing amplitudes after tau_i, and whether their continued inverse-decay contribution is negligible requires the matched coefficients c_2,3 and d_2,3 of Eqs. (3.9)-(3.10), which the manuscript explicitly does not report. Because the first-peak amplitude, the dip shape, the extracted slope m, and the f_NL peaks all depend on this cutoff, the quantitative signatures are currently supported by an assertion rather than by the matched solutions the paper derives. Please either report the matched coefficients and quantify the residual source for tau' > tau_i, or perform a numerical integration with the full gauge mode functions to validate the truncation.
  2. [Section 5, Eq. (5.11) and Figs. 7-9] The functions F_1(h,z_i,z_e) and F_2(h,z_i,z_e) in Eq. (5.11) are said to be 'too complicated to be insightful' and are not given. Since f_2(xi_k) in Eqs. (5.6), (5.14), and (5.19) is evaluated with these functions, the reported values of m ~ 8.6, the peak amplitudes, and the dip-to-peak ratios in Figs. 7-10 cannot be independently reproduced or checked. This is load-bearing for the paper's main quantitative claim. Please provide explicit formulas for F_1 and F_2, or an ancillary file with the numerical routines and benchmark values for the integrals in Eqs. (5.12)-(5.15).
  3. [Section 6, Eqs. (6.8)-(6.14)] The bispectrum formula (6.8) assumes the same xi_k for all three external momenta, which is only strictly valid for equilateral configurations. The paper acknowledges that only the equilateral shape is plotted because other shapes are numerically expensive, but the abstract and conclusions advertise 'non-trivial shapes and multiple peaks.' The multiple-peak claim is therefore demonstrated only for the equilateral configuration; please either state this limitation explicitly in the abstract and conclusions, or provide at least one representative non-equilateral shape to support the claim of non-trivial shape dependence.
  4. [Section 7, Summary] The summary states 'this can reach to m approx 8.6 for tilde alpha = 27', whereas Fig. 7 and the text in Section 5 report m approx 8.6 for tilde alpha = 25. This inconsistency affects the paper's headline number and must be corrected.
minor comments (5)
  1. [Section 5 and 6, editorial] The manuscript contains several draft artifacts, including duplicated figure captions and an inserted note 'CHECK and COMPARE above with (5.36)' in Section 5. These should be removed before submission.
  2. [Eq. (5.10)] The variable y in I(y, |r|, |r - k_hat|) is not explicitly defined; from the usage in Eq. (5.6) it is xi_k. Please state this after Eq. (5.10).
  3. [Eq. (4.32)] The approximate gauge mode function is stated to be valid for (8 xi_k)^{-1} less than about z less than about 2 xi_k, but the subsequent momentum integrals in Eqs. (4.39) and (5.6) are not restricted to this range. A brief comment on why the dominant contribution comes from this window would help.
  4. [Fig. 8 caption] The caption says the power spectrum exceeds unity for tilde alpha > 27 and perturbativity breaks down; the same statement appears in the text, but the figure itself does not show the breakdown. This is fine, but the reader should be told explicitly that the curve is intended to be extrapolated.
  5. [References] Reference [21] is cited for the dip formula Eq. (5.20); since that formula is used to locate the f_NL peak, please confirm that the cited derivation is consistent with the instantaneous-transition conventions used here.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the two-peak spectrum and k^m scaling are computed consequences of the SR1-USR-SR2 axion-gauge setup, not re-statements of its inputs.

full rationale

The paper's derivation chain is self-contained in the relevant sense: the model inputs are the potential parameters, the coupling tilde-alpha, the piecewise slow-roll parameter epsilon(tau), and the sharpness parameter h. From these inputs, the gauge mode functions are matched across the SR1-USR-SR2 boundaries, the sourced inflaton perturbation is computed through the retarded Green function, and the total power spectrum (5.19) is assembled from the vacuum contribution (5.4) and the inverse-decay contribution (5.14). The claimed features, namely the first peak at kappa = 1 and the steep intermediate scaling P_R proportional to k^m with m > 4, are numerical and analytical consequences of these expressions, not quantities that were defined into existence or fitted from the target data. The truncation J_k(tau') proportional to Theta(tau_i - tau') in Eq. (4.29) is a modeling assumption justified by the exponential falloff of the instability parameter during USR; it is a physical approximation that shapes the quantitative result, but it is not the result itself and it is not derived from the two-peak claim. The paper does cite the authors' own prior work for the USR matching coefficients (Eqs. 4.21-4.22, citing [72]) and for the USR non-Gaussianity formula (Eq. 6.7, citing [13,72]), and these citations are load-bearing in the sense of supplying standard USR machinery. However, the explicit formulas are stated in the paper, the cited results are independent published derivations, and they do not contain or assume the gauge-field-induced first peak or the extracted slope m. No uniqueness theorem from the authors is invoked to forbid alternatives, and no ansatz is smuggled in via self-citation. The main weakness, namely that the matched gauge-mode coefficients c_2,3 and d_2,3 and the functions F_1, F_2 are reported as 'too complicated to be useful' and omitted, is a reproducibility and verification concern, not circularity. The central claim therefore has independent content and is not forced by construction.

Assumptions & free parameters 7 free parameters · 8 assumptions · 0 invented entities

The model is a phenomenological construction: potential parameters, initial field value, coupling, and transition sharpness are chosen by hand to engineer SR-USR-SR with gauge production; no new particle or force is introduced. The analytic results rest on standard but idealized assumptions of instantaneous transitions, negligible backreaction, and truncating the source at τ_i.

free parameters (7)
  • V0 = 4e-10 M_Pl^4
    Global potential scale set to match COBE normalization P_CMB≈2.1e-9.
  • nu = sqrt(0.108) M_Pl
    Potential width parameter chosen for the inflection point geometry in Fig. 1.
  • lambda = 1.4349
    Tuned to create the inflection point and the intermediate USR phase.
  • initial field value phi_i = 3.614 M_Pl
    Initial condition chosen to give ~63 e-folds and USR around N=39-41.
  • tilde alpha (alpha/f_a) = 20 < tilde alpha < 27 (scanned)
    Chern-Simons coupling strength; controls gauge production amplitude and the scaling index m.
  • sharpness parameter h = -6 or -12 in figures
    Transition sharpness parameter; chosen, not predicted, and assumed to satisfy |h|>1.
  • USR duration Delta N = 2.3 or 2.7 e-folds in figures
    Duration of the USR phase, set by potential parameters; controls peak amplitudes.
assumptions (8)
  • ad hoc to paper Instantaneous transitions between SR1, USR, and SR2 phases.
    Section 4.1; enables analytic mode-function gluing and is acknowledged as idealized.
  • domain assumption Sharp transition with |h|>1 so the system quickly reaches the SR2 attractor.
    Section 2; mild transitions would wash out much of the USR non-Gaussianity.
  • domain assumption Negligible backreaction conditions Omega_em << 1 and S_em << 1.
    Section 3.1; verified numerically for the chosen parameter set, not for the full parameter space.
  • ad hoc to paper The gauge field source for inflaton perturbations is truncated at the start of USR, J_k ∝ Θ(τ_i-τ').
    Eq. (4.29); assumes inverse decay after USR begins is negligible.
  • domain assumption Gauge mode approximation (4.32) valid for 8ξ^-1 ≲ z ≲ 2ξ.
    Section 4.2.1; used in all source integrals for the power spectrum and bispectrum.
  • standard math Bunch-Davies initial condition and negligible inflaton mass V_ϕϕ << H^2.
    Section 4.1, Eq. (4.8); standard for subhorizon vacuum fluctuations.
  • domain assumption Common ξ_k for all three external momenta in the bispectrum calculation.
    Section 6; strictly valid only when |k1|=|k2|=|k3|, i.e. the equilateral configuration.
  • domain assumption Mean-field approximation for gauge field sources on the homogeneous background.
    Eqs. (2.4)-(2.5) and footnote 1; standard in axion-gauge inflation literature.

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Cite this review

Pith. "Pith review of Axion USR Inflation." pith.science (2026). https://pith.science/paper/4PW5DXML

@misc{pith2026250702685,
  author       = {Pith},
  title        = {Pith review of: Axion USR Inflation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4PW5DXML}},
  note         = {Machine review of arXiv:2507.02685}
}
abstract

We consider a model of inflation in which the inflaton field is a rolling axion with a potential which is flat enough to support an intermediate phase of USR inflation. Because of the Chern-Simons interaction, one polarization of the gauge field experiences the tachyonic growth during the first slow-roll stage, inducing large corrections in curvature perturbations via the inverse decay effect. A non-trivial feature of our setup is that once the system enters the USR phase, the instability parameter falls off rapidly, terminating the gauge field production efficiently. Consequently, the power spectrum involves two separate peaks, the first peak is induced by the gauge field particles production while the second peak is due to standard USR mechanism. We show that the power spectrum at the intermediate scales develops strong scale-dependence $\propto k^m$ with the index $m >4$. Calculating the bispectrum, we demonstrate that non-Gaussianities with non-trivial shapes and multiple peaks are generated in this setup.

Figures

Figures reproduced from arXiv: 2507.02685 by the authors.

Figure 1
Figure 1. Left: The scalar potential V (ϕ) (2.9). The parameters used are: V0 = 4 × 10−10M4 Pl, ν = √ 0.108MPl and λ = 1.4349. For these choices of parameters, the inflec￾tion point occurs at ϕ = 0.39MPl. Right: The behaviour of ϵ(N) with the initial field value ϕi = 3.614MPl. For these parameters the USR phase is sandwiched in the range 39 − 41 e-folds and inflation lasts for about 63 e-folds. 3 Production of Gauge Field Flu… view at source ↗
Figure 2
Figure 2. The behaviour of the instability parameter [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 4
Figure 4. The behaviours of the backreaction parameters [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figures from the paper (8 more)
Figure 5
Figure 5. Figure 5: Using interaction (2), Loop corrections to the power spectrum coming from inverse decay...... Diagrammatic representation of the one loop terms (5.3) and (5.6). Solid lines denote ￾￾ modes, while wiggly lines denote vector field A modes. The small bullets denote the in…
Figure 6
Figure 6. Figure 6: The effects of the USR phase on the power spectrum [PITH_FULL_IMAGE:figures/full_fig_p020_6.png]
Figure 7
Figure 7. Figure 7: The total power spectrum (5.19) vs κ ≡ k ki for the parameters ˜α = 25, h = −6 and ∆N = 2.7. There are two pronounced peaks: the first peak at κ = 1 is due to gauge field production while the second peak at κ > 1 corresponds to standard USR enhancement. The scaling of …
Figure 8
Figure 8. Figure 8: The scaling parameter m defined via PR ∝ k m for the power spectrum prior to the first peak in terms of the coupling ˜α. For ˜α > 27, the power spectrum exceeds unity and the perturbative treatment breaks down. • There is the plateau on large scales associated to the m…
Figure 9
Figure 9. Figure 9: The total power spectrum (5.19) in terms of κ for various coupling ˜α. For large ˜α, the contribution of the gauge field R (J) k may actually dominate over the contribution of the usual vacuum fluctuations R (vac) k . In our setup, the first peak associated to R (J) k …
Figure 10
Figure 10. Figure 10: The total power spectrum (5.19) for different values of h and ∆N while the dimensionless coupling ˜α = 25 is held fixed. The amplitudes of peaks are sensitive to the duration of the USR phase ∆N while they are less sensitive to the sharpness parameter h. In order to r…
Figure 11
Figure 11. Figure 11: The effective nonlinear parameter f eff NL (6.14) for the equilateral shape x2 = x3 = 1 in terms of κ. The location, shape, and number of peaks vary for different values of ˜α. The beginning of USR corresponds to κ = 1 after which f eff NL falls off quickly. 0.05 0.10…
Figure 12
Figure 12. Figure 12: The effective nonlinear parameter f eff NL (6.14) for the equilateral shape x2 = x3 = 1 for various coupling parameter ˜α. This is the same plot as in [PITH_FULL_IMAGE:figures/full_fig_p028_12.png]

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Reference graph

Works this paper leans on

97 extracted references · 6 canonical work pages · cited by 4 Pith papers

  1. [1]

    Akrami et al., Planck 2018 results

    Planck collaboration, Y. Akrami et al., Planck 2018 results. X. Constraints on inflation , Astron. Astrophys. 641 (2020) A10, [ 1807.06211]

    arXiv 2020

  2. [2]

    Komatsu et al., Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation , Astrophys

    WMAP collaboration, E. Komatsu et al., Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation , Astrophys. J. Suppl. 192 (2011) 18, [1001.4538]

    arXiv 2011

  3. [3]

    J. M. Maldacena, Non-Gaussian features of primordial fluctuations in single field inflationary models, JHEP 05 (2003) 013, [ astro-ph/0210603]

    arXiv 2003

  4. [4]

    W. H. Kinney, Horizon crossing and inflation with large eta , Phys. Rev. D 72 (2005) 023515, [gr-qc/0503017]

    arXiv 2005

  5. [5]

    M. H. Namjoo, H. Firouzjahi and M. Sasaki, Violation of non-Gaussianity consistency relation in a single field inflationary model , EPL 101 (2013) 39001, [ 1210.3692]

    arXiv 2013

  6. [6]

    Martin, H

    J. Martin, H. Motohashi and T. Suyama, Ultra Slow-Roll Inflation and the non-Gaussianity Consistency Relation, Phys. Rev. D 87 (2013) 023514, [ 1211.0083]

    arXiv 2013

  7. [7]

    M. J. P. Morse and W. H. Kinney, Large-η constant-roll inflation is never an attractor , Phys. Rev. D 97 (2018) 123519, [ 1804.01927]

    arXiv 2018

  8. [8]

    Dimopoulos, Ultra slow-roll inflation demystified , Phys

    K. Dimopoulos, Ultra slow-roll inflation demystified , Phys. Lett. B 775 (2017) 262–265, [1707.05644]

    arXiv 2017

Show all 97 references
  1. [9]

    X. Chen, H. Firouzjahi, M. H. Namjoo and M. Sasaki, Fluid Inflation , JCAP 09 (2013) 012, [1306.2901]

    2013 arXiv

  2. [10]

    X. Chen, H. Firouzjahi, M. H. Namjoo and M. Sasaki, A Single Field Inflation Model with Large Local Non-Gaussianity, EPL 102 (2013) 59001, [ 1301.5699]

    2013 arXiv

  3. [11]

    X. Chen, H. Firouzjahi, E. Komatsu, M. H. Namjoo and M. Sasaki, In-in and δN calculations of the bispectrum from non-attractor single-field inflation , JCAP 12 (2013) 039, [ 1308.5341]

    2013 arXiv

  4. [12]

    Akhshik, H

    M. Akhshik, H. Firouzjahi and S. Jazayeri, Cosmological Perturbations and the Weinberg Theorem, JCAP 12 (2015) 027, [ 1508.03293]. 30

    2015 arXiv

  5. [13]

    Y.-F. Cai, X. Chen, M. H. Namjoo, M. Sasaki, D.-G. Wang and Z. Wang, Revisiting non-Gaussianity from non-attractor inflation models , JCAP 05 (2018) 012, [ 1712.09998]

    2018 arXiv

  6. [14]

    Mooij and G

    S. Mooij and G. A. Palma, Consistently violating the non-Gaussian consistency relation , JCAP 11 (2015) 025, [ 1502.03458]

    2015 arXiv

  7. [15]

    Bravo, S

    R. Bravo, S. Mooij, G. A. Palma and B. Pradenas, A generalized non-Gaussian consistency relation for single field inflation , JCAP 05 (2018) 024, [ 1711.02680]

    2018 arXiv

  8. [16]

    Pi and M

    S. Pi and M. Sasaki, Logarithmic Duality of the Curvature Perturbation , Phys. Rev. Lett. 131 (2023) 011002, [ 2211.13932]

    2023 arXiv

  9. [17]

    Ivanov, P

    P. Ivanov, P. Naselsky and I. Novikov, Inflation and primordial black holes as dark matter , Phys. Rev. D 50 (1994) 7173–7178

    1994

  10. [18]

    Garcia-Bellido and E

    J. Garcia-Bellido and E. Ruiz Morales, Primordial black holes from single field models of inflation, Phys. Dark Univ. 18 (2017) 47–54, [ 1702.03901]

    2017 arXiv

  11. [19]

    Germani and T

    C. Germani and T. Prokopec, On primordial black holes from an inflection point , Phys. Dark Univ. 18 (2017) 6–10, [ 1706.04226]

    2017 arXiv

  12. [20]

    Biagetti, G

    M. Biagetti, G. Franciolini, A. Kehagias and A. Riotto, Primordial Black Holes from Inflation and Quantum Diffusion , JCAP 07 (2018) 032, [ 1804.07124]

    2018 arXiv

  13. [21]

    Firouzjahi and A

    H. Firouzjahi and A. Talebian, Induced gravitational waves from ultra slow-roll inflation and pulsar timing arrays observations , JCAP 10 (2023) 032, [ 2307.03164]

    2023 arXiv

  14. [22]

    M. Y. Khlopov, Primordial Black Holes , Res. Astron. Astrophys. 10 (2010) 495–528, [0801.0116]

    2010 arXiv

  15. [23]

    ¨Ozsoy and G

    O. ¨Ozsoy and G. Tasinato, Inflation and Primordial Black Holes , Universe 9 (2023) 203, [2301.03600]

    2023 arXiv

  16. [24]

    C. T. Byrnes and P. S. Cole, Lecture notes on inflation and primordial black holes , 12, 2021, 2112.05716

    2021 arXiv

  17. [25]

    Escriv` a, F

    A. Escriv` a, F. Kuhnel and Y. Tada,Primordial Black Holes , 2211.05767

    arXiv

  18. [26]

    Pi, Non-Gaussianities in primordial black hole formation and induced gravitational waves , 2404.06151

    S. Pi, Non-Gaussianities in primordial black hole formation and induced gravitational waves , 2404.06151

    arXiv

  19. [27]

    Freese, J

    K. Freese, J. A. Frieman and A. V. Olinto, Natural inflation with pseudo - Nambu-Goldstone bosons, Phys. Rev. Lett. 65 (1990) 3233–3236

    1990

  20. [28]

    F. C. Adams, J. R. Bond, K. Freese, J. A. Frieman and A. V. Olinto, Natural inflation: Particle physics models, power law spectra for large scale structure, and constraints from COBE, Phys. Rev. D 47 (1993) 426–455, [ hep-ph/9207245]

    1993 arXiv

  21. [29]

    J. E. Kim, H. P. Nilles and M. Peloso, Completing natural inflation , JCAP 01 (2005) 005, [hep-ph/0409138]. 31

    2005 arXiv

  22. [30]

    Dimopoulos, S

    S. Dimopoulos, S. Kachru, J. McGreevy and J. G. Wacker, N-flation, JCAP 08 (2008) 003, [hep-th/0507205]

    2008 arXiv

  23. [31]

    Easther and L

    R. Easther and L. McAllister, Random matrices and the spectrum of N-flation , JCAP 05 (2006) 018, [ hep-th/0512102]

    2006 arXiv

  24. [32]

    McAllister, E

    L. McAllister, E. Silverstein and A. Westphal, Gravity Waves and Linear Inflation from Axion Monodromy, Phys. Rev. D 82 (2010) 046003, [ 0808.0706]

    2010 arXiv

  25. [33]

    Kaloper and L

    N. Kaloper and L. Sorbo, A Natural Framework for Chaotic Inflation , Phys. Rev. Lett. 102 (2009) 121301, [ 0811.1989]

    2009 arXiv

  26. [34]

    Flauger, L

    R. Flauger, L. McAllister, E. Pajer, A. Westphal and G. Xu, Oscillations in the CMB from Axion Monodromy Inflation , JCAP 06 (2010) 009, [ 0907.2916]

    2010 arXiv

  27. [35]

    Arkani-Hamed, H.-C

    N. Arkani-Hamed, H.-C. Cheng, P. Creminelli and L. Randall, Extra natural inflation , Phys. Rev. Lett. 90 (2003) 221302, [ hep-th/0301218]

    2003 arXiv

  28. [36]

    R. D. Peccei and H. R. Quinn, CP Conservation in the Presence of Instantons , Phys. Rev. Lett. 38 (1977) 1440–1443

    1977

  29. [37]

    Weinberg, A New Light Boson? , Phys

    S. Weinberg, A New Light Boson? , Phys. Rev. Lett. 40 (1978) 223–226

    1978

  30. [38]

    Wilczek, Problem of Strong P and T Invariance in the Presence of Instantons , Phys

    F. Wilczek, Problem of Strong P and T Invariance in the Presence of Instantons , Phys. Rev. Lett. 40 (1978) 279–282

    1978

  31. [39]

    Preskill, M

    J. Preskill, M. B. Wise and F. Wilczek, Cosmology of the Invisible Axion , Phys. Lett. B 120 (1983) 127–132

    1983

  32. [40]

    L. F. Abbott and P. Sikivie, A Cosmological Bound on the Invisible Axion , Phys. Lett. B 120 (1983) 133–136

    1983

  33. [41]

    Dine and W

    M. Dine and W. Fischler, The Not So Harmless Axion , Phys. Lett. B 120 (1983) 137–141

    1983

  34. [42]

    Sikivie, Experimental Tests of the Invisible Axion , Phys

    P. Sikivie, Experimental Tests of the Invisible Axion , Phys. Rev. Lett. 51 (1983) 1415–1417

    1983

  35. [43]

    K. Choi, S. H. Im and C. Sub Shin, Recent Progress in the Physics of Axions and Axion-Like Particles, Ann. Rev. Nucl. Part. Sci. 71 (2021) 225–252, [ 2012.05029]

    2021 arXiv

  36. [44]

    L. Hui, J. P. Ostriker, S. Tremaine and E. Witten, Ultralight scalars as cosmological dark matter, Phys. Rev. D 95 (2017) 043541, [ 1610.08297]

    2017 arXiv

  37. [45]

    C. B. Adams et al., Axion Dark Matter , in Snowmass 2021 , 3, 2022, 2203.14923

    2021 arXiv

  38. [46]

    M. M. Anber and L. Sorbo, N-flationary magnetic fields , JCAP 10 (2006) 018, [astro-ph/0606534]

    2006 arXiv

  39. [47]

    M. M. Anber and L. Sorbo, Naturally inflating on steep potentials through electromagnetic dissipation, Phys. Rev. D 81 (2010) 043534, [ 0908.4089]

    2010 arXiv

  40. [48]

    M. M. Anber and L. Sorbo, Non-Gaussianities and chiral gravitational waves in natural steep inflation, Phys. Rev. D 85 (2012) 123537, [ 1203.5849]. 32

    2012 arXiv

  41. [49]

    Barnaby and M

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

    2011 arXiv

  42. [50]

    Barnaby, R

    N. Barnaby, R. Namba and M. Peloso, Phenomenology of a Pseudo-Scalar Inflaton: Naturally Large Nongaussianity, JCAP 04 (2011) 009, [ 1102.4333]

    2011 arXiv

  43. [51]

    Barnaby, E

    N. Barnaby, E. Pajer and M. Peloso, Gauge Field Production in Axion Inflation: Consequences for Monodromy, non-Gaussianity in the CMB, and Gravitational Waves at Interferometers, Phys. Rev. D 85 (2012) 023525, [ 1110.3327]

    2012 arXiv

  44. [52]

    Peloso, L

    M. Peloso, L. Sorbo and C. Unal, Rolling axions during inflation: perturbativity and signatures, JCAP 09 (2016) 001, [ 1606.00459]

    2016 arXiv

  45. [53]

    P. D. Meerburg and E. Pajer, Observational Constraints on Gauge Field Production in Axion Inflation, JCAP 02 (2013) 017, [ 1203.6076]

    2013 arXiv

  46. [54]

    Durrer, R

    R. Durrer, R. von Eckardstein, D. Garg, K. Schmitz, O. Sobol and S. Vilchinskii, Scalar perturbations from inflation in the presence of gauge fields , Phys. Rev. D 110 (2024) 043533, [2404.19694]

    2024 arXiv

  47. [55]

    Linde, S

    A. Linde, S. Mooij and E. Pajer, Gauge field production in supergravity inflation: Local non-Gaussianity and primordial black holes , Phys. Rev. D 87 (2013) 103506, [ 1212.1693]

    2013 arXiv

  48. [56]

    Bugaev and P

    E. Bugaev and P. Klimai, Axion inflation with gauge field production and primordial black holes, Phys. Rev. D 90 (2014) 103501, [ 1312.7435]

    2014 arXiv

  49. [57]

    Talebian, A

    A. Talebian, A. Nassiri-Rad and H. Firouzjahi, Stochastic effects in axion inflation and primordial black hole formation , Phys. Rev. D 105 (2022) 103516, [ 2202.02062]

    2022 arXiv

  50. [58]

    Talebian, S

    A. Talebian, S. A. Hosseini Mansoori and H. Firouzjahi, Inflation from Multiple Pseudo-scalar Fields: Primordial Black Hole Dark Matter and Gravitational Waves , Astrophys. J. 948 (2023) 48, [ 2210.13822]

    2023 arXiv

  51. [59]

    J. L. Cook and L. Sorbo, Particle production during inflation and gravitational waves detectable by ground-based interferometers, Phys. Rev. D 85 (2012) 023534, [ 1109.0022]

    2012 arXiv

  52. [60]

    Domcke, M

    V. Domcke, M. Pieroni and P. Bin´ etruy,Primordial gravitational waves for universality classes of pseudoscalar inflation , JCAP 06 (2016) 031, [ 1603.01287]

    2016 arXiv

  53. [61]

    Sorbo, Parity violation in the Cosmic Microwave Background from a pseudoscalar inflaton , JCAP 06 (2011) 003, [ 1101.1525]

    L. Sorbo, Parity violation in the Cosmic Microwave Background from a pseudoscalar inflaton , JCAP 06 (2011) 003, [ 1101.1525]

    2011 arXiv

  54. [62]

    Barnaby, J

    N. Barnaby, J. Moxon, R. Namba, M. Peloso, G. Shiu and P. Zhou, Gravity waves and non-Gaussian features from particle production in a sector gravitationally coupled to the inflaton, Phys. Rev. D 86 (2012) 103508, [ 1206.6117]

    2012 arXiv

  55. [63]

    Namba, M

    R. Namba, M. Peloso, M. Shiraishi, L. Sorbo and C. Unal, Scale-dependent gravitational waves from a rolling axion , JCAP 01 (2016) 041, [ 1509.07521]. 33

    2016 arXiv

  56. [64]

    Garcia-Bellido, M

    J. Garcia-Bellido, M. Peloso and C. Unal, Gravitational waves at interferometer scales and primordial black holes in axion inflation , JCAP 12 (2016) 031, [ 1610.03763]

    2016 arXiv

  57. [65]

    Obata and J

    I. Obata and J. Soda, Oscillating Chiral Tensor Spectrum from Axionic Inflation , Phys. Rev. D 94 (2016) 044062, [ 1607.01847]

    2016 arXiv

  58. [66]

    Dimastrogiovanni, M

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

    2017 arXiv

  59. [67]

    Dimastrogiovanni, M

    E. Dimastrogiovanni, M. Fasiello, R. J. Hardwick, H. Assadullahi, K. Koyama and D. Wands, Non-Gaussianity from Axion-Gauge Fields Interactions during Inflation , JCAP 11 (2018) 029, [1806.05474]

    2018 arXiv

  60. [68]

    M. A. Gorji, S. A. Hosseini Mansoori and H. Firouzjahi, Inflation with multiple vector fields and non-Gaussianities , JCAP 11 (2020) 041, [ 2008.08195]

    2020 arXiv

  61. [69]

    Salehian, M

    B. Salehian, M. A. Gorji, S. Mukohyama and H. Firouzjahi, Analytic study of dark photon and gravitational wave production from axion , JHEP 05 (2021) 043, [ 2007.08148]

    2021 arXiv

  62. [70]

    Talebian, A

    A. Talebian, A. Nassiri-Rad and H. Firouzjahi, Revisiting magnetogenesis during inflation , Phys. Rev. D 102 (2020) 103508, [ 2007.11066]

    2020 arXiv

  63. [71]

    Brandenburg, O

    A. Brandenburg, O. Iarygina, E. I. Sfakianakis and R. Sharma, Magnetogenesis from axion-SU(2) inflation , JCAP 12 (2024) 057, [ 2408.17413]

    2024 arXiv

  64. [72]

    Firouzjahi, One-loop corrections in power spectrum in single field inflation , JCAP 10 (2023) 006, [ 2303.12025]

    H. Firouzjahi, One-loop corrections in power spectrum in single field inflation , JCAP 10 (2023) 006, [ 2303.12025]

    2023 arXiv

  65. [73]

    Firouzjahi, Revisiting loop corrections in single field ultraslow-roll inflation , Phys

    H. Firouzjahi, Revisiting loop corrections in single field ultraslow-roll inflation , Phys. Rev. D 109 (2024) 043514, [ 2311.04080]

    2024 arXiv

  66. [74]

    Talebian, A

    A. Talebian, A. Nassiri-Rad and H. Firouzjahi, Stochastic Effects in Anisotropic Inflation , Phys. Rev. D 101 (2020) 023524, [ 1909.12773]

    2020 arXiv

  67. [75]

    Talebian, A

    A. Talebian, A. Nassiri-Rad and H. Firouzjahi, Primordial helical magnetic fields from inflation?, Phys. Rev. D 105 (2022) 023528, [ 2111.02147]

    2022 arXiv

  68. [76]

    H. V. Ragavendra, P. Saha, L. Sriramkumar and J. Silk, Primordial black holes and secondary gravitational waves from ultraslow roll and punctuated inflation , Phys. Rev. D 103 (2021) 083510, [2008.12202]

    2021 arXiv

  69. [77]

    Taoso and A

    M. Taoso and A. Urbano, Non-gaussianities for primordial black hole formation , JCAP 08 (2021) 016, [ 2102.03610]

    2021 arXiv

  70. [78]

    Cheng, D.-S

    S.-L. Cheng, D.-S. Lee and K.-W. Ng, Power spectrum of primordial perturbations during ultra-slow-roll inflation with back reaction effects , Phys. Lett. B 827 (2022) 136956, [2106.09275]

    2022 arXiv

  71. [79]

    Iacconi, D

    L. Iacconi, D. Mulryne and D. Seery, Loop corrections in the separate universe picture , JCAP 06 (2024) 062, [ 2312.12424]. 34

    2024 arXiv

  72. [80]

    Yang, Y.-X

    W. Yang, Y.-X. Kang, A. Ali, T.-T. Sui, C.-H. Wu and Y.-P. Hu, Primordial black holes and secondary gravitational waves from the inflation potential with a tiny Lorentz function bump , 2403.15979

  73. [81]

    Franciolini, A

    G. Franciolini, A. Iovino, Junior., M. Taoso and A. Urbano, Perturbativity in the presence of ultraslow-roll dynamics, Phys. Rev. D 109 (2024) 123550, [ 2305.03491]

    2024 arXiv

  74. [82]

    F. L. Bezrukov and M. Shaposhnikov, The Standard Model Higgs boson as the inflaton , Phys. Lett. B 659 (2008) 703–706, [ 0710.3755]

    2008 arXiv

  75. [83]

    Garcia-Bellido, D

    J. Garcia-Bellido, D. G. Figueroa and J. Rubio, Preheating in the Standard Model with the Higgs-Inflaton coupled to gravity , Phys. Rev. D 79 (2009) 063531, [ 0812.4624]

    2009 arXiv

  76. [84]

    Caravano, E

    A. Caravano, E. Komatsu, K. D. Lozanov and J. Weller, Lattice simulations of axion-U(1) inflation, Phys. Rev. D 108 (2023) 043504, [ 2204.12874]

    2023 arXiv

  77. [85]

    Cheng, W

    S.-L. Cheng, W. Lee and K.-W. Ng, Numerical study of pseudoscalar inflation with an axion-gauge field coupling , Phys. Rev. D 93 (2016) 063510, [ 1508.00251]

    2016 arXiv

  78. [86]

    Domcke, V

    V. Domcke, V. Guidetti, Y. Welling and A. Westphal, Resonant backreaction in axion inflation, JCAP 09 (2020) 009, [ 2002.02952]

    2020 arXiv

  79. [87]

    Peloso and L

    M. Peloso and L. Sorbo, Instability in axion inflation with strong backreaction from gauge modes, JCAP 01 (2023) 038, [ 2209.08131]

    2023 arXiv

  80. [88]

    Kristiano and J

    J. Kristiano and J. Yokoyama, Constraining Primordial Black Hole Formation from Single-Field Inflation , Phys. Rev. Lett. 132 (2024) 221003, [ 2211.03395]

    2024 arXiv

  81. [89]

    C. T. Byrnes, P. S. Cole and S. P. Patil, Steepest growth of the power spectrum and primordial black holes , JCAP 06 (2019) 028, [ 1811.11158]

    2019 arXiv

  82. [90]

    P. S. Cole, A. D. Gow, C. T. Byrnes and S. P. Patil, Smooth vs instant inflationary transitions: steepest growth re-examined and primordial black holes , JCAP 05 (2024) 022, [ 2204.07573]

    2024 arXiv

  83. [91]

    Carrilho, K

    P. Carrilho, K. A. Malik and D. J. Mulryne, Dissecting the growth of the power spectrum for primordial black holes , Phys. Rev. D 100 (2019) 103529, [ 1907.05237]

    2019 arXiv

  84. [92]

    ¨Ozsoy and G

    O. ¨Ozsoy and G. Tasinato, Consistency conditions and primordial black holes in single field inflation, Phys. Rev. D 105 (2022) 023524, [ 2111.02432]

    2022 arXiv

  85. [93]

    Pi and J

    S. Pi and J. Wang, Primordial black hole formation in Starobinsky’s linear potential model , JCAP 06 (2023) 018, [ 2209.14183]

    2023 arXiv

  86. [94]

    Briaud, A

    V. Briaud, A. Karam, N. Koivunen, E. Tomberg, H. Veerm¨ ae and V. Vennin, How deep is the dip and how tall are the wiggles in inflationary power spectra? , JCAP 05 (2025) 097, [2501.14681]

    2025 arXiv

  87. [95]

    Cai, X.-H

    Y.-F. Cai, X.-H. Ma, M. Sasaki, D.-G. Wang and Z. Zhou, Highly non-Gaussian tails and primordial black holes from single-field inflation , JCAP 12 (2022) 034, [ 2207.11910]. 35

    2022 arXiv

  88. [96]

    Firouzjahi and A

    H. Firouzjahi and A. Riotto, Sign of non-Gaussianity and the primordial black holes abundance, Phys. Rev. D 108 (2023) 123504, [ 2309.10536]

    2023 arXiv

  89. [97]

    M. H. Namjoo and B. Nikbakht, Non-Gaussianity consistency relations and their consequences for the peaks, JCAP 08 (2024) 005, [ 2401.12958]. 36

    2024 arXiv

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