Pith. sign in

REVIEW 3 major objections 5 minor 3 cited by

Comparative study of the strong backreaction regime in axion inflation: the effect of the potential

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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

Pith's one-line read Lattice simulations of seven inflationary potentials show the strong backreaction features of axion inflation are universal, with only the lengthening of inflation depending on the potential.

desk verdict A systematic, numerically careful extension of axion-inflation lattice results to seven potentials; the universality claim is qualitatively plausible but partly outruns the tested set and the fixed-background approximation. read the letter →

arxiv 2505.19950 v1 pith:FMNVM35R submitted 2025-05-26 astro-ph.CO hep-ph

Joanes Lizarraga , Carmelo López-Mediavilla , Ander Urio This is my paper
classification astro-ph.COhep-ph
keywords axioninflationstrongbackreactionelectromagneticslow-rolllatticesimulationsChern-Simonscouplinginflationarypotentialhomogeneousmagneticdominance
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 the strong backreaction regime of Abelian axion inflation behaves the same way regardless of which inflationary potential one chooses. Using full lattice simulations of seven single-field potentials, it argues that the electromagnetic slow-roll stage, the dominance of magnetic over electric energy, the one-bump evolution of the Hubble slow-roll parameter, and the failure of the homogeneous backreaction approximation all appear for every potential studied. The principal quantitative difference between potentials is the lengthening of inflation, measured as extra e-folds $N_{\mathrm{end}}$, which grows almost linearly with the axion-gauge coupling. The point of the claim is practical: reliable predictions in this regime must come from a fully inhomogeneous lattice treatment, for any potential.

What carries the argument

The central machinery is the lattice implementation of the Chern-Simons coupling $\frac{\alpha_\Lambda}{4}\frac{\phi}{m_p}F_{\mu\nu}\tilde F^{\mu\nu}$ on a fixed FLRW background, with the scale factor driven by volume-averaged energy densities through the Friedmann equations (2.22) and (2.23). The discretisation, based on a shift-symmetric and gauge-invariant action, evolves the axion and gauge fields with full spatial inhomogeneities, so the backreaction is local rather than averaged over modes. The key dynamical indicator is the Hubble slow-roll parameter $\epsilon_H = -\dot H/H^2$; its single bump followed by smooth growth defines the electromagnetic slow-roll stage, and the condition $\epsilon_H = 1$ marks the delayed end of inflation. Comparing this $\epsilon_H$ evolution, the energy-density decompositions, and $N_{\mathrm{end}}$ across seven potentials with the homogeneous backreaction scheme is what carries the universality and failure-of-homogeneity claims.

What would settle it

Extend the lattice code to include scalar metric perturbations and recompute $N_{\mathrm{end}}$ for the $\alpha$-attractor(4) potential at the largest coupling; if the extra e-folds change by more than the current 3–4% convergence uncertainty, or if the single-bump shape of $\epsilon_H$ disappears, the universality claim is refuted. A second, simpler check is to simulate a potential with a sharp step or oscillatory feature, which the paper did not include, and test whether the one-bump magnetic-dominated stage still appears.

Watch

Extended reading notes

Core claim

On its own terms, the paper's discovery is that the novel strong-backreaction features identified earlier for a quadratic potential are universal in $\phi F \tilde F$ Abelian axion inflation and independent of the specific form of the potential. Across natural, monodromy, Starobinsky, hilltop, chaotic, and two $\alpha$-attractor potentials, the lattice dynamics show the same qualitative sequence: backreaction onset produces a single bump in $\epsilon_H = -\dot H/H^2$, after which a magnetic-dominated electromagnetic slow-roll stage extends inflation until $\epsilon_H = 1$. In every case the gradient energy of the inflaton becomes comparable to and then exceeds its kinetic energy, reaching roughly ten percent of the total energy budget, and the number of extra e-folds $N_{\mathrm{end}}$ grows in a quasi-linear, universal-slope pattern with the coupling. The same comparison shows that the homogeneous backreaction approximation, in which the inflaton stays homogeneous and only the average of $\vec E \cdot \vec B$ feeds back, fails to reproduce these features for any of the potentials and shows no tendency to converge to the lattice result.

Load-bearing premise

The load-bearing premise is that a fixed FLRW background with volume-averaged Friedmann equations captures the expansion history; if the strong inhomogeneities, with gradient energy near ten percent of the total, source significant gravitational backreaction from metric perturbations, the extra e-folds and the claimed universality could change.

Editorial extensions

If this is right

  • For every potential simulated, the end of inflation is delayed by extra e-folds that grow almost linearly with the coupling, so the potential mainly sets the slope and hence the duration of inflation rather than the nature of the regime.
  • The homogeneous backreaction method predicts a qualitatively different dynamics: oscillatory bumps in $\epsilon_H$ and a clustered, non-linear dependence of $N_{\mathrm{end}}$ on coupling, confirming that it is not a reliable tool in the strong backreaction regime for any of the potentials.
  • Potentials cluster into three groups — natural/chaotic/$\alpha$-attractor(2), monodromy/Starobinsky/hilltop, and $\alpha$-attractor(4) — which is useful for choosing representative models in future simulations.
  • Because the lengthening of inflation shifts the number of e-folds before the end of inflation at which observable scales exit the horizon, phenomenological predictions for axion inflation must be computed case by case with local backreaction.
  • The near-universal power-law index $a \sim 1.2$ suggests that the functional form of the coupling growth of $N_{\mathrm{end}}$ is a generic feature of the model.

Reading between the lines

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

  • If the universality extends beyond the simulated couplings, then constraints on axion inflation derived from homogeneous backreaction may be systematically biased; the bias would be set mostly by the potential-dependent $N_{\mathrm{end}}$.
  • The universal power index $a \sim 1.2$ hints that $N_{\mathrm{end}}$ scales with $(\alpha_\Lambda - \alpha_{\Lambda,0})^{1.2}$ for reasons tied to the tachyonic instability rate rather than to potential shape; a direct test would be a potential engineered with a very different $\eta_V$ profile.
  • Since metric perturbations are neglected, a natural next step is to quantify gravitational backreaction from the roughly ten percent gradient energy; if it is significant, the universal picture could acquire corrections at the strongest couplings.
  • The same electromagnetic slow-roll mechanism may operate in models with non-Abelian gauge sectors or multiple axions, in which case the potential-independent features found here would anchor a broader universality class.
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

3 major / 5 minor

Summary. Lizarraga, López-Mediavilla, and Urio study the strong backreaction (SBR) regime of Abelian axion inflation, in which an axion inflaton is coupled to a U(1) gauge field through a Chern-Simons term. Using the CosmoLattice code modified for this model, they simulate seven single-field potentials (Chaotic, Natural, Monodromy, Starobinsky, Hilltop, α-attractor(2), α-attractor(4)) with couplings starting at a per-potential 'SBR-limit' and increasing in +5% steps up to +20%. They report that the qualitative features previously found for the quadratic potential—the electromagnetic slow-roll phase, magnetic dominance over the electric contribution, a single-bump evolution of ϵH, and the failure of homogeneous backreaction—are common to all seven potentials, and they quantify the extra e-folds Nend, fitting its growth with αΛ by a linear and a power-law form. They conclude that these features are universal and intrinsic to the model and independent of the potential, and they discuss observational implications. The paper includes full simulation parameters, convergence checks on ϵH at the end of inflation, and comparisons with homogeneous-backreaction runs for all potentials.

Significance. The paper makes a valuable systematic contribution. If the claimed universality holds, it would mean that SBR phenomenology (large extra e-folds, magnetic dominance, UV sensitivity) is controlled by the Chern-Simons coupling rather than the potential shape, which would simplify model-independent predictions for axion-inflation observables and strengthen the case against homogeneous approximations. The numerical study is carefully documented: all lattice parameters are tabulated, the resolution is varied to demonstrate convergence of ϵH to 1% (3–4% for α-attractor(4)), the code is based on the public CosmoLattice package, and the failure of homogeneous backreaction is demonstrated across all potentials rather than for a single benchmark. However, the strength of the conclusion is not matched by the evidence: the universality claim rests on seven specific potentials and on simulations that neglect metric perturbations, both of which are acknowledged limitations. These gaps are fixable in a revision.

major comments (3)
  1. [Sec. 3.1, Eq. (3.1)] Equation (3.1) for ϵH is inconsistent with the Friedmann equations as written. Combining Eqs. (2.7) and (2.8) gives ȧ? ȧ? = -a?/a - H^2 = -(3ρK+ρG+2ρEM)/(3m_p^2), so ϵH = -Hdot/H^2 = (3ρK+ρG+2ρEM)/ρtot = 1+(2ρK-ρV+ρEM)/ρtot, not 1+(2ρK-ρV+2ρEM)/ρtot as printed. Since ρEM is sizeable during the electromagnetic slow-roll phase, the coefficient error changes the value of the ϵH=1 crossing and thus all Nend entries in Table 3 and the fit parameters in Table 4 via Eqs. (3.2)-(3.3). Please state which expression was actually implemented in the code and, if the printed formula was used, recompute the affected results.
  2. [Sec. 2, Eqs. (2.22)-(2.23); Sec. 4] The central claim of potential independence is made within a fixed-FLRW approximation: the lattice matter sector evolves on a single scale factor a(t) satisfying volume-averaged Friedmann equations, with metric perturbations neglected. The authors acknowledge in Sec. 4 that metric perturbations are 'another issue to be considered.' Because gradient energy reaches about 10% of the total energy budget (Sec. 3.1), scalar metric perturbations can backreact on the local expansion and on the φ equation of motion; if this backreaction is potential-dependent, the observed pattern of Nend and the universality of the new features could be altered. I ask for either a quantitative estimate of metric backreaction (for example, by comparing the gradient-energy contribution to the scalar perturbation source terms) or a reformulation of the claim as holding within the homogeneous-background approximation.
  3. [Sec. 4] The conclusion that the features are 'universal in φF̃F Abelian axion inflation and independent of the specific form of the inflation potential' is stronger than the evidence supports. The study covers seven well-motivated potentials, but this is a finite sample, and no scaling argument is given to show that the SBR dynamics cannot depend on potential shape in some other realization. I recommend rephrasing to 'universal across the potentials considered' or adding an analytical argument for why the dynamics depends only on, e.g., the local slow-roll parameters at the onset of backreaction.
minor comments (5)
  1. [Fig. 5 caption] The caption states that the parameters of the linear fits are given in Tab. 2, but the fit parameters actually appear in Table 4; please correct the cross-reference.
  2. [Sec. 2.3] The SBR-limit is defined only by reference to the right panel of Fig. 7 of [43]. Please provide the operational criterion (e.g., the first coupling that produces a non-zero Nend without exiting inflation) so that the per-potential coupling ranges can be reproduced without consulting [43].
  3. [Sec. 2.1] Immediately after the definition of Ei there is a stray semicolon and comma ('˙Ai , ; E(2)'); please clean up this typo.
  4. [Table 1] The amplitude parameters for the α-attractor models are denoted Λ, the same symbol used for αΛ in Eq. (2.1); consider renaming one of them to avoid confusion.
  5. [Sec. 3.1, Table 4] The statement that the data 'seem to prefer... a common power index of a ∼ 1.2 for all potentials' is stronger than the quoted errors warrant; some exponents differ by more than 1σ (e.g., Starobinsky 1.243±0.047 versus α-attractor(2) 1.1656±0.0020). A brief comment on the consistency across fits would be helpful.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the universality claim rests on direct lattice simulations, while the curve fits and self-citations are descriptive or methodological rather than load-bearing.

full rationale

Walking the derivation chain: the paper integrates the discretised matter equations (2.19)-(2.21) together with the volume-averaged Friedmann equations (2.22)-(2.23) for seven potentials (Table 1) at five coupling values each (Table 2), and then reads off energy densities, epsilon_H (Eq. 3.1), and N_end (Table 3). The Sec. 4 conclusion that the electromagnetic slow-roll stage, magnetic dominance, one-bump epsilon_H evolution, and failure of homogeneous backreaction are universal is a comparison of those simulated outputs, not a quantity reconstructed from the inputs by definition. Equations (3.2)-(3.3) are explicitly presented as fits ('we propose two possible fits to interpolate the results'); they do not feed back into the universality claim, and the potential grouping is inferred from the simulated slopes, not from the fit being imposed. The SBR-limit is a normalization convention carried over from [43] to select comparable couplings; applying the same +5% to +20% increments is a methodological choice, not a prediction forced by the data. The homogeneous-backreaction failure is established by direct numerical comparison (Figs. 6-8) rather than by defining failure as disagreement, and the paper quantifies differences in N_end and in the oscillatory structure of epsilon_H. Self-citations [42,43] supply the lattice formulation, initialisation procedure, and code validation; as method references rather than theorems invoked to forbid alternatives, they are not load-bearing in the derivation of universality. The stated limitation that metric perturbations are left for future work ('The role of metric perturbations and their impact on the matter sector during the strong backreaction regime is another issue to be considered') is a possible threat to external validity of the universality claim, but it is not a circular step: the derivation does not assume what it concludes. No equation in the paper reduces to its own output, and no fitted parameter is renamed as a prediction. Hence no circularity is present.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claim rests on numerical simulations whose key inputs are the lattice discretisation, initial conditions, and the selected potentials. No new entities are introduced. The main data-fitted quantities are the SBR-limit couplings and the descriptive fits of Nend; these anchor the scan but do not by themselves force the qualitative universality.

free parameters (3)
  • SBR-limit coupling alpha_Lambda per potential = 12.6 (alpha-attractor(4)) to 20.8 (Hilltop)
    Data-dependent threshold defined in Sec. 2.3 as the minimum coupling giving extra e-folds without excursions out of inflation; it anchors the +5% to +20% scan and is not an externally fixed constant.
  • Linear fit slope m in Eq. (3.2) = 0.328 (Hilltop) to 1.422 (alpha-attractor(4))
    Fitted to the simulated Nend values in Table 4 to describe the relation between extra e-folds and coupling strength.
  • Power-law exponent a and coefficient b in Eq. (3.3) = a from 1.17 to 1.24; b from Table 4
    Two-parameter fits to the same Nend data; the near-common exponent a ~ 1.2 is used as evidence of a universal growth pattern.
assumptions (4)
  • domain assumption The matter sector can be evolved on a fixed FLRW background with volume-averaged Friedmann equations (Eqs. 2.22 and 2.23), neglecting metric perturbations.
    Sec. 2 and Sec. 4: the scale factor is solved from averaged energy densities; gravitational backreaction from inhomogeneities is not included and is deferred to future work.
  • domain assumption The hybrid lattice discretisation of Refs. [42,43,61] correctly represents the continuum dynamics within the stated tolerances.
    Sec. 2.1: the paper uses this discretisation and relies on previous validations; convergence is checked only for epsilon_H at the end of inflation.
  • domain assumption Initialising gauge fields with excited super-Hubble modes as in Ref. [43] does not bias the strong-backreaction dynamics.
    Sec. 2.1.1: the initialisation is a non-vacuum spectrum; the paper refers to [43] for validation rather than demonstrating independence here.
  • ad hoc to paper The seven selected potentials are representative enough to support a claim of independence from the choice of inflationary potential.
    Sec. 2.2: the set is well-motivated but finite; the abstract's 'universal' claim goes beyond the tested ensemble.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Comparative study of the strong backreaction regime in axion inflation: the effect of the potential." pith.science (2026). https://pith.science/paper/FMNVM35R

@misc{pith2026250519950,
  author       = {Pith},
  title        = {Pith review of: Comparative study of the strong backreaction regime in axion inflation: the effect of the potential},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FMNVM35R}},
  note         = {Machine review of arXiv:2505.19950}
}
read the original abstract

Recent works have demonstrated the necessity of capturing the local inhomogeneous physics in axion inflation, and showed new genuine features, most notably the extension of the inflationary period dictated by an electromagnetic slow-roll phase. In this work, we further investigate the model by performing a systematic study of the effect of the inflationary potential in the dynamics during the strong backreaction regime. The results indicate that the novel features associated with the local backreaction are universal and intrinsic to the model, hence independent on the choice of inflationary potential. We find that the main quantitative differences between the different choices manifest in the lengthening of inflation. We discuss the possible observational impact of this. Finally, we assess the possible reconciliation of the homogeneous backreaction method with fully inhomogeneous lattice techniques, and obtain that the former fails to provide a correct description for the regime studied in this work.

Discussion (0). Sign in to comment.

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Axion Inflation: Perturbative control in the strong backreaction regime

    astro-ph.CO 2026-08 conditional novelty 7.0 of 10

    Axion inflation with strong gauge-field backreaction is generically non-perturbative for ξ ≳ 2.5, yet a newly found steady 'mild backreaction' phase at large β can stay perturbatively controlled.

  2. CosmoLattice 2.0

    astro-ph.CO 2026-07 conditional novelty 6.0 of 10

    CosmoLattice v2.0 extends lattice cosmology simulations with non-minimal scalars, ALP–gauge couplings, defect networks, low-storage RK integrators, optimized GWs, and O(10) GPU speedups.

  3. The BAO-CMB Tension and Implications for Inflation

    astro-ph.CO 2025-07 accept novelty 5.0 of 10

    The upward shift in the scalar spectral index n_s in CMB+BAO analyses is driven by the combined effects of a known CMB degeneracy and the tension between CMB and DESI BAO data, not by new information about n_s itself.

Reference graph

Works this paper leans on

81 extracted references · 8 canonical work pages · cited by 3 Pith papers

  1. [43]

    Figueroa, J

    D.G. Figueroa, J. Lizarraga, N. Loayza, A. Urio and J. Urrestilla,Nonlinear dynamics of axion inflation: A detailed lattice study, Phys. Rev. D111 (2025) 063545 [2411.16368]

    arXiv 2025

  2. [1]

    Martin, C

    J. Martin, C. Ringeval and V. Vennin,Encyclopædia Inflationaris: Opiparous Edition, Phys. Dark Univ. 5-6 (2014) 75 [1303.3787]

    arXiv 2014

  3. [2]

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

    arXiv 2020

  4. [3]

    Lyth and A

    D.H. Lyth and A. Riotto,Particle physics models of inflation and the cosmological density perturbation, Phys. Rept. 314 (1999) 1 [hep-ph/9807278]

    arXiv 1999

  5. [4]

    Baumann,Inflation, inTheoretical Advanced Study Institute in Elementary Particle Physics: Physics of the Large and the Small, pp

    D. Baumann,Inflation, inTheoretical Advanced Study Institute in Elementary Particle Physics: Physics of the Large and the Small, pp. 523–686, 2011, DOI [0907.5424]

    arXiv 2011

  6. [5]

    Pajer and M

    E. Pajer and M. Peloso,A review of Axion Inflation in the era of Planck, Class. Quant. Grav. 30 (2013) 214002 [1305.3557]

    arXiv 2013

  7. [6]

    Baumann and L

    D. Baumann and L. McAllister,Inflation and String Theory, Cambridge Monographs on Mathematical Physics, Cambridge University Press (5, 2015), 10.1017/CBO9781316105733, [1404.2601]

    arXiv 2015

  8. [7]

    Freese, J.A

    K. Freese, J.A. Frieman and A.V. Olinto,Natural inflation with pseudo - Nambu-Goldstone bosons, Phys. Rev. Lett.65 (1990) 3233. – 22 –

    1990

Show all 81 references
  1. [8]

    Adams, J.R

    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 [hep-ph/9207245]

    1993 arXiv

  2. [9]

    Anber and L

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

    2006 arXiv

  3. [10]

    Anber and L

    M.M. Anber and L. Sorbo,Naturally inflating on steep potentials through electromagnetic dissipation, Phys. Rev. D81 (2010) 043534 [0908.4089]

    2010 arXiv

  4. [11]

    Turner and L.M

    M.S. Turner and L.M. Widrow,Gravitational Production of Scalar Particles in Inflationary Universe Models, Phys. Rev. D37 (1988) 3428

    1988

  5. [12]

    Garretson, G.B

    W.D. Garretson, G.B. Field and S.M. Carroll,Primordial magnetic fields from pseudoGoldstone bosons, Phys. Rev. D46 (1992) 5346 [hep-ph/9209238]

    1992 arXiv

  6. [13]

    Barnaby and M

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

    2011 arXiv

  7. [14]

    Adshead, E

    P. Adshead, E. Martinec and M. Wyman,Gauge fields and inflation: Chiral gravitational waves, fluctuations, and the Lyth bound, Phys. Rev. D88 (2013) 021302 [1301.2598]

    2013 arXiv

  8. [15]

    Cheng, W

    S.-L. Cheng, W. Lee and K.-W. Ng,Numerical study of pseudoscalar inflation with an axion-gauge field coupling, Phys. Rev. D93 (2016) 063510 [1508.00251]

    2016 arXiv

  9. [16]

    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

  10. [17]

    Cook and L

    J.L. Cook and L. Sorbo,Particle production during inflation and gravitational waves detectable by ground-based interferometers, Phys. Rev. D85 (2012) 023534 [1109.0022]

    2012 arXiv

  11. [18]

    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. D85 (2012) 023525 [1110.3327]

    2012 arXiv

  12. [19]

    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

  13. [20]

    Cook and L

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

    2013 arXiv

  14. [21]

    Bastero-Gil and A.T

    M. Bastero-Gil and A.T. Manso,Parity violating gravitational waves at the end of inflation, JCAP 08 (2023) 001 [2209.15572]

    2023 arXiv

  15. [22]

    Garcia-Bellido, A

    J. Garcia-Bellido, A. Papageorgiou, M. Peloso and L. Sorbo,A flashing beacon in axion inflation: recurring bursts of gravitational waves in the strong backreaction regime, JCAP 01 (2024) 034 [2303.13425]

    2024 arXiv

  16. [23]

    Adshead, J.T

    P. Adshead, J.T. Giblin, T.R. Scully and E.I. Sfakianakis,Gauge-preheating and the end of axion inflation, JCAP 12 (2015) 034 [1502.06506]

    2015 arXiv

  17. [24]

    Cuissa and D.G

    J.R.C. Cuissa and D.G. Figueroa,Lattice formulation of axion inflation. Application to preheating, JCAP 06 (2019) 002 [1812.03132]

    2019 arXiv

  18. [25]

    Adshead, J.T

    P. Adshead, J.T. Giblin, R. Grutkoski and Z.J. Weiner,Gauge preheating with full general relativity, JCAP 03 (2024) 017 [2311.01504]

    2024 arXiv

  19. [26]

    Adshead, J.T

    P. Adshead, J.T. Giblin and Z.J. Weiner,Gravitational waves from gauge preheating, Phys. Rev. D 98 (2018) 043525 [1805.04550]

    2018 arXiv

  20. [27]

    Adshead, J.T

    P. Adshead, J.T. Giblin, M. Pieroni and Z.J. Weiner,Constraining Axion Inflation with Gravitational Waves across 29 Decades in Frequency, Phys. Rev. Lett.124 (2020) 171301 [1909.12843]. – 23 –

    2020 arXiv

  21. [28]

    Adshead, J.T

    P. Adshead, J.T. Giblin, M. Pieroni and Z.J. Weiner,Constraining axion inflation with gravitational waves from preheating, Phys. Rev. D101 (2020) 083534 [1909.12842]

    2020 arXiv

  22. [29]

    Notari and K

    A. Notari and K. Tywoniuk,Dissipative Axial Inflation, JCAP 12 (2016) 038 [1608.06223]

    2016 arXiv

  23. [30]

    Dall’Agata, S

    G. Dall’Agata, S. González-Martín, A. Papageorgiou and M. Peloso,Warm dark energy, JCAP 08 (2020) 032 [1912.09950]

    2020 arXiv

  24. [31]

    Sobol, E.V

    O.O. Sobol, E.V. Gorbar and S.I. Vilchinskii,Backreaction of electromagnetic fields and the Schwinger effect in pseudoscalar inflation magnetogenesis, Phys. Rev. D100 (2019) 063523 [1907.10443]

    2019 arXiv

  25. [32]

    Domcke, V

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

    2020 arXiv

  26. [33]

    Gorbar, K

    E.V. Gorbar, K. Schmitz, O.O. Sobol and S.I. Vilchinskii,Gauge-field production during axion inflation in the gradient expansion formalism, Phys. Rev. D104 (2021) 123504 [2109.01651]

    2021 arXiv

  27. [34]

    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

  28. [35]

    Durrer, O

    R. Durrer, O. Sobol and S. Vilchinskii,Backreaction from gauge fields produced during inflation, Phys. Rev. D108 (2023) 043540 [2303.04583]

    2023 arXiv

  29. [36]

    von Eckardstein, M

    R. von Eckardstein, M. Peloso, K. Schmitz, O. Sobol and L. Sorbo,Axion inflation in the strong-backreaction regime: decay of the Anber-Sorbo solution, JHEP 11 (2023) 183 [2309.04254]

    2023 arXiv

  30. [37]

    Galanti, P

    D.C. Galanti, P. Conzinu, G. Marozzi and S. Santos da Costa,Gauge invariant quantum backreaction in U(1) axion inflation, Phys. Rev. D110 (2024) 123510 [2406.19960]

    2024 arXiv

  31. [38]

    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. D110 (2024) 043533 [2404.19694]

    2024 arXiv

  32. [39]

    von Eckardstein, K

    R. von Eckardstein, K. Schmitz and O. Sobol,On the Schwinger effect during axion inflation, JHEP 02 (2025) 096 [2408.16538]

    2025 arXiv

  33. [40]

    Caravano, E

    A. Caravano, E. Komatsu, K.D. Lozanov and J. Weller,Lattice simulations of Abelian gauge fields coupled to axions during inflation, Phys. Rev. D105 (2022) 123530 [2110.10695]

    2022 arXiv

  34. [41]

    Caravano, E

    A. Caravano, E. Komatsu, K.D. Lozanov and J. Weller,Lattice simulations of axion-U(1) inflation, Phys. Rev. D108 (2023) 043504 [2204.12874]

    2023 arXiv

  35. [42]

    Figueroa, J

    D.G. Figueroa, J. Lizarraga, A. Urio and J. Urrestilla,Strong Backreaction Regime in Axion Inflation, Phys. Rev. Lett.131 (2023) 151003 [2303.17436]

    2023 arXiv

  36. [44]

    Sharma, A

    R. Sharma, A. Brandenburg, K. Subramanian and A. Vikman,Lattice simulations of axion-U(1) inflation: gravitational waves, magnetic fields, and scalar statistics, 2411.04854

    arXiv

  37. [45]

    BICEP, Keck collaboration, Improved Constraints on Primordial Gravitational Waves using Planck, WMAP, and BICEP/Keck Observations through the 2018 Observing Season, Phys. Rev. Lett.127 (2021) 151301 [2110.00483]

    2021

  38. [46]

    Meerburg and E

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

    2013 arXiv

  39. [47]

    Linde, S

    A. Linde, S. Mooij and E. Pajer,Gauge field production in supergravity inflation: Local non-Gaussianity and primordial black holes, Phys. Rev. D87 (2013) 103506 [1212.1693]

    2013 arXiv

  40. [48]

    Anber and E

    M.M. Anber and E. Sabancilar,Hypermagnetic Fields and Baryon Asymmetry from Pseudoscalar Inflation, Phys. Rev. D92 (2015) 101501 [1507.00744]. – 24 –

    2015 arXiv

  41. [49]

    Domcke and K

    V. Domcke and K. Mukaida,Gauge Field and Fermion Production during Axion Inflation, JCAP 11 (2018) 020 [1806.08769]

    2018 arXiv

  42. [50]

    Domcke, Y

    V. Domcke, Y. Ema and K. Mukaida,Chiral Anomaly, Schwinger Effect, Euler-Heisenberg Lagrangian, and application to axion inflation, JHEP 02 (2020) 055 [1910.01205]

    2020 arXiv

  43. [51]

    Cado and M

    Y. Cado and M. Quirós,Numerical study of the Schwinger effect in axion inflation, Phys. Rev. D 106 (2022) 123527 [2208.10977]

    2022 arXiv

  44. [52]

    Domcke, Y

    V. Domcke, Y. Ema and S. Sandner,Perturbatively including inhomogeneities in axion inflation, JCAP 03 (2024) 019 [2310.09186]

    2024 arXiv

  45. [53]

    Fujita, K

    T. Fujita, K. Mukaida and T. Tsuji,Reheating after Axion Inflation, 2503.01228

    arXiv

  46. [54]

    He, K.-G

    J.-F. He, K.-G. Zhang, C. Fu and Z.-K. Guo,Strong backreaction of gauge quanta produced during inflation, Phys. Rev. D111 (2025) 103525 [2502.13158]

    2025 arXiv

  47. [55]

    J. Kume, M. Peloso and N. Bartolo,Revisiting the Chern-Simons interaction during inflation with a non-canonical pseudo-scalar, 2501.02890

  48. [56]

    Corbà,Gravitational wave anisotropies from axion inflation, 2504.13156

    S.P. Corbà,Gravitational wave anisotropies from axion inflation, 2504.13156

    arXiv

  49. [57]

    Özsoy, A

    O. Özsoy, A. Papageorgiou and M. Fasiello,Scale-dependent chirality as a smoking gun for Abelian gauge fields during inflation, JCAP 12 (2024) 008 [2405.14963]

    2024 arXiv

  50. [58]

    Corbà and L

    S.P. Corbà and L. Sorbo,Correlated scalar perturbations and gravitational waves from axion inflation, JCAP 10 (2024) 024 [2403.03338]

    2024 arXiv

  51. [59]

    Gorbar, A.I

    E.V. Gorbar, A.I. Momot, O.O. Prikhodko and O.M. Teslyk,Hydrodynamical approach to chirality production during axion inflation, Phys. Rev. D109 (2024) 023536 [2311.07429]

    2024 arXiv

  52. [60]

    C. Unal, A. Papageorgiou and I. Obata,Axion-gauge dynamics during inflation as the origin of pulsar timing array signals and primordial black holes, Phys. Lett. B856 (2024) 138873 [2307.02322]

    2024 arXiv

  53. [61]

    Figueroa and M

    D.G. Figueroa and M. Shaposhnikov,Lattice implementation of Abelian gauge theories with Chern–Simons number and an axion field, Nucl. Phys. B 926 (2018) 544 [1705.09629]

    2018 arXiv

  54. [62]

    Carpenter and C.A

    M.H. Carpenter and C.A. Kennedy,Third-order 2n-storage runge-kutta schemes with error control, 1994, https://api.semanticscholar.org/CorpusID:118434708

    1994

  55. [63]

    Carpenter and C.A

    M.H. Carpenter and C.A. Kennedy,Fourth-order 2n-storage runge-kutta schemes, 1994, https://api.semanticscholar.org/CorpusID:116658826

    1994

  56. [64]

    Figueroa, A

    D.G. Figueroa, A. Florio, T. Opferkuch and B.A. Stefanek,Lattice simulations of non-minimally coupled scalar fields in the Jordan frame, SciPost Phys. 15 (2023) 077 [2112.08388]

    2023 arXiv

  57. [65]

    Figueroa, A

    D.G. Figueroa, A. Florio, F. Torrenti and W. Valkenburg,The art of simulating the early Universe – Part I, JCAP 04 (2021) 035 [2006.15122]

    2021 arXiv

  58. [66]

    Figueroa, A

    D.G. Figueroa, A. Florio, F. Torrenti and W. Valkenburg,CosmoLattice: A modern code for lattice simulations of scalar and gauge field dynamics in an expanding universe, Comput. Phys. Commun. 283 (2023) 108586 [2102.01031]

    2023 arXiv

  59. [67]

    ACT collaboration, The Atacama Cosmology Telescope: DR6 Constraints on Extended Cosmological Models, 2503.14454

    arXiv

  60. [68]

    ACT collaboration, The Atacama Cosmology Telescope: DR6 Power Spectra, Likelihoods and ΛCDM Parameters, 2503.14452

    arXiv

  61. [69]

    Figueroa and N

    D.G. Figueroa and N. Loayza,Geometric reheating of the Universe, JCAP 03 (2025) 073 [2406.02689]

    2025 arXiv

  62. [70]

    Linde,Chaotic Inflation, Phys

    A.D. Linde,Chaotic Inflation, Phys. Lett. B129 (1983) 177. – 25 –

    1983

  63. [71]

    Freese,Natural Inflation, in37th Yamada Conference: Evolution of the Universe and its Observational Quest, pp

    K. Freese,Natural Inflation, in37th Yamada Conference: Evolution of the Universe and its Observational Quest, pp. 49–58, 6, 1993 [astro-ph/9310012]

    1993 arXiv

  64. [72]

    Silverstein and A

    E. Silverstein and A. Westphal,Monodromy in the CMB: Gravity Waves and String Inflation, Phys. Rev. D78 (2008) 106003 [0803.3085]

    2008 arXiv

  65. [73]

    Starobinsky,A New Type of Isotropic Cosmological Models Without Singularity, Phys

    A.A. Starobinsky,A New Type of Isotropic Cosmological Models Without Singularity, Phys. Lett. B 91 (1980) 99

    1980

  66. [74]

    Maeda,Towards the Einstein-Hilbert Action via Conformal Transformation, Phys

    K.-i. Maeda,Towards the Einstein-Hilbert Action via Conformal Transformation, Phys. Rev. D 39 (1989) 3159

    1989

  67. [75]

    Whitt,Fourth Order Gravity as General Relativity Plus Matter, Phys

    B. Whitt,Fourth Order Gravity as General Relativity Plus Matter, Phys. Lett. B145 (1984) 176

    1984

  68. [76]

    Kallosh and A

    R. Kallosh and A. Linde,Universality Class in Conformal Inflation, JCAP 07 (2013) 002 [1306.5220]

    2013 arXiv

  69. [77]

    Kallosh, A

    R. Kallosh, A. Linde and D. Roest,Superconformal Inflationaryα-Attractors, JHEP 11 (2013) 198 [1311.0472]

    2013 arXiv

  70. [78]

    Galante, R

    M. Galante, R. Kallosh, A. Linde and D. Roest,Unity of Cosmological Inflation Attractors, Phys. Rev. Lett.114 (2015) 141302 [1412.3797]

    2015 arXiv

  71. [79]

    Kallosh and A

    R. Kallosh and A. Linde,Planck, LHC, andα-attractors, Phys. Rev. D91 (2015) 083528 [1502.07733]

    2015 arXiv

  72. [80]

    Boubekeur and D.H

    L. Boubekeur and D.H. Lyth,Hilltop inflation, JCAP 07 (2005) 010 [hep-ph/0502047]

    2005 arXiv

  73. [81]

    Kallosh and A

    R. Kallosh and A. Linde,On hilltop and brane inflation after Planck, JCAP 09 (2019) 030 [1906.02156]. – 26 –

    2019 arXiv

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.