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arxiv: 2605.28752 · v2 · pith:DUJH37A4new · submitted 2026-05-27 · ✦ hep-th · astro-ph.CO· gr-qc

Inflation with vector fields revisited: non-Gaussianities

Chong-Bin Chen This is my paper

Pith reviewed 2026-06-29 10:57 UTC · model grok-4.3

classification ✦ hep-th astro-ph.COgr-qc
keywords inflationvector fieldsbispectrumnon-Gaussianitieseffective field theorycurvature perturbationskinetic couplingisotropic background
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The pith

The bispectrum distinguishes vector-supported inflation even for an exactly isotropic background.

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

The paper organizes inflation with kinetically coupled vector fields around a parameter h that measures the vector kinetic energy relative to the scalar field. In the strong-vector regime h much greater than one, it derives an effective theory by integrating out a heavy entropic mode, leaving a curvature perturbation with imaginary sound speed that grows transiently before horizon crossing. This produces bispectrum contributions scaling as h cubed and h squared in flattened shapes plus a local projection scaling as h, unlike the small-h regime where a local signal grows as h squared times N_K cubed. Their competition means the dominant shape switches from local at intermediate h to flattened at larger h. A reader would care because this shape dependence offers a way to detect vector dynamics in the primordial perturbations without requiring any anisotropy in the background.

Core claim

For h much greater than one the entropic perturbation is integrated out to obtain a low-energy effective theory for the curvature mode, which then has an imaginary sound speed and undergoes transient growth before horizon crossing. In addition to the known flattened-enhanced signals scaling as h cubed, this yields a flattened-enhanced signal scaling as h squared and a pronounced local projection scaling as h. Their competition produces a local-dominated bispectrum for intermediate h and a flattened-dominated signal at larger h.

What carries the argument

The parameter h measuring the vector kinetic contribution relative to the scalar field, together with the low-energy EFT obtained by integrating out the heavy entropic perturbation.

If this is right

  • In the large-h regime the bispectrum receives flattened contributions scaling as h cubed and h squared in addition to a local contribution scaling as h.
  • The dominant shape switches from local at intermediate h to flattened at larger h.
  • This shape dependence persists even though the background remains exactly isotropic.
  • The small-h regime instead produces a local-type signal enhanced by h squared N_K cubed with persistent vector transfer outside the horizon.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • CMB bispectrum measurements could in principle bound the allowed range of h without needing to detect background anisotropy.
  • The transient growth phase before horizon crossing might produce scale-dependent features in the power spectrum or higher correlators that could be searched for separately.
  • Similar EFT reductions might apply to other kinetically coupled multi-field models where one mode becomes heavy.

Load-bearing premise

For large h the entropic perturbation can be integrated out without leaving residual effects on the curvature mode.

What would settle it

A direct computation of the mode functions or the bispectrum for large but finite h that shows either no imaginary sound speed, no transient growth, or bispectrum scalings that fail to match the predicted h, h squared, and h cubed coefficients.

Figures

Figures reproduced from arXiv: 2605.28752 by Chong-Bin Chen.

Figure 1
Figure 1. Figure 1: FIG. 1: (left) Vertex of exchanging [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Correlations of the [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Correlations of the [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Projected amplitudes of the flattened-enhanced bulk interactions, shown without the [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Projected amplitudes of the [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Total projected amplitudes after restoring all coefficients Λ [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Total shape function at [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
read the original abstract

We revisit the resulting bispectrum of inflation with kinetic-coupled vector fields by organizing the dynamics in terms of $h$, which measures the vector kinetic contribution relative to that of the scalar field. We evaluate the bispectrum in the strong-vector regime and derive a low-energy effective field theory (EFT) for the large-$h$ regime. For $h\gg1$, the entropic perturbation becomes heavy and can be integrated out; the remaining curvature mode has an imaginary sound speed and undergoes transient growth before horizon crossing. In contrast to $h\ll1$ regime, where transfer from the vector sector persists outside the horizon and produces a local-type contribution enhanced as $h^2N_K^3$, we find that in addition to the known flattened-enhanced signals scaling as $h^3$, a flattened-enhanced signal scaling as $h^2$ and a pronounced local projection scaling as $h$ are present. Their competition yields a local-dominated signal for intermediate $h$ and a flattened-dominated signal at larger $h$. The bispectrum therefore distinguishes vector-supported inflationary dynamics even for an exactly isotropic background.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The paper revisits inflation with kinetic-coupled vector fields, organizing the dynamics in terms of the parameter h measuring the vector kinetic contribution relative to the scalar. In the h ≫ 1 regime it derives a low-energy EFT by integrating out the heavy entropic perturbation; the resulting curvature mode has an imaginary sound speed and undergoes only transient growth before horizon crossing. This produces bispectrum contributions scaling as h³ (flattened), h² (flattened), and h (local). Their competition yields a local-dominated signal at intermediate h and a flattened-dominated signal at larger h. In contrast to the h ≪ 1 regime (local-type signal enhanced by h² N_K³), these features allow the bispectrum to distinguish vector-supported inflationary dynamics even for an exactly isotropic background.

Significance. If the EFT reduction and bispectrum scalings hold, the work supplies a concrete, h-dependent set of non-Gaussianity signatures that can probe vector contributions without background anisotropy. The competition between local and flattened shapes as a function of h offers potentially distinguishable predictions from both single-field inflation and the h ≪ 1 vector case. The choice to parameterize the entire analysis by the single ratio h is a clear organizational strength that makes the scaling results falsifiable in principle.

major comments (1)
  1. [Abstract (EFT derivation paragraph)] Abstract (paragraph on EFT derivation): the statement that the entropic perturbation 'can be integrated out without residual effects' for h ≫ 1, leaving only transient growth despite an imaginary sound speed, is load-bearing for the reported h² flattened and h local contributions. An imaginary sound speed normally signals tachyonic instability; without explicit mode-equation solutions, growth-factor bounds, or error estimates showing that any instability remains strictly pre-horizon-crossing and does not contaminate the bispectrum, the distinction from the h ≪ 1 local-type signal cannot be verified.
minor comments (1)
  1. The definition of h as the ratio of kinetic terms should be written explicitly with the relevant Lagrangian terms at its first appearance in the introduction.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive feedback. We address the single major comment below and will revise the manuscript accordingly to strengthen the presentation of the EFT analysis.

read point-by-point responses

  1. Referee: [Abstract (EFT derivation paragraph)] Abstract (paragraph on EFT derivation): the statement that the entropic perturbation 'can be integrated out without residual effects' for h ≫ 1, leaving only transient growth despite an imaginary sound speed, is load-bearing for the reported h² flattened and h local contributions. An imaginary sound speed normally signals tachyonic instability; without explicit mode-equation solutions, growth-factor bounds, or error estimates showing that any instability remains strictly pre-horizon-crossing and does not contaminate the bispectrum, the distinction from the h ≪ 1 local-type signal cannot be verified.

    Authors: We agree that the abstract statement is concise and that the referee's concern about explicit verification of the transient nature of the growth is well-taken. The manuscript derives the EFT by integrating out the heavy entropic mode for h ≫ 1, yielding the curvature perturbation equation with imaginary sound speed; the bispectrum is then computed via the in-in formalism within this EFT. To make the pre-horizon-crossing character fully explicit and address potential contamination concerns, the revised version will include (i) the explicit mode equation solutions in the EFT regime, (ii) analytic growth-factor bounds demonstrating that any amplification remains bounded and terminates before horizon exit, and (iii) error estimates on the EFT validity range confirming that post-horizon effects do not enter the bispectrum. These additions will also sharpen the contrast with the h ≪ 1 regime where vector transfer persists outside the horizon. revision: yes

Circularity Check

0 steps flagged

No significant circularity; bispectrum scalings derived from model dynamics

full rationale

The paper defines h directly from the Lagrangian as the ratio of vector to scalar kinetic terms and computes the bispectrum via standard cosmological perturbation theory in the h ≪ 1 and h ≫ 1 regimes. In the large-h case the EFT integration of the entropic mode produces the reported h^3, h^2 and h scalings as explicit outcomes of the mode equations and sound-speed analysis, not as redefinitions of the input parameter. No self-citation is invoked as a load-bearing uniqueness theorem, no fitted subset is relabeled as a prediction, and the derivation remains self-contained against the given action without reducing any claimed result to its own definition by construction.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the standard slow-roll and perturbation assumptions of inflationary cosmology plus the specific kinetic coupling of the vector field; h itself functions as an organizing parameter rather than a fitted constant.

free parameters (1)
  • h
    Dimensionless ratio of vector to scalar kinetic energy used to delineate weak and strong vector regimes.
axioms (1)
  • domain assumption The entropic perturbation becomes heavy for h ≫ 1 and can be integrated out to obtain an effective theory for the curvature mode.
    Invoked to derive the imaginary sound speed and transient growth in the large-h regime.

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discussion (0)

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Reference graph

Works this paper leans on

58 extracted references · 54 canonical work pages · 39 internal anchors

  1. [1]

    h 8 √ 2 3 Rc ˙F+ 8 √ 2HR cF ! +h 2 −32 3 HR2 c − 16 3 Rc ˙Rc + 16HF 2 + 16 3 F ˙F # ,(A10) a−3ΠF = ˙F+ 1√ 2ϵMpl

    Smallh For smallh, the cubic action can be expanded in powers ofh. The leading-order terms are L(3) h≪1 ≃ a3 Mpl √ 2ϵ L(3) 0 +hL (3) 1 +h 2L(3) 2 +O(h 3) ,(A6) 15 where L(3) 0 =− 4 3 Rc ˙F2 −8HR cF ˙F −12H 2RcF2 + 2 a2 Rc∂iF∂ iF −Ξ U Rc,(A7) L(3) 1 = 8 √ 2 3 Rc ˙Rc ˙F+ 8 √ 2HR cF ˙Rc + 16 √ 2 3 HR2 c ˙F+ 16 √ 2H2R2 cF − 4 √ 2 3 F ˙F2 −8 √ 2HF 2 ˙F −12 √ 2...

  2. [2]

    Largeh For large h, the heavy field can be integrated out by inserting the leading solution FLO into the cubic Lagrangian. This gives L(3) eff = a3 Mpl √ 2ϵ 216(2h3 +h) 2 (3 + 2h2)3 H2R3 c + 216(2h3 +h) 2 (3 + 2h2)3 HR2 c ˙Rc + 2(12h4 + 4h2 −3)(12h 4 + 8h2 + 3) h2(3 + 2h2)3 Rc ˙R2 c + 2(48h8 + 48h6 + 8h4 −12h 2 −9) 3h2(3 + 2h2)3 1 H ˙R3 c + 12(2h3 +h) 2 a...

  3. [3]

    Ratra, Astrophys

    B. Ratra, Astrophys. J. Lett.391, L1 (1992)

    1992

  4. [4]

    M. S. Turner and L. M. Widrow, Phys. Rev. D37, 2743 (1988)

    1988

  5. [5]

    Consistent Lorentz Violation in Flat and Curved Space

    G. Dvali, O. Pujolas, and M. Redi, Phys. Rev. D76, 044028 (2007), arXiv:hep-th/0702117

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  6. [6]

    Generation of Large-Scale Magnetic Fields in Single-Field Inflation

    J. Martin and J. Yokoyama, JCAP01, 025 (2008), arXiv:0711.4307 [astro-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  7. [7]

    Magnetic fields from inflation?

    V. Demozzi, V. Mukhanov, and H. Rubinstein, JCAP08, 025 (2009), arXiv:0907.1030 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  8. [8]

    M. a. Watanabe, S. Kanno, and J. Soda, Phys. Rev. Lett.102, 191302 (2009), arXiv:0902.2833 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  9. [9]

    M. a. Watanabe, S. Kanno, and J. Soda, Prog. Theor. Phys.123, 1041 (2010), arXiv:1003.0056 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  10. [10]

    Anisotropic Power-law Inflation

    S. Kanno, J. Soda, and M. a. Watanabe, JCAP12, 024 (2010), arXiv:1010.5307 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  11. [11]

    Inflation with Multi-Vector-Hair: The Fate of Anisotropy

    K. Yamamoto, M. a. Watanabe, and J. Soda, Class. Quant. Grav.29, 145008 (2012), arXiv:1201.5309 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  12. [12]

    Gauge Fields and Inflation

    A. Maleknejad, M. M. Sheikh-Jabbari, and J. Soda, Phys. Rept.528, 161 (2013), arXiv:1212.2921 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  13. [13]

    The anisotropic power spectrum and bispectrum in the f(phi) F^2 mechanism

    N. Bartolo, S. Matarrese, M. Peloso, and A. Ricciardone, Phys. Rev. D87, 023504 (2013), arXiv:1210.3257 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  14. [14]

    Spectrum of Perturbations in Anisotropic Inflationary Universe with Vector Hair

    B. Himmetoglu, JCAP03, 023 (2010), arXiv:0910.3235 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  15. [15]

    A. E. Gumrukcuoglu, B. Himmetoglu, and M. Peloso, Phys. Rev. D81, 063528 (2010), arXiv:1001.4088 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  16. [16]

    A. E. Gumrukcuoglu, C. R. Contaldi, and M. Peloso, JCAP11, 005 (2007), arXiv:0707.4179 [astro-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  17. [17]

    Curvature Perturbations in Anisotropic Inflation with Symmetry Breaking

    R. Emami and H. Firouzjahi, JCAP10, 041 (2013), arXiv:1301.1219 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  18. [18]

    Local non-Gaussianity from inflation

    D. Wands, Class. Quant. Grav.27, 124002 (2010), arXiv:1004.0818 [astro-ph.CO] . 17

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  19. [19]

    Primordial Non-Gaussianities from Inflation Models

    X. Chen, Adv. Astron.2010, 638979 (2010), arXiv:1002.1416 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  20. [20]

    Inflation, Cosmic Perturbations and Non-Gaussianities

    Y. Wang, Commun. Theor. Phys.62, 109 (2014), arXiv:1303.1523 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  21. [21]

    Primordial non-Gaussianities after Planck 2015: an introductory review

    S. Renaux-Petel, Comptes Rendus Physique16, 969 (2015), arXiv:1508.06740 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  22. [22]

    M. A. Gorji, S. A. Hosseini Mansoori, and H. Firouzjahi, JCAP11, 041 (2020), arXiv:2008.08195 [astro-ph.CO]

    work page arXiv 2020

  23. [23]

    Primordial Fluctuations from Inflation with a Triad of Background Gauge Fields

    K. Yamamoto, Phys. Rev. D85, 123504 (2012), arXiv:1203.1071 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  24. [24]

    Primordial bispectrum from inflation with background gauge fields

    H. Funakoshi and K. Yamamoto, Class. Quant. Grav.30, 135002 (2013), arXiv:1212.2615 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  25. [25]

    Anisotropic inflation reexamined: upper bound on broken rotational invariance during inflation

    A. Naruko, E. Komatsu, and M. Yamaguchi, JCAP04, 045 (2015), arXiv:1411.5489 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  26. [26]

    Does Anisotropic "Inflation" Produce a Small Statistical Anisotropy?

    T. Fujita and I. Obata, JCAP01, 049 (2018), arXiv:1711.11539 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  27. [27]

    Chen and J

    C.-B. Chen and J. Soda, JCAP05, 029 (2022), arXiv:2201.03160 [hep-th]

    work page arXiv 2022

  28. [28]

    Chen, JCAP11, 063 (2024), arXiv:2312.06105 [astro-ph.CO]

    C.-B. Chen, JCAP11, 063 (2024), arXiv:2312.06105 [astro-ph.CO]

    work page arXiv 2024

  29. [29]

    Chen, B.-X

    C.-B. Chen, B.-X. An, and F.-W. Shu, Phys. Rev. D112, 10 (2025), arXiv:2507.16807 [astro-ph.CO]

    work page arXiv 2025

  30. [30]

    The Effective Field Theory of Inflation

    C. Cheung, P. Creminelli, A. L. Fitzpatrick, J. Kaplan, and L. Senatore, JHEP03, 014 (2008), arXiv:0709.0293 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  31. [31]

    Features of heavy physics in the CMB power spectrum

    A. Achucarro, J. O. Gong, S. Hardeman, G. A. Palma, and S. P. Patil, JCAP01, 030 (2011), arXiv:1010.3693 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  32. [32]

    Effective theories of single field inflation when heavy fields matter

    A. Achucarro, J. O. Gong, S. Hardeman, G. A. Palma, and S. P. Patil, JHEP05, 066 (2012), arXiv:1201.6342 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  33. [33]

    Equilateral Non-Gaussianity and New Physics on the Horizon

    D. Baumann and D. Green, JCAP09, 014 (2011), arXiv:1102.5343 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  34. [34]

    A. R. Brown, Phys. Rev. Lett.121, 251601 (2018), arXiv:1705.03023 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  35. [35]

    Primordial perturbations from inflation with a hyperbolic field-space

    S. Mizuno and S. Mukohyama, Phys. Rev. D96, 103533 (2017), arXiv:1707.05125 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  36. [36]

    Hyperinflation generalised: from its attractor mechanism to its tension with the `swampland conjectures'

    T. Bjorkmo and M. C. D. Marsh, JHEP04, 172 (2019), arXiv:1901.08603 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  37. [37]

    Geometrical Destabilization of Inflation

    S. Renaux-Petel and K. Turzynski, Phys. Rev. Lett.117, 141301 (2016), arXiv:1510.01281 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  38. [38]

    Primordial fluctuations and non-Gaussianities in sidetracked inflation

    S. Garcia-Saenz, S. Renaux-Petel, and J. Ronayne, JCAP07, 057 (2018), arXiv:1804.11279 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  39. [39]

    Geometrical destabilization, premature end of inflation and Bayesian model selection

    S. Renaux-Petel, K. Turzynski, and V. Vennin, JCAP11, 006 (2017), arXiv:1706.01835 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  40. [40]

    Flattened non-Gaussianities from the effective field theory of inflation with imaginary speed of sound

    S. Garcia-Saenz and S. Renaux-Petel, JCAP11, 005 (2018), arXiv:1805.12563 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  41. [41]

    Fumagalli, S

    J. Fumagalli, S. Garcia-Saenz, L. Pinol, S. Renaux-Petel, and J. Ronayne, Phys. Rev. Lett.123, 201302 (2019), arXiv:1902.03221 [hep-th]

    work page arXiv 2019

  42. [42]

    Garcia-Saenz, L

    S. Garcia-Saenz, L. Pinol, and S. Renaux-Petel, JHEP01, 073 (2020), arXiv:1907.10403 [hep-th]

    work page arXiv 2020

  43. [43]

    M. C. Bento, O. Bertolami, P. V. Moniz, J. M. Mourao, and P. M. Sa, Class. Quant. Grav.10, 285 (1993), arXiv:gr-qc/9302034

    work page internal anchor Pith review Pith/arXiv arXiv 1993

  44. [44]

    Vector Inflation

    A. Golovnev, V. Mukhanov, and V. Vanchurin, JCAP06, 009 (2008), arXiv:0802.2068 [astro-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  45. [45]

    Firouzjahi, M

    H. Firouzjahi, M. A. Gorji, S. A. Hosseini Mansoori, A. Karami, and T. Rostami, Phys. Rev. D100, 043530 (2019), arXiv:1812.07464 [hep-th]

    work page arXiv 2019

  46. [46]

    Anisotropic Inflation with Non-Abelian Gauge Kinetic Function

    K. Murata and J. Soda, JCAP06, 037 (2011), arXiv:1103.6164 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  47. [47]

    Chen and J

    C.-B. Chen and J. Soda, JCAP09, 026 (2021), arXiv:2106.04813 [hep-th]

    work page arXiv 2021

  48. [48]

    The shape of non-Gaussianities

    D. Babich, P. Creminelli, and M. Zaldarriaga, JCAP08, 009 (2004), arXiv:astro-ph/0405356

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  49. [49]

    J. R. Fergusson and E. P. S. Shellard, Phys. Rev. D80, 043510 (2009), arXiv:0812.3413 [astro-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  50. [50]

    G. A. Palma, S. Sypsas, and C. Zenteno, Phys. Rev. Lett.125, 121301 (2020), arXiv:2004.06106 [astro-ph.CO]

    work page arXiv 2020

  51. [51]

    Fumagalli, S

    J. Fumagalli, S. Renaux-Petel, J. W. Ronayne, and L. T. Witkowski, Phys. Lett. B841, 137921 (2023), arXiv:2004.08369 [hep-th]

    work page arXiv 2023

  52. [52]

    Braglia, D

    M. Braglia, D. K. Hazra, F. Finelli, G. F. Smoot, L. Sriramkumar, and A. A. Starobinsky, JCAP08, 001 (2020), arXiv:2005.02895 [astro-ph.CO]

    work page arXiv 2020

  53. [53]

    Fumagalli, S

    J. Fumagalli, S. Renaux-Petel, and L. T. Witkowski, JCAP08, 030 (2021), arXiv:2012.02761 [astro-ph.CO]

    work page arXiv 2021

  54. [54]

    Fumagalli, S

    J. Fumagalli, S. ´ e. Renaux-Petel, and L. T. Witkowski, JCAP08, 059 (2021), arXiv:2105.06481 [astro-ph.CO]

    work page arXiv 2021

  55. [55]

    Fumagalli, G

    J. Fumagalli, G. A. Palma, S. Renaux-Petel, S. Sypsas, L. T. Witkowski, and C. Zenteno, JHEP03, 196 (2022), arXiv:2111.14664 [astro-ph.CO]

    work page arXiv 2022

  56. [56]

    Chen and A

    C. Chen and A. Ota, Phys. Rev. D106, 063507 (2022), arXiv:2205.07810 [astro-ph.CO]

    work page arXiv 2022

  57. [57]

    Probing small-scale anisotropic inflation with stochastic gravitational-wave background

    Y.-T. Kuang, J.-Z. Zhou, Z. Chang, and D. Wu, Chin. Phys. C50, 055104 (2026), arXiv:2309.06676 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  58. [58]

    Exploring the statistical anisotropy of primordial curvature perturbations with pulsar timing arrays

    F. Xie, Z.-C. Zhao, Q.-H. Zhu, and X. Li, (2026), arXiv:2604.21642 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2026