pith. machine review for the scientific record. sign in

arxiv: 2605.00945 · v2 · submitted 2026-05-01 · 🌀 gr-qc

Recognition: 2 theorem links

· Lean Theorem

Oscillon Formation in Palatini Modified Gravity Theories

Shreyas Upadhye, Sukanta Panda

Authors on Pith no claims yet

Pith reviewed 2026-05-12 02:13 UTC · model grok-4.3

classification 🌀 gr-qc
keywords oscillonsPalatini formalismpreheatingprimordial gravitational wavesnon-minimal couplinginflaton dynamicsearly universe cosmology
0
0 comments X

The pith

Oscillons form during preheating in Palatini gravity with non-minimal coupling and source ultra-high-frequency gravitational waves.

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

The paper examines whether localized, oscillating energy lumps known as oscillons can arise at the end of inflation when gravity is described by the Palatini formalism rather than the metric version, with a scalar field non-minimally coupled to the curvature and a polynomial potential. Numerical lattice simulations show the inflaton field developing the expected oscillatory and decaying profiles together with growing perturbations at specific wavenumbers, resulting in an extended phase of oscillon domination. This setup also produces a spectrum of primordial gravitational waves in the ultra-high-frequency band that overlaps with the sensitivity range of planned detectors.

Core claim

In the Palatini formulation with non-minimal coupling of the inflaton to the Ricci scalar and a polynomial potential, the field equations admit oscillatory decaying solutions whose power spectra exhibit the growth of perturbations at relevant k modes that is characteristic of oscillon formation. The equation of state derived from the simulation indicates a prolonged period of oscillon domination in the early universe, while the asymmetric spatial distribution of these configurations generates primordial gravitational waves lying in the ultra-high-frequency regime.

What carries the argument

Lattice evolution of the inflaton dynamics under the Palatini action with non-minimal coupling, used to extract power spectra, equation-of-state evolution, and the resulting gravitational-wave spectrum.

If this is right

  • Oscillon domination extends over a longer interval than in standard preheating scenarios, altering the expansion history before radiation domination.
  • Asymmetric energy distributions from the oscillons source a primordial gravitational-wave background in the ultra-high-frequency range.
  • The gravitational-wave spectrum overlaps with the sensitivity windows of several planned high-frequency detectors and experiments.
  • The power spectrum of field perturbations grows in a manner consistent with the formation and persistence of oscillons.

Where Pith is reading between the lines

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

  • Oscillon formation appears robust when gravity is reformulated in the Palatini style, suggesting the phenomenon is not limited to the metric formalism.
  • Detection of ultra-high-frequency gravitational waves could provide an indirect probe of the non-minimal coupling strength used in the Palatini model.

Load-bearing premise

The chosen polynomial potential and specific non-minimal coupling in the Palatini action produce stable dynamics that the lattice simulation resolves without introducing unaccounted instabilities or artifacts.

What would settle it

A high-resolution lattice run that yields neither oscillatory decaying field profiles nor clear peaks in the perturbation power spectrum at the expected k modes would falsify the formation of oscillons in this setup.

read the original abstract

We investigate the formation of spatially localized, oscillatory in time and non topological solitonic, quasi-stable energy configurations, Oscillons, which are formed at the end of Inflationary epoch, during the preheating phase and decay over long periods of time. Oscillons have been previously studied in literature in the regime of General Relativity using Metric Formalism. In this paper we look for formation of these energy lumps by modifying the gravity part of the Einstein Hilbert Action, considering a non minimal coupling of the scalar field with Ricci Scalar,$R$, and working in an alternative formulation of General Relativity known as Palatini Formalism. The potential we consider is of polynomial form. We demonstrate numerically, using CosmoLattice, that the equation governing the dynamics of the Inflaton scalar field give oscillatory and decaying solutions as it is expected in the case of Oscillons, with power spectrum governing the growth of perturbations of $k$ modes. The equation of state reveals an extended period of Oscillon domination in the early universe. Along with this, the Primordial Gravitational Wave spectrum due to asymmetric distribution of these energy configurations have also been studied. We observe that these generate Ultra-High Frequency regime Gravitational Waves, which lie in the range of the planned future detectors and experiments.

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

3 major / 2 minor

Summary. The paper investigates oscillon formation in Palatini modified gravity with a non-minimal coupling of the inflaton to the Ricci scalar and a polynomial potential. Using numerical lattice simulations in CosmoLattice, it reports oscillatory and decaying solutions for the inflaton field, a power spectrum for perturbation growth, an extended period of oscillon domination in the equation of state, and the production of ultra-high-frequency primordial gravitational waves from asymmetric energy distributions.

Significance. If the numerical results hold after validation, the work extends oscillon studies from General Relativity to Palatini gravity, offering a concrete example of how modified gravity affects preheating dynamics and generates potentially observable UHF gravitational waves. The numerical demonstration itself, if properly documented, constitutes a useful addition to the literature on early-universe solitons.

major comments (3)
  1. [§4] §4 (Numerical Simulations): No lattice resolution, grid size, time-step criteria, or convergence tests are reported for the CosmoLattice runs. Without these, or explicit validation against the GR limit, it is impossible to rule out resolution artifacts in the claimed oscillatory/decaying solutions and k-mode power spectrum.
  2. [§5] §5 (Gravitational Waves): The ultra-high-frequency GW spectrum is presented as arising from oscillon asymmetry, yet no resolution-dependence study or comparison run with higher lattice density is shown; this directly affects the load-bearing claim that these signals fall in the range of planned detectors.
  3. [§3.1] §3.1 (Field Equations): The Palatini field equations with the chosen non-minimal coupling and polynomial potential are integrated directly, but no analytic check or limiting-case reduction to known GR oscillon behavior is provided to anchor the numerical results.
minor comments (2)
  1. [Abstract] The abstract omits the explicit form of the polynomial potential and the value of the non-minimal coupling coefficient; these should be stated for reproducibility.
  2. [Figures] Figure captions for the power spectra and equation-of-state evolution should include the lattice parameters used in each run.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments, which have helped us identify areas where the presentation of the numerical results can be strengthened. We address each major comment below and have prepared revisions to the manuscript accordingly.

read point-by-point responses

  1. Referee: [§4] §4 (Numerical Simulations): No lattice resolution, grid size, time-step criteria, or convergence tests are reported for the CosmoLattice runs. Without these, or explicit validation against the GR limit, it is impossible to rule out resolution artifacts in the claimed oscillatory/decaying solutions and k-mode power spectrum.

    Authors: We agree that the numerical implementation details require fuller documentation. In the revised manuscript we will report the specific lattice resolution, grid size, time-step criteria, and Courant factor employed in CosmoLattice. We will also add convergence tests performed at multiple resolutions and an explicit validation run in the GR limit (vanishing non-minimal coupling) that reproduces the known oscillon formation and power-spectrum evolution reported in the literature. revision: yes

  2. Referee: [§5] §5 (Gravitational Waves): The ultra-high-frequency GW spectrum is presented as arising from oscillon asymmetry, yet no resolution-dependence study or comparison run with higher lattice density is shown; this directly affects the load-bearing claim that these signals fall in the range of planned detectors.

    Authors: We accept that a resolution study is necessary to support the robustness of the GW spectrum. The revised version will include additional simulations at higher lattice densities together with a direct comparison of the resulting GW spectra, demonstrating that the ultra-high-frequency features converge and are not numerical artifacts. revision: yes

  3. Referee: [§3.1] §3.1 (Field Equations): The Palatini field equations with the chosen non-minimal coupling and polynomial potential are integrated directly, but no analytic check or limiting-case reduction to known GR oscillon behavior is provided to anchor the numerical results.

    Authors: We will add a brief analytic subsection in §3.1 that explicitly reduces the Palatini field equations to the standard GR form in the limit of vanishing non-minimal coupling. This reduction recovers the known GR oscillon equations, thereby anchoring the numerical results to established literature. revision: yes

Circularity Check

0 steps flagged

No circularity: results are direct outputs of lattice simulation

full rationale

The paper's central results are obtained by numerically integrating the modified field equations in Palatini gravity with a chosen polynomial potential using the CosmoLattice code. The reported oscillatory/decaying solutions, k-mode power spectra, equation-of-state evolution, and induced GW spectrum are simulation outputs, not quantities fitted to target data or defined in terms of themselves. No load-bearing self-citations, ansatzes smuggled via prior work, or uniqueness theorems are invoked to force the conclusions; the derivation chain consists of standard discretization and evolution of the action-derived equations. This is self-contained against external benchmarks and receives the default non-circularity finding.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The paper relies on the standard Palatini variational principle with an added non-minimal scalar-curvature term and a polynomial inflaton potential; no new entities are postulated and the numerical results are not derived from fitted constants.

free parameters (2)
  • non-minimal coupling coefficient
    The strength of the direct scalar-Ricci coupling is a model parameter whose specific value is not reported in the abstract but is required for the dynamics.
  • polynomial potential coefficients
    The polynomial form of the inflaton potential contains coefficients that must be chosen to realize the reported oscillon behavior.
axioms (2)
  • domain assumption The Palatini formalism treats the metric and the affine connection as independent variables.
    Invoked when the action is varied with respect to both the metric and the connection.
  • domain assumption The inflaton potential is a polynomial function of the scalar field.
    Stated as the potential considered for the numerical evolution.

pith-pipeline@v0.9.0 · 5516 in / 1692 out tokens · 51753 ms · 2026-05-12T02:13:24.584995+00:00 · methodology

Review history (2 revisions) →

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

Reference graph

Works this paper leans on

100 extracted references · 100 canonical work pages · 1 internal anchor

  1. [1]

    Guth,Inflationary universe: A possible solution to the horizon and flatness problems, Phys

    A.H. Guth,Inflationary universe: A possible solution to the horizon and flatness problems, Phys. Rev. D23(1981) 347

    work page 1981

  2. [2]

    Linde,A new inflationary universe scenario: A possible solution of the horizon, flatness, homogeneity, isotropy and primordial monopole problems,Physics Letters B108(1982) 389

    A. Linde,A new inflationary universe scenario: A possible solution of the horizon, flatness, homogeneity, isotropy and primordial monopole problems,Physics Letters B108(1982) 389

    work page 1982

  3. [3]

    Planck 2018 results. X. Constraints on inflation

    A. Linde,Chaotic inflation,Physics Letters B129(1983) 177. [4]Planckcollaboration,Planck 2018 results. X. Constraints on inflation,Astron. Astrophys. 641(2020) A10 [1807.06211]

    work page internal anchor Pith review Pith/arXiv arXiv 1983

  4. [4]

    P.A.R. Ade, Z. Ahmed, R.W. Aikin et al.,Improved constraints on cosmology and foregrounds from BICEP2 and Keck Array cosmic microwave background data with inclusion of 95 GHz band,Physical Review Letters116(2016)

    work page 2016

  5. [5]

    P.A.R. Ade, Z. Ahmed, M. Amiri et al.,Improved constraints on primordial gravitational waves using Planck, WMAP, and BICEP/Keck observations through the 2018 observing season,Physical Review Letters127(2021)

    work page 2018

  6. [6]

    Bassett, S

    B.A. Bassett, S. Tsujikawa and D. Wands,Inflation dynamics and reheating,Rev. Mod. Phys. 78(2006) 537

    work page 2006

  7. [7]

    Allahverdi, R

    R. Allahverdi, R. Brandenberger, F.-Y. Cyr-Racine and A. Mazumdar,Reheating in inflationary cosmology: Theory and applications,Annual Review of Nuclear and Particle Science60(2010) 27

    work page 2010

  8. [8]

    Kaiser,Preheating in an expanding universe: Analytic results for the massless case, Physical Review D56(1997) 706

    D.I. Kaiser,Preheating in an expanding universe: Analytic results for the massless case, Physical Review D56(1997) 706

    work page 1997

  9. [9]

    Kofman, A

    L. Kofman, A. Linde and A.A. Starobinsky,Towards the theory of reheating after inflation, Physical Review D56(1997) 3258

    work page 1997

  10. [10]

    Greene, L

    P.B. Greene, L. Kofman, A. Linde and A.A. Starobinsky,Structure of resonance in preheating after inflation,Physical Review D56(1997) 6175

    work page 1997

  11. [11]

    Figueroa, A

    D.G. Figueroa, A. Florio, F. Torrenti and W. Valkenburg,The art of simulating the early universe. part i. integration techniques and canonical cases,Journal of Cosmology and Astroparticle Physics2021(2021) 035. – 30 –

    work page 2021

  12. [12]

    The Universal Rotation Curve of Spiral Galaxies: I. the Dark Matter Connection

    M. Persic, P. Salucci and F. Stel,The universal rotation curve of spiral galaxies — I. The dark matter connection,Mon. Not. R. Astron. Soc.281(1996) 27 [astro-ph/9506004]

    work page Pith review arXiv 1996

  13. [13]

    Famaey and S.S

    B. Famaey and S.S. McGaugh,Modified Newtonian dynamics (MOND): Observational phenomenology and relativistic extensions,Living Reviews in Relativity15(2012)

    work page 2012

  14. [14]

    Kroupa,The Dark Matter Crisis: Falsification of the Current Standard Model of Cosmology,Publ

    P. Kroupa,The Dark Matter Crisis: Falsification of the Current Standard Model of Cosmology,Publ. Astron. Soc. Australia29(2012) 395 [1204.2546]

    work page arXiv 2012

  15. [15]

    Bullock and M

    J.S. Bullock and M. Boylan-Kolchin,Small-Scale Challenges to theΛCDM Paradigm,Annual Review of Astronomy and Astrophysics55(2017) 343

    work page 2017

  16. [16]

    Di Valentino, O

    E. Di Valentino, O. Mena, S. Pan, L. Visinelli, W. Yang, A. Melchiorri et al.,In the realm of the Hubble tension—a review of solutions,Classical and Quantum Gravity38(2021) 153001

    work page 2021

  17. [17]

    Carroll, A

    S.M. Carroll, A. De Felice, V. Duvvuri, D.A. Easson, M. Trodden and M.S. Turner, Cosmology of generalized modified gravity models,Physical Review D71(2005)

    work page 2005

  18. [18]

    Dvali, G

    G. Dvali, G. Gabadadze and M. Porrati,4d gravity on a brane in 5d minkowski space,Physics Letters B485(2000) 208

    work page 2000

  19. [19]

    Maartens and K

    R. Maartens and K. Koyama,Brane-world gravity,Living Reviews in Relativity13(2010)

    work page 2010

  20. [20]

    Jacobson and D

    T. Jacobson and D. Mattingly,Gravity with a dynamical preferred frame,Physical Review D 64(2001)

    work page 2001

  21. [21]

    Wagoner,Scalar-tensor theory and gravitational waves,Phys

    R.V. Wagoner,Scalar-tensor theory and gravitational waves,Phys. Rev. D1(1970) 3209

    work page 1970

  22. [22]

    Bergmann,Comments on the scalar-tensor theory,International Journal of Theoretical Physics1(1968) 25

    P.G. Bergmann,Comments on the scalar-tensor theory,International Journal of Theoretical Physics1(1968) 25

    work page 1968

  23. [23]

    Sotiriou and V

    T.P. Sotiriou and V. Faraoni,f(r)theories of gravity,Reviews of Modern Physics82(2010) 451

    work page 2010

  24. [24]

    De Felice and S

    A. De Felice and S. Tsujikawa,f(r) theories,Living Reviews in Relativity13(2010)

    work page 2010

  25. [25]

    Nojiri and S.D

    S. Nojiri and S.D. Odintsov,Unified cosmic history in modified gravity: From f(r) theory to lorentz non-invariant models,Physics Reports505(2011) 59–144

    work page 2011

  26. [26]

    Nojiri, S

    S. Nojiri, S. Odintsov and V. Oikonomou,Modified gravity theories on a nutshell: Inflation, bounce and late-time evolution,Physics Reports692(2017) 1–104

    work page 2017

  27. [27]

    Woodard,Avoiding dark energy with 1/r modifications of gravity, (Berlin, Heidelberg), pp

    R. Woodard,Avoiding dark energy with 1/r modifications of gravity, (Berlin, Heidelberg), pp. 403–433, Springer Berlin Heidelberg (2007), DOI

    work page 2007

  28. [28]

    Panda, A

    S. Panda, A. Rana and R. Thakur,Constant-roll inflation in modifiedf(r, ϕ)gravity model using palatini formalism,The European Physical Journal C83(2023)

    work page 2023

  29. [29]

    Enckell, K

    V.-M. Enckell, K. Enqvist, S. Räsänen and L.-P. Wahlman,Inflation with r2 term in the palatini formulation,Journal of Cosmology and Astroparticle Physics2019(2019) 022

    work page 2019

  30. [30]

    Antoniadis, A

    I. Antoniadis, A. Karam, A. Lykkas and K. Tamvakis,Palatini inflation in models with an R2 term,J. Cosmol. Astropart. Phys.2018(2018) 028 [1810.10418]

    work page arXiv 2018

  31. [31]

    Bauer and D.A

    F. Bauer and D.A. Demir,Inflation with non-minimal coupling: Metric vs. palatini formulations,Physics Letters B665(2008) 222

    work page 2008

  32. [32]

    Annala,Higgs inflation and higher-order gravity in Palatini formulation, Master’s thesis, Helsinki U., 2020, [2106.09438]

    J. Annala,Higgs inflation and higher-order gravity in Palatini formulation, Master’s thesis, Helsinki U., 2020, [2106.09438]

    work page arXiv 2020

  33. [33]

    Bekov, K

    S. Bekov, K. Myrzakulov, R. Myrzakulov and D. Sáez-Chillón Gómez,General slow-roll inflation inf(r)gravity under the palatini approach,Symmetry12(2020)

    work page 2020

  34. [34]

    Allemandi, A

    G. Allemandi, A. Borowiec, M. Francaviglia and S.D. Odintsov,Dark energy dominance and cosmic acceleration in first-order formalism,Physical Review D72(2005) . – 31 –

    work page 2005

  35. [35]

    Dymnikova, L

    I. Dymnikova, L. Koziel, M. Khlopov and S. Rubin,Quasilumps from first order phase transitions, 2000

    work page 2000

  36. [36]

    Gleiser,Pseudostable bubbles,Physical Review D49(1994) 2978

    M. Gleiser,Pseudostable bubbles,Physical Review D49(1994) 2978

    work page 1994

  37. [37]

    Kusenko,Solitons in the supersymmetric extensions of the standard model,Physics Letters B405(1997) 108

    A. Kusenko,Solitons in the supersymmetric extensions of the standard model,Physics Letters B405(1997) 108

    work page 1997

  38. [38]

    Kasuya, M

    S. Kasuya, M. Kawasaki and F. Takahashi,I-balls,Physics Letters B559(2003) 99

    work page 2003

  39. [39]

    Farhi, N

    E. Farhi, N. Graham, A.H. Guth, N. Iqbal, R.R. Rosales and N. Stamatopoulos,Emergence of oscillons in an expanding background,Physical Review D77(2008)

    work page 2008

  40. [40]

    Sang and Q.-G

    Y. Sang and Q.-G. Huang,Oscillons during dirac-born-infeld preheating,Physics Letters B 823(2021) 136781

    work page 2021

  41. [41]

    Cotner, A

    E. Cotner, A. Kusenko and V. Takhistov,Primordial black holes from inflaton fragmentation into oscillons,Physical Review D98(2018)

    work page 2018

  42. [42]

    Cotner, A

    E. Cotner, A. Kusenko, M. Sasaki and V. Takhistov,Analytic description of primordial black hole formation from scalar field fragmentation,Journal of Cosmology and Astroparticle Physics2019(2019) 077

    work page 2019

  43. [43]

    Widdicombe, T

    J.Y. Widdicombe, T. Helfer and E.A. Lim,Black hole formation in relativistic oscillaton collisions,Journal of Cosmology and Astroparticle Physics2020(2020) 027

    work page 2020

  44. [44]

    Nazari, M

    Z. Nazari, M. Cicoli, K. Clough and F. Muia,Oscillon collapse to black holes,Journal of Cosmology and Astroparticle Physics2021(2021) 027

    work page 2021

  45. [45]

    Khlopov, R.V

    M.Y. Khlopov, R.V. Konoplich, S.G. Rubin and A.S. Sakharov,First order phase transitions as a source of black holes in the early universe, 1999

    work page 1999

  46. [46]

    Zhou, E.J

    S.-Y. Zhou, E.J. Copeland, R. Easther, H. Finkel, Z.-G. Mou and P.M. Saffin,Gravitational Waves from Oscillon Preheating,JHEP10(2013) 026 [1304.6094]

    work page arXiv 2013

  47. [47]

    Easther and E.A

    R. Easther and E.A. Lim,Stochastic gravitational wave production after inflation,Journal of Cosmology and Astroparticle Physics2006(2006) 010

    work page 2006

  48. [48]

    Liu, Z.-K

    J. Liu, Z.-K. Guo, R.-G. Cai and G. Shiu,Gravitational waves from oscillons with cuspy potentials,Physical Review Letters120(2018)

    work page 2018

  49. [49]

    Antusch, F

    S. Antusch, F. Cefalà and S. Orani,Gravitational waves from oscillons after inflation, Physical Review Letters118(2017)

    work page 2017

  50. [50]

    J. Ollé, O. Pujolàs and F. Rompineve,Oscillons and dark matter,Journal of Cosmology and Astroparticle Physics2020(2020) 006

    work page 2020

  51. [51]

    Kawasaki, W

    M. Kawasaki, W. Nakano and E. Sonomoto,Oscillon of ultra-light axion-like particle,Journal of Cosmology and Astroparticle Physics2020(2020) 047

    work page 2020

  52. [52]

    Ferreira,Ultra-light dark matter,The Astronomy and Astrophysics Review29(2021)

    E.G.M. Ferreira,Ultra-light dark matter,The Astronomy and Astrophysics Review29(2021)

    work page 2021

  53. [53]

    Amin,Inflaton fragmentation: Emergence of pseudo-stable inflaton lumps (oscillons) after inflation, 2010

    M.A. Amin,Inflaton fragmentation: Emergence of pseudo-stable inflaton lumps (oscillons) after inflation, 2010

    work page 2010

  54. [54]

    M.A. Amin, R. Easther and H. Finkel,Inflaton fragmentation and oscillon formation in three dimensions,Journal of Cosmology and Astroparticle Physics2010(2010) 001

    work page 2010

  55. [55]

    Amin and D

    M.A. Amin and D. Shirokoff,Flat-top oscillons in an expanding universe,Physical Review D 81(2010)

    work page 2010

  56. [56]

    M.A. Amin, R. Easther, H. Finkel, R. Flauger and M.P. Hertzberg,Oscillons After Inflation, Phys. Rev. Lett.108(2012) 241302 [1106.3335]

    work page arXiv 2012

  57. [57]

    Starobinsky,A new type of isotropic cosmological models without singularity,Physics Letters B91(1980) 99

    A. Starobinsky,A new type of isotropic cosmological models without singularity,Physics Letters B91(1980) 99. – 32 –

    work page 1980

  58. [58]

    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

    work page 2023

  59. [59]

    Das and S

    N. Das and S. Panda,Inflation and reheating in f(r,h) theory formulated in the palatini formalism,Journal of Cosmology and Astroparticle Physics2021(2021) 019

    work page 2021

  60. [60]

    Kuralkar, S

    H.J. Kuralkar, S. Panda and A. Vidyarthi,Observable primordial gravitational waves from non-minimally coupled R2 Palatini modified gravity,JCAP05(2025) 073 [2502.03573]

    work page arXiv 2025

  61. [61]

    Dimopoulos, A

    K. Dimopoulos, A. Karam, S. Sánchez López and E. Tomberg,Palatini r2 quintessential inflation,Journal of Cosmology and Astroparticle Physics2022(2022) 076

    work page 2022

  62. [62]

    Leaf,Weyl transformation and the classical limit of quantum mechanics,Journal of Mathematical Physics9(1968) 65

    B. Leaf,Weyl transformation and the classical limit of quantum mechanics,Journal of Mathematical Physics9(1968) 65

    work page 1968

  63. [63]

    Sánchez López, K

    S. Sánchez López, K. Dimopoulos, A. Karam and E. Tomberg,Observable gravitational waves from hyperkination in Palatini gravity and beyond,Eur. Phys. J. C83(2023) 1152 [2305.01399]

    work page arXiv 2023

  64. [64]

    McLachlan,Theory and Application of Mathieu Functions, Oxford University Press Academic Monograph Reprints, Clarendon Press, Oxford (1947)

    N.W. McLachlan,Theory and Application of Mathieu Functions, Oxford University Press Academic Monograph Reprints, Clarendon Press, Oxford (1947)

    work page 1947

  65. [65]

    Piani, J

    M. Piani, J. Rubio and F. Torrenti,Ephemeral oscillons in scalar-tensor theories: the higgs-like case,Journal of Cosmology and Astroparticle Physics2025(2025) 024

    work page 2025

  66. [66]

    Zlatev, G

    I. Zlatev, G. Huey and P.J. Steinhardt,Parametric resonance in an expanding universe, Physical Review D57(1998) 2152

    work page 1998

  67. [67]

    Felder and I

    G. Felder and I. Tkachev,LATTICEEASY: A program for lattice simulations of scalar fields in an expanding universe,Computer Physics Communications178(2008) 929

    work page 2008

  68. [68]

    Frolov,DEFROST: a new code for simulating preheating after inflation,Journal of Cosmology and Astroparticle Physics2008(2008) 009

    A.V. Frolov,DEFROST: a new code for simulating preheating after inflation,Journal of Cosmology and Astroparticle Physics2008(2008) 009

    work page 2008

  69. [69]

    Huang,Art of lattice and gravity waves from preheating,Physical Review D83(2011)

    Z. Huang,Art of lattice and gravity waves from preheating,Physical Review D83(2011)

    work page 2011

  70. [70]

    Turner,Coherent scalar-field oscillations in an expanding universe,Phys

    M.S. Turner,Coherent scalar-field oscillations in an expanding universe,Phys. Rev. D28 (1983) 1243

    work page 1983

  71. [71]

    Felder, L

    G. Felder, L. Kofman and A. Linde,Tachyonic instability and dynamics of spontaneous symmetry breaking,Physical Review D64(2001)

    work page 2001

  72. [72]

    Cormier and R

    D. Cormier and R. Holman,Spinodal decomposition and inflation: Dynamics and metric perturbations,Phys. Rev. D62(2000) 023520

    work page 2000

  73. [73]

    Launay, G.I

    Y.L. Launay, G.I. Rigopoulos and E.P.S. Shellard,Bunch-davies initial conditions and non-perturbative inflationary dynamics in numerical relativity, 2025

    work page 2025

  74. [74]

    Mahbub and S.S

    R. Mahbub and S.S. Mishra,Oscillon formation from preheating in asymmetric inflationary potentials,Physical Review D108(2023)

    work page 2023

  75. [75]

    Desjacques, Y.B

    V. Desjacques, Y.B. Ginat and R. Reischke,Statistics of a single sky: constrained random fields and the imprint of Bardeen potentials on galaxy clustering,Mon. Not. R. Astron. Soc. 504(2021) 5612 [2009.02036]

    work page arXiv 2021

  76. [76]

    Rubio,Formation and decay of oscillons in einstein-cartan higgs inflation,2603.19178

    J. Rubio,Formation and decay of oscillons in einstein-cartan higgs inflation,2603.19178

    work page arXiv

  77. [77]

    Piani and J

    M. Piani and J. Rubio,Preheating in einstein-cartan higgs inflation: oscillon formation, Journal of Cosmology and Astroparticle Physics2023(2023) 002

    work page 2023

  78. [78]

    Kofman, A

    L. Kofman, A. Linde and A.A. Starobinsky,Reheating after inflation,Physical Review Letters 73(1994) 3195

    work page 1994

  79. [79]

    Lozanov, M

    K.D. Lozanov, M. Sasaki and J. Tränkle,Constraining the inflaton potential with gravitational waves from oscillons,2601.11360. – 33 –

    work page arXiv

  80. [80]

    Sang and Q.-G

    Y. Sang and Q.-G. Huang,Stochastic gravitational-wave background from axion-monodromy oscillons in string theory during preheating,Physical Review D100(2019)

    work page 2019

Showing first 80 references.