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arxiv: 2605.23827 · v1 · pith:IR5E3M5Qnew · submitted 2026-05-22 · 🌀 gr-qc · astro-ph.CO· hep-ph

Natural Metric-Affine Inflation: Reloaded

D. Kraiko , A. Racioppi This is my paper

Pith reviewed 2026-05-25 03:53 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.COhep-ph
keywords natural inflationmetric-affine gravityNieh-Yan termnon-minimal couplingperiodic couplingRicci scalarinflationary cosmology
0
0 comments X

The pith

Periodic non-minimal couplings to the Nieh-Yan term and Ricci scalar rescue natural inflation in metric-affine gravity even for sub-Planckian scales.

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

The paper examines natural inflation inside metric-affine gravity when the inflaton has a periodic non-minimal coupling to the Nieh-Yan term. That coupling by itself produces linear inflation predictions that do not match data. Adding an analogous periodic coupling to the Ricci scalar changes the dynamics so that the model agrees with observations. The combined setup remains viable when the periodicity scale lies below the Planck mass and the couplings stay order one in size.

Core claim

In metric-affine gravity, natural inflation can be made consistent with data by introducing periodic non-minimal couplings of the inflaton to both the Nieh-Yan term and the Ricci scalar; the joint effect produces viable predictions even when the periodicity scale is sub-Planckian and the coupling strengths are relatively small.

What carries the argument

Periodic non-minimal couplings of the inflaton to the Nieh-Yan term and the Ricci scalar.

If this is right

  • The inflationary observables match current CMB constraints.
  • The scenario works for sub-Planckian values of the periodicity scale.
  • Only couplings of order one are required.
  • The dynamics remain inside metric-affine gravity without additional corrections.

Where Pith is reading between the lines

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

  • Similar periodic couplings might restore viability for other axion-based models that currently conflict with data.
  • Precision measurements of the running of the spectral index could distinguish this mechanism from standard natural inflation.
  • The approach suggests a general way to embed periodic structures into metric-affine extensions of gravity.

Load-bearing premise

The non-minimal couplings to the Nieh-Yan term and Ricci scalar can be chosen periodic and of comparable strength while remaining inside the metric-affine framework without new instabilities or higher-order corrections that spoil inflation.

What would settle it

A future measurement of the tensor-to-scalar ratio or spectral index lying outside the range produced by the combined-coupling model for sub-Planckian periodicity would rule out the claimed viability.

read the original abstract

We revisit natural inflation within the framework of metric-affine gravity, considering the impact of a periodic non-minimal coupling between the inflaton and the Nieh-Yan term. Such a term, alone, leads to linear inflation predictions in the strong coupling limit and cannot help to rescue the natural inflation scenario. However, once an analogous non-minimal coupling with the Ricci scalar is added, agreement with data can be easily achieved. Remarkably, the scenario remains viable even with a sub-Planckian periodicity scale and relatively small (order of one) non-minimal couplings.

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

2 major / 0 minor

Summary. The manuscript revisits natural inflation in metric-affine gravity, showing that a periodic non-minimal coupling of the inflaton to the Nieh-Yan term alone produces linear inflation in the strong-coupling limit and fails to rescue the scenario. Adding an analogous periodic non-minimal coupling to the Ricci scalar allows the model to match observational data, remaining viable even for sub-Planckian periodicity scales and non-minimal couplings of order one.

Significance. If the central derivations hold, the result offers a concrete mechanism to restore viability to natural inflation within the metric-affine framework without invoking super-Planckian excursions or large couplings. The explicit demonstration that both periodic terms are required, together with the reported parameter ranges, constitutes a falsifiable prediction that can be tested against CMB data.

major comments (2)
  1. The viability claim for sub-Planckian periodicity and O(1) couplings rests on the unverified assumption that the chosen periodic functions for the Nieh-Yan and Ricci couplings introduce neither ghosts, tachyons, nor additional propagating degrees of freedom that would alter the effective potential or slow-roll parameters. This assumption is load-bearing for the central claim but receives no explicit check in the metric-affine field equations.
  2. No explicit slow-roll parameters, effective potential after integrating out the connection, or numerical comparison to Planck 2018 constraints (e.g., n_s and r values) are supplied in the abstract or visible derivations, preventing direct assessment of whether the reported agreement with data is robust or merely qualitative.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and insightful comments, which have helped us identify areas for improvement. We address each major comment below and outline the revisions we will make.

read point-by-point responses

  1. Referee: The viability claim for sub-Planckian periodicity and O(1) couplings rests on the unverified assumption that the chosen periodic functions for the Nieh-Yan and Ricci couplings introduce neither ghosts, tachyons, nor additional propagating degrees of freedom that would alter the effective potential or slow-roll parameters. This assumption is load-bearing for the central claim but receives no explicit check in the metric-affine field equations.

    Authors: We agree that an explicit check for the absence of ghosts, tachyons, and extra degrees of freedom is important to support the viability claims. In our setup the affine connection is non-dynamical and solved algebraically, yielding an effective single-field theory; however, we did not provide a dedicated stability analysis of the quadratic action. In the revised manuscript we will add a short appendix deriving the second-order action for metric and scalar perturbations around the inflationary background and confirming that no additional propagating modes or instabilities arise from the periodic couplings. revision: yes

  2. Referee: No explicit slow-roll parameters, effective potential after integrating out the connection, or numerical comparison to Planck 2018 constraints (e.g., n_s and r values) are supplied in the abstract or visible derivations, preventing direct assessment of whether the reported agreement with data is robust or merely qualitative.

    Authors: We acknowledge that the abstract and main derivations as presented do not contain the explicit slow-roll expressions or numerical comparisons. The manuscript derives the effective potential after solving the connection equations, but these steps and the resulting n_s, r values are not displayed in a form that allows immediate quantitative comparison. In the revised version we will insert the explicit effective potential and slow-roll parameters in the main text, add a table of representative (n_s, r) values for the viable parameter ranges, and update the abstract to reference the agreement with Planck 2018 constraints. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation self-contained against external benchmarks

full rationale

The abstract and skeptic summary present a theoretical model in metric-affine gravity where periodic non-minimal couplings to the Nieh-Yan term and Ricci scalar are introduced to modify natural inflation predictions. No equations, fitting procedures, self-citations, or definitional reductions are visible that would make any prediction equivalent to its inputs by construction. The viability claim rests on solving the modified equations of motion, which is presented as an independent calculation within the framework rather than a renaming or self-referential fit. This is the most common honest finding for papers without visible load-bearing self-citations or ansatz smuggling.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only abstract available; no explicit free parameters, axioms, or invented entities can be extracted.

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Works this paper leans on

96 extracted references · 96 canonical work pages · 25 internal anchors

  1. [1]

    Collaboration,Planck 2018 results

    P. Collaboration,Planck 2018 results. vi. cosmological parameters,Astronomy & Astrophysics 641(2020) A6

    work page 2018

  2. [2]

    Alam and et al.,The clustering of galaxies in the completed sdss-iii baryon oscillation spectroscopic survey,Mon

    S. Alam and et al.,The clustering of galaxies in the completed sdss-iii baryon oscillation spectroscopic survey,Mon. Not. Roy. Astron. Soc.470(2017) 2617

    work page 2017

  3. [3]

    Colless and et al.,The 2df galaxy redshift survey: spectra and redshifts,Mon

    M. Colless and et al.,The 2df galaxy redshift survey: spectra and redshifts,Mon. Not. Roy. Astron. Soc.328(2001) 1039

    work page 2001

  4. [4]

    A. A. Starobinsky,A New Type of Isotropic Cosmological Models Without Singularity,Phys. Lett.B91(1980) 99

    work page 1980

  5. [5]

    A. H. Guth,The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems,Phys.Rev.D23(1981) 347

    work page 1981

  6. [6]

    A. D. Linde,A New Inflationary Universe Scenario: A Possible Solution of the Horizon, Flatness, Homogeneity, Isotropy and Primordial Monopole Problems,Phys.Lett.B108(1982) 389

    work page 1982

  7. [7]

    Planck 2018 results. X. Constraints on inflation

    A. Albrecht and P. J. Steinhardt,Cosmology for Grand Unified Theories with Radiatively Induced Symmetry Breaking,Phys.Rev.Lett.48(1982) 1220. [8]Planckcollaboration,Planck 2018 results. X. Constraints on inflation,Astron. Astrophys. 641(2020) A10 [1807.06211]. [9]BICEP, Keckcollaboration,Improved Constraints on Primordial Gravitational Waves using Planck,...

    work page internal anchor Pith review Pith/arXiv arXiv 1982

  8. [8]

    Freese, J

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

    work page 1990

  9. [9]

    J. E. Kim, H. P. Nilles and M. Peloso,Completing natural inflation,JCAP01(2005) 005 [hep-ph/0409138]

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  10. [10]

    Visinelli,Natural Warm Inflation,JCAP09(2011) 013 [1107.3523]

    L. Visinelli,Natural Warm Inflation,JCAP09(2011) 013 [1107.3523]

    work page arXiv 2011

  11. [11]

    Saving Natural Inflation

    D. Croon and V. Sanz,Saving Natural Inflation,JCAP02(2015) 008 [1411.7809]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  12. [12]

    On the viability of m**2 phi**2 and natural inflation

    A. Ach´ ucarro, V. Atal and Y. Welling,On the viability ofm 2ϕ2 and natural inflation,JCAP 07(2015) 008 [1503.07486]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  13. [13]

    R. Z. Ferreira, A. Notari and G. Simeon,Natural Inflation with a periodic non-minimal coupling,JCAP11(2018) 021 [1806.05511]. – 12 –

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  14. [14]

    Rescuing Quartic and Natural Inflation in the Palatini Formalism

    I. Antoniadis, A. Karam, A. Lykkas, T. Pappas and K. Tamvakis,Rescuing Quartic and Natural Inflation in the Palatini Formalism,JCAP1903(2019) 005 [1812.00847]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  15. [15]

    Salvio,Quasi-Conformal Models and the Early Universe,Eur

    A. Salvio,Quasi-Conformal Models and the Early Universe,Eur. Phys. J. C79(2019) 750 [1907.00983]

    work page arXiv 2019

  16. [16]

    Simeon,Scalar-tensor extension of Natural Inflation,JCAP07(2020) 028 [2002.07625]

    G. Simeon,Scalar-tensor extension of Natural Inflation,JCAP07(2020) 028 [2002.07625]

    work page arXiv 2020

  17. [17]

    McDonough, A

    E. McDonough, A. H. Guth and D. I. Kaiser,Nonminimal Couplings and the Forgotten Field of Axion Inflation,2010.04179

    work page arXiv 2010

  18. [18]

    Salvio,Natural-scalaron inflation,JCAP10(2021) 011 [2107.03389]

    A. Salvio,Natural-scalaron inflation,JCAP10(2021) 011 [2107.03389]

    work page arXiv 2021

  19. [19]

    Salvio,BICEP/Keck data and quadratic gravity,JCAP09(2022) 027 [2202.00684]

    A. Salvio,BICEP/Keck data and quadratic gravity,JCAP09(2022) 027 [2202.00684]

    work page arXiv 2022

  20. [20]

    Bostan,Non-minimally coupled Natural Inflation: Palatini and Metric formalism with the recent BICEP/Keck,JCAP02(2023) 063 [2209.02434]

    N. Bostan,Non-minimally coupled Natural Inflation: Palatini and Metric formalism with the recent BICEP/Keck,JCAP02(2023) 063 [2209.02434]

    work page arXiv 2023

  21. [21]

    Salvio and S

    A. Salvio and S. Sciusco,(Multi-field) natural inflation and gravitational waves,JCAP03 (2024) 018 [2311.00741]

    work page arXiv 2024

  22. [22]

    Mukuno and J

    A. Mukuno and J. Soda,Chromonatural warm inflation,Phys. Rev. D109(2024) 123504 [2402.08849]

    work page arXiv 2024

  23. [23]

    Racioppi and A

    A. Racioppi and A. Salvio,Natural metric-affine inflation,JCAP06(2024) 033 [2403.18004]

    work page arXiv 2024

  24. [24]

    Racioppi and A

    A. Racioppi and A. Salvio,Natural Metric-Affine Inflation,PoSCOSMICWISPers2024 (2025) 007

    work page 2025

  25. [25]

    D. L. Lorenzoni, D. I. Kaiser and E. McDonough,Natural inflation with exponentially small tensor-to-scalar ratio,Phys. Rev. D110(2024) L061302 [2405.13881]

    work page arXiv 2024

  26. [26]

    Michelotti, R

    M. Michelotti, R. Gonzalez Quaglia, E. Dimastrogiovanni, M. Fasiello and D. Roest,Kinetic Gauge Friction in Natural Inflation,2411.19892

    work page arXiv

  27. [27]

    Bostan, R

    N. Bostan, R. H. Dejrah, C. Dioguardi and A. Racioppi,Natural inflation in Palatini F(R,X), JCAP07(2025) 082 [2503.16324]

    work page arXiv 2025

  28. [28]

    Bostan, R

    N. Bostan, R. H. Dejrah, C. Dioguardi and A. Racioppi,Natural inflation in PalatiniF(R), 2511.20557

    work page arXiv

  29. [29]

    Pure Natural Inflation Passes the ACT

    C. Zenteno Gatica, A. Papageorgiou and M. Fasiello,Pure Natural Inflation Passes the ACT, 2603.09413

    work page internal anchor Pith review Pith/arXiv arXiv

  30. [30]

    The Geometrical Trinity of Gravity

    J. Beltr´ an Jim´ enez, L. Heisenberg and T. S. Koivisto,The Geometrical Trinity of Gravity, Universe5(2019) 173 [1903.06830]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  31. [31]

    Rigouzzo and S

    C. Rigouzzo and S. Zell,Coupling metric-affine gravity to the standard model and dark matter fermions,Phys. Rev. D108(2023) 124067 [2306.13134]

    work page arXiv 2023

  32. [32]

    Cosmological perturbations in the Palatini formulation of modified gravity

    T. Koivisto and H. Kurki-Suonio,Cosmological perturbations in the palatini formulation of modified gravity,Class. Quant. Grav.23(2006) 2355 [astro-ph/0509422]

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  33. [33]

    Inflation with Non-Minimal Coupling: Metric vs. Palatini Formulations

    F. Bauer and D. A. Demir,Inflation with Non-Minimal Coupling: Metric versus Palatini Formulations,Phys. Lett.B665(2008) 222 [0803.2664]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  34. [34]

    Coleman-Weinberg linear inflation: metric vs. Palatini formulation

    A. Racioppi,Coleman-Weinberg linear inflation: metric vs. Palatini formulation,JCAP12 (2017) 041 [1710.04853]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  35. [35]

    The Palatini side of inflationary attractors

    L. J¨ arv, A. Racioppi and T. Tenkanen,Palatini side of inflationary attractors,Phys. Rev. D 97(2018) 083513 [1712.08471]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  36. [36]

    New universal attractor in nonmininally coupled gravity: Linear inflation

    A. Racioppi,New universal attractor in nonminimally coupled gravity: Linear inflation,Phys. Rev. D97(2018) 123514 [1801.08810]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  37. [37]

    A minimal model of inflation and dark radiation

    K. Kannike, A. Kubarski, L. Marzola and A. Racioppi,A minimal model of inflation and dark radiation,Phys. Lett. B792(2019) 74 [1810.12689]. – 13 –

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  38. [38]

    Racioppi,Non-Minimal (Self-)Running Inflation: Metric vs

    A. Racioppi,Non-Minimal (Self-)Running Inflation: Metric vs. Palatini Formulation,JHEP 21(2020) 011 [1912.10038]

    work page arXiv 2020

  39. [39]

    J¨ arv, A

    L. J¨ arv, A. Karam, A. Kozak, A. Lykkas, A. Racioppi and M. Saal,Equivalence of inflationary models between the metric and Palatini formulation of scalar-tensor theories, Phys. Rev. D102(2020) 044029 [2005.14571]

    work page arXiv 2020

  40. [40]

    I. D. Gialamas, A. Karam and A. Racioppi,Dynamically induced Planck scale and inflation in the Palatini formulation,JCAP11(2020) 014 [2006.09124]

    work page arXiv 2020

  41. [41]

    Racioppi, J

    A. Racioppi, J. Rajasalu and K. Selke,Multiple point criticality principle and Coleman-Weinberg inflation,JHEP06(2022) 107 [2109.03238]

    work page arXiv 2022

  42. [42]

    Racioppi and M

    A. Racioppi and M. Vasar,On the number of e-folds in the Jordan and Einstein frames,Eur. Phys. J. Plus137(2022) 637 [2111.09677]

    work page arXiv 2022

  43. [43]

    H. G. Lillepalu and A. Racioppi,Generalized hilltop inflation,Eur. Phys. J. Plus138(2023) 894 [2211.02426]

    work page arXiv 2023

  44. [44]

    I. D. Gialamas, A. Karam, T. D. Pappas and E. Tomberg,Implications of Palatini gravity for inflation and beyond,Int. J. Geom. Meth. Mod. Phys.20(2023) 2330007 [2303.14148]

    work page arXiv 2023

  45. [45]

    Piani and J

    M. Piani and J. Rubio,Preheating in Einstein-Cartan Higgs Inflation: oscillon formation, JCAP12(2023) 002 [2304.13056]

    work page arXiv 2023

  46. [46]

    Barker and C

    W. Barker and C. Marzo,Particle spectra of general Ricci-type Palatini or metric-affine theories,Phys. Rev. D109(2024) 104017 [2402.07641]

    work page arXiv 2024

  47. [47]

    Dioguardi, A

    C. Dioguardi, A. Racioppi and E. Tomberg,Slow-roll inflation in Palatini F(R) gravity, JHEP06(2022) 106 [2112.12149]

    work page arXiv 2022

  48. [48]

    Racioppi,Slow-roll inflation in PalatiniF(R)gravity,PoSICHEP2022(2022) 073

    A. Racioppi,Slow-roll inflation in PalatiniF(R)gravity,PoSICHEP2022(2022) 073

    work page 2022

  49. [49]

    Dioguardi, A

    C. Dioguardi, A. Racioppi and E. Tomberg,Beyond (and back to) Palatini quadratic gravity and inflation,JCAP03(2024) 041 [2212.11869]

    work page arXiv 2024

  50. [50]

    Dioguardi and A

    C. Dioguardi and A. Racioppi,Palatini F(R,X): A new framework for inflationary attractors, Phys. Dark Univ.45(2024) 101509 [2307.02963]

    work page arXiv 2024

  51. [51]

    Kannike, A

    K. Kannike, A. Kubarski, L. Marzola and A. Racioppi,Pseudo-Goldstone dark matter in a radiative inverse seesaw scenario,JHEP12(2023) 166 [2306.07865]

    work page arXiv 2023

  52. [52]

    J. J. Terente D´ ıaz, K. Dimopoulos, M. Karˇ ciauskas and A. Racioppi,Quintessence in the Weyl-Gauss-Bonnet model,JCAP02(2024) 040 [2310.08128]

    work page arXiv 2024

  53. [53]

    Marzo,Can MAG be a predictive EFT? Radiative Stability and Ghost Resurgence in Massive Vector Models,2403.15003

    C. Marzo,Can MAG be a predictive EFT? Radiative Stability and Ghost Resurgence in Massive Vector Models,2403.15003

    work page arXiv

  54. [54]

    Iosifidis and S

    D. Iosifidis and S. Karamitsos,Pole inflation from extended metric-affine gravity,2510.20585

    work page arXiv

  55. [55]

    I. D. Gialamas, A. Karam, A. Racioppi and M. Raidal,Has ACT measured radiative corrections to the tree-level Higgs-like inflation?,Phys. Rev. D112(2025) 103544 [2504.06002]

    work page arXiv 2025

  56. [56]

    Dioguardi, A

    C. Dioguardi, A. J. Iovino and A. Racioppi,Fractional attractors in light of the latest ACT observations,Phys. Lett. B868(2025) 139664 [2504.02809]

    work page arXiv 2025

  57. [57]

    Dimopoulos, C

    K. Dimopoulos, C. Dioguardi, G. H¨ utsi and A. Racioppi,Quintessential inflation in Palatini F(R, X) gravity,Eur. Phys. J. Plus140(2025) 1109 [2503.21610]

    work page arXiv 2025

  58. [58]

    Dioguardi and A

    C. Dioguardi and A. Karam,Palatini linear attractors are back in action,Phys. Rev. D111 (2025) 123521 [2504.12937]

    work page arXiv 2025

  59. [59]

    G. K. Karananas,Geometrical origin of inflation in Weyl-invariant Einstein-Cartan gravity, Phys. Lett. B862(2025) 139343 [2501.16416]. – 14 –

    work page arXiv 2025

  60. [60]

    Barker, C

    W. Barker, C. Marzo and A. Santoni,Can metric-affine gravity be saved?,Phys. Rev. D112 (2025) 044032 [2505.23894]

    work page arXiv 2025

  61. [61]

    Barker, C

    W. Barker, C. Marzo and A. Santoni,Infrared foundations for quantum geometry I: Catalogue of totally symmetric rank-three field theories,2506.21662

    work page arXiv

  62. [62]

    Barker, C

    W. Barker, C. Marzo and A. Santoni,Infrared foundations for quantum geometry II: Catalogue of all torsion-like theories including new ghost-tachyon-free cases,2507.05349

    work page arXiv

  63. [63]

    Quasi-pole inflation in metric-affine gravity

    A. Racioppi,Quasi-pole inflation in metric-affine gravity,Gen. Rel. Grav.58(2026) 44 [2512.16815]

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  64. [64]

    Dimopoulos, C

    K. Dimopoulos, C. Dioguardi, I. D. Gialamas and A. Racioppi,Quasi-pole quintessential inflation in metric-affine gravity,2603.15776

    work page arXiv

  65. [65]

    Einstein-Cartan pseudoscalaron inflation, reheating and nonthermal leptogenesis

    C. Di Benedetto, A. Di Marco, E. Orazi and G. Pradisi,Einstein-Cartan pseudoscalaron inflation, reheating and nonthermal leptogenesis,2605.09571

    work page internal anchor Pith review Pith/arXiv arXiv

  66. [66]

    Hojman, C

    R. Hojman, C. Mukku and W. A. Sayed,PARITY VIOLATION IN METRIC TORSION THEORIES OF GRAVITATION,Phys. Rev. D22(1980) 1915

    work page 1980

  67. [67]

    P. C. Nelson,Gravity With Propagating Pseudoscalar Torsion,Phys. Lett. A79(1980) 285

    work page 1980

  68. [68]

    Barbero's Hamiltonian derived from a generalized Hilbert-Palatini action

    S. Holst,Barbero’s Hamiltonian derived from a generalized Hilbert-Palatini action,Phys. Rev. D53(1996) 5966 [gr-qc/9511026]

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  69. [69]

    R. D. Hecht, J. M. Nester and V. V. Zhytnikov,Some Poincare gauge theory Lagrangians with well posed initial value problems,Phys. Lett. A222(1996) 37

    work page 1996

  70. [70]

    Beltr´ an Jim´ enez and F

    J. Beltr´ an Jim´ enez and F. J. Maldonado Torralba,Revisiting the stability of quadratic Poincar´ e gauge gravity,Eur. Phys. J. C80(2020) 611 [1910.07506]

    work page arXiv 2020

  71. [71]

    L˚ angvik, J.-M

    M. L˚ angvik, J.-M. Ojanper¨ a, S. Raatikainen and S. Rasanen,Higgs inflation with the Holst and the Nieh–Yan term,Phys. Rev. D103(2021) 083514 [2007.12595]

    work page arXiv 2021

  72. [72]

    Rigouzzo and S

    C. Rigouzzo and S. Zell,Coupling metric-affine gravity to a Higgs-like scalar field,Phys. Rev. D106(2022) 024015 [2204.03003]

    work page arXiv 2022

  73. [73]

    Shaposhnikov, A

    M. Shaposhnikov, A. Shkerin, I. Timiryasov and S. Zell,Higgs inflation in Einstein-Cartan gravity,JCAP02(2021) 008 [2007.14978]

    work page arXiv 2021

  74. [74]

    Pradisi and A

    G. Pradisi and A. Salvio,(In)equivalence of metric-affine and metric effective field theories, Eur. Phys. J. C82(2022) 840 [2206.15041]

    work page arXiv 2022

  75. [75]

    Salvio,Inflating and reheating the Universe with an independent affine connection,Phys

    A. Salvio,Inflating and reheating the Universe with an independent affine connection,Phys. Rev. D106(2022) 103510 [2207.08830]

    work page arXiv 2022

  76. [76]

    Piani and J

    M. Piani and J. Rubio,Higgs-Dilaton inflation in Einstein-Cartan gravity,JCAP05(2022) 009 [2202.04665]

    work page arXiv 2022

  77. [77]

    Di Marco, E

    A. Di Marco, E. Orazi and G. Pradisi,Einstein–Cartan pseudoscalaron inflation,Eur. Phys. J. C84(2024) 146 [2309.11345]

    work page arXiv 2024

  78. [78]

    I. D. Gialamas and K. Tamvakis,Inflation in metric-affine quadratic gravity,JCAP03(2023) 042 [2212.09896]

    work page arXiv 2023

  79. [79]

    I. D. Gialamas, T. Katsoulas and K. Tamvakis,Inflation and reheating in quadratic metric-affine gravity with derivative couplings,JCAP06(2024) 005 [2403.08530]

    work page arXiv 2024

  80. [80]

    I. D. Gialamas and K. Tamvakis,Inflation in Weyl-invariant Einstein-Cartan gravity, 2410.16364

    work page arXiv

Showing first 80 references.