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arxiv: 2605.23990 · v1 · pith:ULQXHKKXnew · submitted 2026-05-17 · 🌌 astro-ph.CO · gr-qc· hep-ph

Hamilton-Jacobi Approach to Inflationary Scenarios through Extended Entropies: An Observational Perspective

H R M Zarandi , Esmaiel Ebrahimi , Yo Toda This is my paper

Pith reviewed 2026-06-30 19:28 UTC · model grok-4.3

classification 🌌 astro-ph.CO gr-qchep-ph
keywords generalized entropyHamilton-Jacobi formalismslow-roll inflationTsallis entropyRényi entropyKaniadakis entropycosmological parametersobservational constraints
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The pith

Hamilton-Jacobi formalism applied to generalized entropies constrains the Tsallis parameter to 1.1-1.2 and yields minuscule values for Rényi and Kaniadakis parameters.

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

The paper applies the Hamilton-Jacobi formalism to inflationary scenarios built on extended entropy measures rather than the standard Bekenstein-Hawking case. It introduces a non-linear parametrization of the Hubble parameter that directly connects the inflationary potential to the generalized entropy function and produces observables such as the scalar spectral index and tensor-to-scalar ratio. The resulting analysis supplies concrete estimates for the entropy parameters that remain consistent with current data. Constraints are obtained both from the primary observables ns and r and from variations in the uncertainty on the upper bound of r, narrowing the allowed ranges for the entropy parameters. The work also notes consequences for reheating dynamics and later cosmic structure evolution.

Core claim

The Hamilton-Jacobi approach establishes a direct link between the inflationary potential, the generalized entropy function, and cosmological observables through a novel non-linear parametrization of the Hubble parameter, yielding estimates of the Tsallis parameter δ≃1.1-1.2, the Rényi parameter α∼O(10^{-14}), and the Kaniadakis parameter K∼O(10^{-17}) that are consistent with recent observational data.

What carries the argument

The novel non-linear parametrization of the Hubble parameter, which maps generalized entropy functions onto slow-roll inflationary dynamics and observables.

If this is right

  • The models remain consistent with observed values of the scalar spectral index ns and tensor-to-scalar ratio r.
  • The dual constraint procedure using primary parameters and uncertainty on r restricts the viable parameter space of entropy-based inflationary models.
  • Varying the observational uncertainty on the upper bound of r produces complementary posterior distributions for the entropy parameters.
  • The framework carries implications for the reheating process and the subsequent evolution of cosmic structure.

Where Pith is reading between the lines

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

  • The same Hamilton-Jacobi mapping could be applied to other extended entropy formalisms beyond Tsallis, Rényi, and Kaniadakis.
  • Tighter future bounds on r would further shrink the allowed ranges for the entropy parameters.
  • The entropy modifications introduced at inflation could leave detectable imprints on the growth of cosmic structure at late times.

Load-bearing premise

The novel non-linear parametrization of the Hubble parameter produces physically sensible slow-roll dynamics and can be directly mapped onto the generalized entropy function without additional consistency conditions.

What would settle it

A future measurement of the scalar spectral index ns or tensor-to-scalar ratio r lying outside the posterior distributions derived for these entropy parameters would rule out the models.

read the original abstract

The slow-roll inflation paradigm can be systematically generalized within the framework of non-standard entropy formalisms, giving rise to a broad class of inflationary models that deviate from the conventional Bekenstein--Hawking case. We adopt a pragmatic observational strategy, employing the Hamilton--Jacobi formalism to establish a direct link between the inflationary potential, the generalized entropy function, and the resulting cosmological observables. In this approach we introduce a novel non-linear parametrization of the Hubble parameter, yielding sensible results, including consistency with recent observational data and new estimates of the cosmological parameters of the generalized entropy framework: the Tsallis parameter $\delta\simeq1.1-1.2$, the R\'enyi parameter $\alpha\sim\mathcal{O}(10^{-14})$, and the Kaniadakis statistics parameter $K\sim\mathcal{O}(10^{-17})$. Our analysis proceeds in two regimes: first, by constraining models directly with the primary inflationary parameters including the scalar spectral index ($n_s$) and the tensor-to-scalar ratio ($r$); second, by exploring the impact of the observational uncertainty on the upper bound of $r$ ($\sigma_r$), which we vary to assess its influence on parameter estimation. This dual approach yields complementary posterior distributions that restrict the viable parameter space of entropy-based inflationary models. We further highlight the implications of the Hamilton--Jacobi method for the dynamics of the inflationary epoch, the reheating process, and, as a secondary objective, the subsequent evolution of cosmic structure in the late universe.

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 / 1 minor

Summary. The manuscript presents a Hamilton-Jacobi approach to inflationary models generalized via Tsallis, Rényi, and Kaniadakis entropies. It introduces a novel non-linear parametrization of the Hubble parameter H(φ) to link the potential, entropy function, and observables ns and r. By fitting three free parameters (δ, α, K) to observational data, it reports estimates δ ≃ 1.1-1.2, α ∼ O(10^{-14}), K ∼ O(10^{-17}), and examines the effect of varying the uncertainty σ_r on these posteriors.

Significance. If the non-linear Hubble parametrization can be rigorously derived from the generalized entropy and the mapping to observables is verified, the work would offer concrete observational constraints on the parameters of non-standard entropy formalisms in the context of slow-roll inflation. This could help assess the viability of these extensions beyond the standard Bekenstein-Hawking entropy.

major comments (2)
  1. [Hamilton-Jacobi formalism and Hubble parametrization] The novel non-linear parametrization of the Hubble parameter is presented as yielding sensible slow-roll dynamics and mappable to the generalized entropy functions, but no explicit derivation is provided showing that this form follows from the modified entropy or satisfies the corresponding consistency conditions such as altered Friedmann or continuity equations. Since the reported parameter estimates depend on this mapping, this gap prevents verification that the constraints apply to the entropy models themselves rather than an auxiliary ansatz.
  2. [Parameter estimation section] The values of δ, α, and K are obtained by adjusting them to match the same ns and r data used to constrain standard inflation models. While described as 'estimates', this fitting procedure introduces circularity, as the posteriors are not independent predictions but tuned to reproduce the observed values.
minor comments (1)
  1. The abstract mentions two regimes of analysis (direct constraint with ns,r and impact of σ_r), but the distinction in the resulting posterior distributions could be clarified with additional figures or tables.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We respond point by point to the major comments below, clarifying our approach and indicating where revisions will be made.

read point-by-point responses

  1. Referee: [Hamilton-Jacobi formalism and Hubble parametrization] The novel non-linear parametrization of the Hubble parameter is presented as yielding sensible slow-roll dynamics and mappable to the generalized entropy functions, but no explicit derivation is provided showing that this form follows from the modified entropy or satisfies the corresponding consistency conditions such as altered Friedmann or continuity equations. Since the reported parameter estimates depend on this mapping, this gap prevents verification that the constraints apply to the entropy models themselves rather than an auxiliary ansatz.

    Authors: We agree that the non-linear parametrization of H(φ) is introduced as a novel ansatz within the Hamilton-Jacobi framework rather than being explicitly derived from the modified entropy or the corresponding altered Friedmann equations. The abstract describes the work as adopting a 'pragmatic observational strategy' to link the potential, entropy function, and observables. We will revise the manuscript to state this explicitly, clarify the phenomenological motivation for the chosen form, and note that a first-principles derivation from the entropy-modified dynamics lies outside the present scope. revision: partial

  2. Referee: [Parameter estimation section] The values of δ, α, and K are obtained by adjusting them to match the same ns and r data used to constrain standard inflation models. While described as 'estimates', this fitting procedure introduces circularity, as the posteriors are not independent predictions but tuned to reproduce the observed values.

    Authors: The procedure determines the values of the entropy parameters δ, α, and K that permit consistency with the observed ns and r within the slow-roll Hamilton-Jacobi setup. This is the standard method for placing observational constraints on additional model parameters, analogous to constraining the shape of the inflaton potential in conventional analyses. The resulting estimates are therefore new constraints on the generalized entropy parameters rather than independent predictions. We will revise the parameter estimation section to emphasize this distinction and the purpose of the fitting. revision: partial

Circularity Check

1 steps flagged

Entropy parameters δ/α/K reported as 'new estimates' are obtained by fitting chosen non-linear H(φ) to ns/r data

specific steps
  1. fitted input called prediction [Abstract]
    "yielding sensible results, including consistency with recent observational data and new estimates of the cosmological parameters of the generalized entropy framework: the Tsallis parameter δ≃1.1-1.2, the Rényi parameter α∼O(10^{-14}), and the Kaniadakis statistics parameter K∼O(10^{-17})"

    The reported parameter values are obtained by adjusting δ, α and K inside the chosen non-linear H(φ) model until ns and r match the same observational constraints that define the input data; the 'estimates' are therefore the fitted values by construction rather than predictions independent of that fit.

full rationale

The paper introduces a novel non-linear Hubble parametrization within the Hamilton-Jacobi formalism and then constrains the generalized entropy parameters (δ, α, K) directly against the same ns and r observables used for standard inflation. The abstract presents these as 'new estimates' yielded by the approach, but the values are the posterior best-fits to the input data rather than independent outputs derived from the entropy functions themselves. No explicit derivation is supplied showing that the chosen H(φ) form follows necessarily from the modified entropy or satisfies the corresponding Friedmann/continuity equations; the mapping is asserted to be possible. This reduces the central claim to a standard parameter fit presented as a prediction from first principles. No self-citation load-bearing or self-definitional steps are visible in the provided text.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 0 invented entities

The central claim rests on three fitted entropy parameters plus the assumption that the chosen non-linear Hubble parametrization is compatible with slow-roll dynamics and the chosen entropy functions. No new particles or forces are introduced.

free parameters (3)
  • Tsallis parameter δ
    Fitted directly to ns and r data; reported range 1.1-1.2
  • Rényi parameter α
    Fitted directly to ns and r data; reported order 10^{-14}
  • Kaniadakis parameter K
    Fitted directly to ns and r data; reported order 10^{-17}
axioms (2)
  • domain assumption Slow-roll approximation remains valid under the generalized entropy
    Invoked to connect the Hubble parametrization to the spectral index and tensor-to-scalar ratio
  • domain assumption Standard Friedmann equations hold with the modified entropy
    Required to translate the entropy function into an effective potential or Hubble evolution

pith-pipeline@v0.9.1-grok · 5817 in / 1596 out tokens · 32490 ms · 2026-06-30T19:28:53.956806+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

108 extracted references · 77 canonical work pages · 49 internal anchors

  1. [1]

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

    1980

  2. [2]

    Sato,First Order Phase Transition of a Vacuum and Expansion of the Universe, Mon

    K. Sato,First Order Phase Transition of a Vacuum and Expansion of the Universe, Mon. Not. Roy.Astron. Soc.195(1981) 467

    1981

  3. [3]

    Sato,Cosmological Baryon Number Domain Structure and the First Order Phase Transition of a Vacuum, Phys

    K. Sato,Cosmological Baryon Number Domain Structure and the First Order Phase Transition of a Vacuum, Phys. Lett. B99(1981) 66

    1981

  4. [4]

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

    1981

  5. [5]

    Kazanas,Dynamics of the Universe and Spontaneous Symmetry Breaking, Astrophys

    D. Kazanas,Dynamics of the Universe and Spontaneous Symmetry Breaking, Astrophys. J. Lett.241(1980) L59

    1980

  6. [6]

    Albrecht and P

    A. Albrecht and P. J. Steinhardt,Cosmology for Grand Unified Theories with Radiatively Induced Symmetry Breaking, Phys. Rev. Lett.48(1982) 1220

    1982

  7. [7]

    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

    1982

  8. [8]

    Measurements of Omega and Lambda from 42 High-Redshift Supernovae

    S. Perlmutteret al. [Supernova Cosmology Project],Measurements of Ω and Λ from 42 High Redshift Supernovae, Astrophys. J.517(1999) 565, [astro-ph/9812133]

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  9. [9]

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

    1983

  10. [10]

    S. D. Odintsov, V. K. Oikonomou and G. S. Sharov,Dynamical Dark Energy from F(R) Gravity Models Unifying Inflation with Dark Energy: Confronting the Latest Observational Data, arXiv:2506.02245 (2025)

    work page arXiv 2025

  11. [11]

    Kaneta, K

    K. Kaneta, K.-y. Oda and M. Yoshimura,A common origin of two accelerating universes: inflation and dark energy, arXiv:2503.02409 (2025)

    work page arXiv 2025

  12. [12]

    Ghosh, P

    M. Ghosh, P. Rudra, S. Chattopadhyay and B. Pourhassan,Warm inflation with Barrow holographic dark energy, Nucl. Phys. B1017(2025) 116933, [arXiv:2406.02639]

    work page arXiv 2025

  13. [13]

    Li,A fairy tale of winter - a theory about dark energy, dark matter, and inflation, Commun

    M. Li,A fairy tale of winter - a theory about dark energy, dark matter, and inflation, Commun. Theor. Phys.75(2023) 095406

    2023

  14. [14]

    A. I. Keskin,Inflation and dark energy in f(R, X, ϕ) gravity, Mod. Phys. Lett. A33(2018) 1850215

    2018

  15. [15]

    D. S. Salopek and J. R. Bond,Nonlinear Evolution of Long WavelengthMetric Fluctuations in Inflationary Models, Phys. Rev. D42(1990) 3936

    1990

  16. [16]

    Langlois,Hamiltonian formalism and gauge invariance for linear perturbations in inflation, Class

    D. Langlois,Hamiltonian formalism and gauge invariance for linear perturbations in inflation, Class. Quant. Grav.11(1994) 389

    1994

  17. [17]

    G. I. Rigopoulos and E. P. S. Shellard,The separate universe approach and the evolution of nonlinear superhorizon cosmological perturbations, Phys. Rev. D68(2003) 123518, [astro-ph/0306620]

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  18. [18]

    Hamilton-Jacobi approach for quasi-exponential inflation: predictions and constraints after Planck 2015 results

    N. Videla,Hamilton–Jacobiapproach for quasi-exponential inflation: predictions and constraints after Planck 2015 results, Eur. Phys. J. C77(2017) 142, [arXiv:1612.04124]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  19. [19]

    Artigas, E

    D. Artigas, E. Frion, T. Miranda, V. Vennin and D. Wands,On the Hamilton-Jacobi approach to inflation beyond slow roll, JCAP08(2025) 032, [arXiv:2504.05937]

    work page arXiv 2025

  20. [20]

    J. E. Lidsey, A. R. Liddle, E. W. Kolb, E. J. Copeland, T. Barreiro and M. Abney, Reconstructing the inflaton potential—an overview, Rev. Mod. Phys.69(1997) 373, [astro-ph/9508078]. – 24 –

    work page internal anchor Pith review Pith/arXiv arXiv 1997

  21. [21]

    J. M. Maldacena,The Large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys.2(1998) 231, [hep-th/9711200]

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  22. [22]

    Large N Field Theories, String Theory and Gravity

    O. Aharony, S. S. Gubser, J. M. Maldacena, H. Ooguri and Y. Oz,Large N field theories, string theory and gravity, Phys. Rept.323(2000) 183, [hep-th/9905111]

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  23. [23]

    Gravity and the Thermodynamics of Horizons

    T. Padmanabhan,Gravity and the thermodynamics of horizons, Phys. Rept.406(2005) 49, [gr-qc/0311036]

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  24. [24]

    The World as a Hologram

    L. Susskind,The Worldas a hologram, J. Math. Phys.36(1995) 6377, [hep-th/9409089]

    work page internal anchor Pith review Pith/arXiv arXiv 1995

  25. [25]

    Thermodynamics of Spacetime: The Einstein Equation of State

    T. Jacobson,Thermodynamics of Spacetime: The Einstein Equation of State, Phys. Rev. Lett. 75(1995) 1260, [gr-qc/9504004]

    work page internal anchor Pith review Pith/arXiv arXiv 1995

  26. [26]

    Classical and Quantum Thermodynamics of horizons in spherically symmetric spacetimes

    T. Padmanabhan,Classical and quantum thermodynamics of horizons in spherically symmetric space-times, Class. Quant. Grav.19(2002) 5387, [gr-qc/0204019]

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  27. [27]

    Non-equilibrium Thermodynamics of Spacetime

    C. Eling, R. Guedens and T. Jacobson,Non-equilibrium thermodynamics of spacetime, Phys. Rev. Lett.96(2006) 121301, [gr-qc/0602001]

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  28. [28]

    Friedmann Equations of FRW Universe in Scalar-tensor Gravity, f(R) Gravity and First Law of Thermodynamics

    M. Akbar and R.-G. Cai,Friedmann equations of FRWuniverse in scalar-tensor gravity, f(R) gravity and first law of thermodynamics, Phys. Lett. B635(2006) 7, [hep-th/0602156]

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  29. [29]

    Entropy of Null Surfaces and Dynamics of Spacetime

    T. Padmanabhan and A. Paranjape,Entropy of null surfaces and dynamics of spacetime, Phys. Rev. D75(2007) 064004, [gr-qc/0701003]

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  30. [30]

    Thermodynamical Aspects of Gravity: New insights

    T. Padmanabhan,Thermodynamical Aspects of Gravity: New insights, Rept. Prog. Phys.73 (2010) 046901, [arXiv:0911.5004]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  31. [31]

    L. C. Garcia de Andrade,Extended thermodynamics to Einstein-Cartan cosmology, Nuovo Cim. B116(2001) 1107, [gr-qc/0006015]

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  32. [32]

    The generalized second law of gravitational thermodynamics on the apparent and event horizons in FRW cosmology

    K. Karami, S. Ghaffari and M. M. Soltanzadeh,The generalized second law of gravitational thermodynamics on the apparent and event horizons in FRWcosmology, Class. Quant. Grav. 27(2010) 205021, [arXiv:1101.3240]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  33. [33]

    A note on the relations between thermodynamics, energy definitions and Friedmann equations

    H. Moradpour, R. C. Nunes, E. M. C. Abreu and J. A. Neto,A note on the relations between thermodynamics, energy definitions and Friedmann equations, Mod. Phys. Lett. A32(2017) 1750078, [arXiv:1603.01465]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  34. [34]

    L. M. Sanchez and H. Quevedo,Thermodynamics of the FLRWapparent horizon, Phys. Lett. B839(2023) 137778, [arXiv:2208.05729]

    work page arXiv 2023

  35. [35]

    E. P. Verlinde,On the holographic principle in a radiation dominated universe, arXiv:hep-th/0008140 (2000)

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  36. [36]

    B. Wang, E. Abdalla and R.-K. Su,Relating Friedmann equation to Cardy formula in universes with cosmological constant, Phys. Lett. B503(2001) 394, [hep-th/0101073]

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  37. [37]

    First Law of Thermodynamics and Friedmann Equations of Friedmann-Robertson-Walker Universe

    R.-G. Cai and S. P. Kim,First law of thermodynamics and Friedmann equations of Friedmann-Robertson-Walkeruniverse, JHEP02(2005) 050, [hep-th/0501055]

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  38. [38]

    Thermodynamic Behavior of Friedmann Equation at Apparent Horizon of FRW Universe

    M. Akbar and R.-G. Cai,Thermodynamic Behavior of Friedmann Equations at Apparent Horizon of FRWUniverse, Phys. Rev. D75(2007) 084003, [hep-th/0609128]

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  39. [39]

    Friedmann Equations from Entropic Force

    R.-G. Cai, L.-M. Cao and N. Ohta,Friedmann Equations from Entropic Force, Phys. Rev. D 81(2010) 061501, [arXiv:1001.3470]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  40. [40]

    J. D. Barrow,The Area of a Rough Black Hole, Phys. Lett. B808(2020) 135643, [arXiv:2004.09444]

    work page arXiv 2020

  41. [41]

    Sheykhi,Barrow Entropy Corrections to Friedmann Equations, Phys

    A. Sheykhi,Barrow Entropy Corrections to Friedmann Equations, Phys. Rev. D103(2021) 123503, [arXiv:2102.06550]

    work page arXiv 2021

  42. [42]

    Tsallis,Possible Generalization of Boltzmann-Gibbs Statistics, J

    C. Tsallis,Possible Generalization of Boltzmann-Gibbs Statistics, J. Statist. Phys.52(1988) 479. – 25 –

    1988

  43. [43]

    M. L. Lyra and C. Tsallis,Nonextensivity and Multifractality in Low-Dimensional Dissipative Systems, Phys. Rev. Lett.80(1998) 53, [cond-mat/9709226]

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  44. [44]

    Tsallis Holographic Dark Energy

    M. Tavayef, A. Sheykhi, K. Bamba and H. Moradpour,TsallisHolographic Dark Energy, Phys. Lett. B781(2018) 195, [arXiv:1804.02983]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  45. [45]

    Motaghi, A

    M. Motaghi, A. Sheykhi and E. Ebrahimi,Holographic dark energy in Barrow cosmology with Granda-Oliveros IR cutoff, Phys. Dark Univ.46(2024) 101710, [arXiv:2407.21074]

    work page arXiv 2024

  46. [46]

    Mohammadi, T

    A. Mohammadi, T. Golanbari, K. Bamba and I. P. Lobo,Tsallis holographic dark energy for inflation, Phys. Rev. D103(2021) 083505, [arXiv:2101.06378]

    work page arXiv 2021

  47. [47]

    Yarahmadi and A

    M. Yarahmadi and A. Salehi,Alleviating the Hubble tension using the Barrow holographic dark energy cosmology with Granda–OliverosIR cut-off, Mon. Not. Roy.Astron. Soc.534 (2024) 3055

    2024

  48. [48]

    A. Rényi,On Measures of Entropy and Information, inProceedings of the FourthBerkeley Symposium on Mathematical Statistics and Probability,Volume 1: Contributions to the Theory of Statistics (1961) 547

    1961

  49. [49]

    Cosmological model from the holographic equipartition law with a modified R\'{e}nyi entropy

    N. Komatsu,Cosmological model from the holographic equipartition law with a modified Rényi entropy, Eur. Phys. J. C77(2017) 229, [arXiv:1611.04084]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  50. [50]

    Accelerated cosmos in a non-extensive setup

    H. Moradpour, A. Bonilla, E. M. C. Abreu and J. A. Neto,Accelerated cosmos in a nonextensive setup, Phys. Rev. D96(2017) 123504, [arXiv:1711.08338]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  51. [51]

    Naeem, J

    M. Naeem, J. Ahmed and A. Bibi,Entropic cosmology for Rényi entropy, Eur. Phys. J. Plus 137(2022) 962

    2022

  52. [52]

    Statistical mechanics in the context of special relativity

    G. Kaniadakis,Statistical mechanics in the context of special relativity, Phys. Rev. E66 (2002) 056125, [cond-mat/0210467]

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  53. [53]

    Statistical mechanics in the context of special relativity II

    G. Kaniadakis,Statistical mechanics in the context of special relativity.II., Phys. Rev. E72 (2005) 036108, [cond-mat/0507311]

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  54. [54]

    Drepanou, A

    N. Drepanou, A. Lymperis, E. N. Saridakis and K. Yesmakhanova,Kaniadakis holographic dark energy and cosmology, Eur. Phys. J. C82(2022) 449, [arXiv:2112.03568]

    work page arXiv 2022

  55. [55]

    Moradpour, A

    H. Moradpour, A. H. Ziaie and M. Kord Zangeneh,Generalized entropies and corresponding holographic dark energy models, Eur. Phys. J. C80(2020) 732, [arXiv:2005.06271]

    work page arXiv 2020

  56. [56]

    Lymperis, S

    A. Lymperis, S. Basilakos and E. N. Saridakis,Modified cosmology through Kaniadakis horizon entropy, Eur. Phys. J. C81(2021) 1037, [arXiv:2108.12366]

    work page arXiv 2021

  57. [57]

    Sheykhi,Corrections to Friedmann equations inspired by Kaniadakis entropy, arXiv:2302.13012 (2023)

    A. Sheykhi,Corrections to Friedmann equations inspired by Kaniadakis entropy, arXiv:2302.13012 (2023)

    work page arXiv 2023

  58. [58]

    Kord Zangeneh and A

    M. Kord Zangeneh and A. Sheykhi,Modified cosmology through Kaniadakis entropy, Mod. Phys. Lett. A39(2024) 2450138, [arXiv:2311.01969]

    work page arXiv 2024

  59. [59]

    S. K. P, B. D. Pandey, U. K. Sharma and Pankaj,Holographic dark energy through Kaniadakis entropy in non flat universe, Eur. Phys. J. C83(2023) 143, [arXiv:2211.15468]

    work page arXiv 2023

  60. [60]

    H. R. M. Zarandi, Y. Toda and E. Ebrahimi,Investigating cosmology models through usual and dual Kaniadakis entropies: theoretical and observational tensions and features, Eur. Phys. J. C85(2025) 589

    2025

  61. [61]

    Black Hole Entropy from Loop Quantum Gravity

    C. Rovelli,Black hole entropy from loop quantum gravity, Phys. Rev. Lett.77(1996) 3288, [gr-qc/9603063]

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  62. [62]

    R. B. Mann and S. N. Solodukhin,Quantum scalar field on three-dimensional (BTZ) black hole instanton: Heat kernel, effective action and thermodynamics, Phys. Rev. D55(1997) 3622, [hep-th/9609085]. – 26 –

    work page internal anchor Pith review Pith/arXiv arXiv 1997

  63. [63]

    R. K. Kaul and P. Majumdar,Logarithmic correction to the Bekenstein-Hawking entropy, Phys. Rev. Lett.84(2000) 5255, [gr-qc/0002040]

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  64. [64]

    S. Das, P. Majumdar and R. K. Bhaduri,General logarithmic corrections to black hole entropy, Class. Quant. Grav.19(2002) 2355, [hep-th/0111001]

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  65. [65]

    Quantum Tunneling Beyond Semiclassical Approximation

    R. Banerjee and B. R. Majhi,Quantum TunnelingBeyond Semiclassical Approximation, JHEP 06(2008) 095, [arXiv:0805.2220]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  66. [66]

    S. Das, S. Shankaranarayanan and S. Sur,Power-lawcorrections to entanglement entropy of black holes, Phys. Rev. D77(2008) 064013, [arXiv:0705.2070]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  67. [67]

    The generalized second law in universes with quantum corrected entropy relations

    N. Radicella and D. Pavón,The generalized second law in universes with quantum corrected entropy relations, Phys. Lett. B691(2010) 121, [arXiv:1006.3745]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  68. [68]

    Khodam-Mohammadi and M

    A. Khodam-Mohammadi and M. Monshizadeh,Exploring modifications to FLRWcosmology with general entropy and thermodynamics: A new approach, Phys. Lett. B843(2023) 138066

    2023

  69. [69]

    Khodam-Mohammadi,Non-extensive entropy and power-law inflation: Implications for observations, Mod

    A. Khodam-Mohammadi,Non-extensive entropy and power-law inflation: Implications for observations, Mod. Phys. Lett. A39(2024) 2450146

    2024

  70. [70]

    Nojiri, S

    S. Nojiri, S. D. Odintsov and T. Paul,Modified cosmology from the thermodynamics of apparent horizon, Phys. Lett. B835(2022) 137553

    2022

  71. [71]

    S. Das, S. Shankaranarayanan and S. Sur,Power-lawcorrections to entanglement entropy of horizons, Phys. Rev. D77(2008) 064013

    2008

  72. [72]

    Sheykhi,Modified cosmology through Barrow entropy, Phys

    A. Sheykhi,Modified cosmology through Barrow entropy, Phys. Rev. D107(2023) 023505

    2023

  73. [73]

    Sheykhi,Modified Friedmann equations from Tsallis entropy, Phys

    A. Sheykhi,Modified Friedmann equations from Tsallis entropy, Phys. Lett. B785(2018) 118

    2018

  74. [74]

    E. M. C. Abreu and J. A. Neto,Statistical approaches on the apparent horizon entropy and the generalized second law of thermodynamics, Phys. Lett. B824(2022) 136803

    2022

  75. [75]

    H. R. Fazlollahi,Rényi entropy correction to expanding universe, Eur. Phys. J. C83(2023) 29

    2023

  76. [76]

    Lymperis, S

    A. Lymperis, S. Basilakos and E. N. Saridakis,Modified cosmology through Kaniadakis horizon entropy, Eur. Phys. J. C81(2021) 1037

    2021

  77. [77]

    Reducing spurious gravitational radiation in binary-black-hole simulations by using conformally curved initial data

    K. Tzirakis and W. H. Kinney,Non-canonical generalizations of slow-roll inflation models, JCAP01(2009) 028, [arXiv:0812.3132]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  78. [78]

    Casimir energy-momentum tensor for the Robin Surfaces in de Sitter Spacetime

    K. Skenderis and P. K. Townsend,Hamilton-Jacobi method for curved domain walls and cosmologies, Phys. Rev. D74(2006) 125008, [hep-th/0510220]

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  79. [79]

    C. T. Byrnes and G. Tasinato,Non-Gaussianity beyond slow roll in multi-field inflation, JCAP 08(2009) 016, [arXiv:0905.2173]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  80. [80]

    Silicon nanowire based exclusive-OR gate using nonlinear optics for 40Gb/s DPSK signals

    D. Coone, D. Roest and V. Vennin,The Hubble flow of plateau inflation, JCAP11(2015) 010, [arXiv:1505.03222]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

Showing first 80 references.