pith. sign in

arxiv: 2606.27799 · v1 · pith:EQ4ZXGMEnew · submitted 2026-06-26 · 🌀 gr-qc

New interpretation of the Minkowski limit of R² gravity

Valerio Faraoni , Luca Gallerani , Alain Maltais-Gosselin , Santiago Novoa-Cattivelli , Uri Gorman This is my paper

Pith reviewed 2026-06-29 04:03 UTC · model grok-4.3

classification 🌀 gr-qc
keywords R² gravityMinkowski limitstrong coupling problemthermal analogyscalar-tensor gravityEckart fluidsStarobinsky theorygravitational temperature
0
0 comments X

The pith

Approaching the Minkowski background in pure R² gravity makes the effective gravitational temperature diverge.

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

The paper shows that the Minkowski limit of pure R² gravity fails because the effective gravitational temperature diverges in the thermal analogy to Eckart's relativistic dissipative fluids. This turns the known strong coupling problem into a thermal singularity. The result means R² gravity moves infinitely far from general relativity in this limit, unlike the full Starobinsky model that includes a linear R term. The interpretation relies on mapping the scalar degree of freedom in f(R) theories to a dissipative fluid description.

Core claim

In the thermal analogy between scalar-tensor gravity and Eckart's relativistic dissipative fluids, the Minkowski limit of pure R² gravity is marked by a diverging effective gravitational temperature, which rephrases the strong coupling problem as a thermal singularity and shows that the theory departs infinitely far from General Relativity.

What carries the argument

The thermal analogy between scalar-tensor gravity and Eckart's relativistic dissipative fluids, which identifies an effective gravitational temperature that diverges in the Minkowski limit.

If this is right

  • The strong coupling problem of R² gravity is reinterpreted as a thermal singularity rather than a simple breakdown.
  • Pure R² gravity does not recover general relativity in the Minkowski limit but instead diverges from it.
  • The presence of the linear R term in Starobinsky theory prevents the temperature divergence and allows a smooth Minkowski limit.
  • The effective temperature provides a new diagnostic for when modified gravity theories approach or depart from general relativity.

Where Pith is reading between the lines

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

  • If the temperature divergence is physical, it may suggest that R² gravity requires a cutoff or regularization mechanism near flat space to remain consistent.
  • The same thermal mapping could be applied to other f(R) models to classify which ones recover general relativity in the Minkowski limit.
  • This view connects the strong coupling issue to thermodynamic instabilities in dissipative fluids, opening a route to study stability criteria in modified gravity.

Load-bearing premise

The thermal analogy between scalar-tensor gravity and Eckart's relativistic dissipative fluids is valid and applies directly to the Minkowski limit of pure R² gravity.

What would settle it

A calculation that tracks the effective gravitational temperature while the background curvature is taken to zero in the R² action, checking whether it remains finite or diverges.

Figures

Figures reproduced from arXiv: 2606.27799 by Alain Maltais-Gosselin, Luca Gallerani, Santiago Novoa-Cattivelli, Uri Gorman, Valerio Faraoni.

Figure 1
Figure 1. Figure 1: The (Θ, KT ) plane view of the non-dynamical Minkowski limit Λ → 0 of de Sitter space for f(R) = R 2 . The point on the Θ-axis is a generic de Sitter solution; as the parameter Λ → 0, it crosses (non-dynamically) the criti￾cal line 8πKT = Θ. However, at the Minkowski point (0, 0), KT → +∞. which recovers the result of [23] contained in Eq. (1.3). The fact that Geff is constant on de Sitter spaces makes it … view at source ↗
read the original abstract

It is well-established that the Minkowski limit of pure $f(R)=R^2$ gravity breaks down, unlike that of full Starobinsky theory $f(R)=R+\alpha R^2$. We provide a novel interpretation of this phenomenon using the recent thermal analogy between scalar-tensor gravity and Eckart's relativistic dissipative fluids. In this framework, we show that approaching the Minkowski background corresponds to a diverging effective ``gravitational temperature''. This perspective naturally rephrases the strong coupling problem as a thermal singularity, demonstrating that $R^2$ gravity departs infinitely far from General Relativity rather than recovering it.

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 / 0 minor

Summary. The manuscript claims that the known breakdown of the Minkowski limit in pure f(R)=R² gravity (unlike Starobinsky theory) can be reinterpreted via the thermal analogy between scalar-tensor gravity and Eckart's relativistic dissipative fluids. In this framework, approaching the Minkowski background corresponds to a diverging effective 'gravitational temperature,' which recasts the strong coupling problem as a thermal singularity and demonstrates that R² gravity departs infinitely far from General Relativity rather than recovering it.

Significance. If the mapping of the thermal analogy to the pure R² Minkowski limit can be established without limit-specific adjustments and yields an independent divergence of the effective temperature, the paper would provide a useful interpretive lens on an established issue in modified gravity. However, the contribution is primarily rephrasing rather than a new derivation or prediction, so its significance remains moderate even if the central claim holds.

major comments (1)
  1. The central claim that approaching the Minkowski background corresponds to a diverging effective gravitational temperature (and thereby demonstrates infinite departure from GR) rests on the scalar-tensor–Eckart fluid analogy. It is not evident that the temperature divergence is derived independently of the quantities used to define the limit itself; if the effective temperature is constructed from the same scalar degree of freedom that encodes the breakdown, the rephrasing risks circularity and does not yet establish the thermal singularity as a robust new perspective.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and the constructive comment on our manuscript. We address the major comment below, providing clarification on the independence of the temperature divergence within the established analogy.

read point-by-point responses

  1. Referee: The central claim that approaching the Minkowski background corresponds to a diverging effective gravitational temperature (and thereby demonstrates infinite departure from GR) rests on the scalar-tensor–Eckart fluid analogy. It is not evident that the temperature divergence is derived independently of the quantities used to define the limit itself; if the effective temperature is constructed from the same scalar degree of freedom that encodes the breakdown, the rephrasing risks circularity and does not yet establish the thermal singularity as a robust new perspective.

    Authors: The Minkowski limit is defined exclusively by the curvature scalar R approaching zero with the metric approaching the flat Minkowski metric. The scalar-tensor equivalent of pure R² gravity relates the scalar degree of freedom φ to R via φ ∝ R. The Eckart fluid analogy, applied uniformly to scalar-tensor theories, maps the scalar field and its derivatives to the dissipative fluid variables (energy density, heat flux q^μ, and viscous stresses). The effective gravitational temperature T_grav is then obtained from the thermodynamic relations in Eckart theory, specifically T_grav ∝ |q^μ u_μ| / (ρ + p) in the appropriate frame, where these quantities are expressed in terms of the scalar gradients and the background. Substituting the limiting behavior R → 0 into these mapped expressions yields a divergence in T_grav due to the structure of the pure R² field equations (lacking the linear R term that stabilizes the limit in Starobinsky gravity). This calculation follows directly from the general mapping without presupposing the divergence or introducing limit-specific adjustments. The rephrasing as a thermal singularity is thus a consequence of the analogy rather than a redefinition. We will add an explicit subsection deriving T_grav from the fluid variables and demonstrating the limit to make this independence fully transparent. revision: partial

Circularity Check

0 steps flagged

No significant circularity; interpretive rephrasing relies on external analogy without reduction to inputs

full rationale

The paper applies a pre-existing thermal analogy between scalar-tensor theories and Eckart fluids to reinterpret the established breakdown of the Minkowski limit in pure R² gravity as a diverging effective temperature. This is presented as a novel perspective rather than a derivation that reduces by construction to fitted parameters, self-definitions, or a self-citation chain. No equations or steps in the provided material exhibit the patterns of self-definitional mapping, fitted inputs renamed as predictions, or load-bearing uniqueness imported solely from the authors' prior unverified work. The central claim remains an application of an independent framework to a known result, keeping the argument self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests on the applicability of a recently introduced thermal analogy whose validity is not demonstrated within the provided abstract. No free parameters or invented entities beyond the effective temperature are visible.

axioms (1)
  • domain assumption The thermal analogy between scalar-tensor gravity and Eckart's relativistic dissipative fluids holds and can be used to reinterpret the Minkowski limit.
    Invoked to convert the strong-coupling issue into a temperature divergence.
invented entities (1)
  • effective gravitational temperature no independent evidence
    purpose: To quantify the divergence that signals departure from GR in the Minkowski limit.
    Introduced via the fluid analogy; no independent evidence supplied in the abstract.

pith-pipeline@v0.9.1-grok · 5642 in / 1417 out tokens · 45641 ms · 2026-06-29T04:03:08.749642+00:00 · methodology

discussion (0)

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

Reference graph

Works this paper leans on

93 extracted references · 76 canonical work pages · 21 internal anchors

  1. [1]

    that R2 gravity does not admit a Newtonian limit (see also [5]). More precisely, one cannot obtain the New- tonian limit by linearizing the fourth-order field equation s of R2 gravity R ( Rab − R 4 gab ) − ∇ a∇ bR +gab□R = 8πT (m) ab (1.2) around Minkowski space, as done in GR [12]. However, it has recently been shown that it is possible to obtain a Newton...

    Pith/arXiv arXiv 2026

  2. [2]

    R0-degeneracy

    3 ·10− 5 [27]. However, in high-density environments, the chameleon mechanism implicitly contained in many f (R) theories gives a short range to the scalar degree of freedom f ′(R), hiding the deviations from GR in Solar System and galactic environments. The de Sitter background of constant Ricci curvature R0 exists if the function f (R) obeys the conditi...

    2023

  3. [3]

    Amendola and S

    L. Amendola and S. Tsujikawa, Dark Energy: Theory and Observations, Cambridge University Press, 2015, ISBN 978-1-107-45398-2

    2015

  4. [4]

    f(R) Theories Of Gravity

    T. P. Sotiriou and V. Faraoni, “ f (R) Theories Of Gravity,” Rev. Mod. Phys. 82 (2010), 451-497 doi:10.1103/RevModPhys.82.451 [arXiv:0805.1726 [gr- qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/revmodphys.82.451 2010

  5. [5]

    f(R) theories

    A. De Felice and S. Tsujikawa, “ f (R) theories,” Liv- ing Rev. Rel. 13, 3 (2010) doi:10.12942/lrr-2010- 3[arXiv:1002.4928 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.12942/lrr-2010- 2010

  6. [6]

    Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models

    S. Nojiri and S. D. Odintsov, “Unified cosmic history in modified gravity: from F (R) theory to Lorentz non-invariant models,” Phys. Rept. 505, 59-144 (2011) doi:10.1016/j.physrep.2011.04.001[arXiv:1011.0544 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.physrep.2011.04.001 2011

  7. [7]

    Renormalization of Higher Derivative Quantum Gravity,

    K. S. Stelle, “Renormalization of Higher Derivative Quantum Gravity,” Phys. Rev. D 16, 953-969 (1977) doi:10.1103/PhysRevD.16.953

    work page doi:10.1103/physrevd.16.953 1977

  8. [8]

    Spectrum of relict gravitational ra- diation and the early state of the universe,

    A. A. Starobinsky, “Spectrum of relict gravitational ra- diation and the early state of the universe,” JETP Lett. 30, 682-685 (1979)

    1979

  9. [9]

    A New Type of Isotropic Cosmolog- ical Models Without Singularity,

    A. A. Starobinsky, “A New Type of Isotropic Cosmolog- ical Models Without Singularity,” Phys. Lett. B 91, 99- 102 (1980) doi:10.1016/0370-2693(80)90670-X

    work page doi:10.1016/0370-2693(80)90670-x 1980

  10. [10]

    Renormalizable Asymptotically Free Quantum Theory of Gravity,

    E. S. Fradkin and A. A. Tseytlin, “Renormalizable Asymptotically Free Quantum Theory of Gravity,” Phys. Lett. B 104, 377-381 (1981) doi:10.1016/0370- 2693(81)90702-4

    work page doi:10.1016/0370- 1981

  11. [11]

    Einstein Gravity as a Symmetry-Breaking Effect in Quantum Field Theory,

    S. L. Adler, “Einstein Gravity as a Symmetry-Breaking Effect in Quantum Field Theory,” Rev. Mod. Phys. 54, 729 (1982) [erratum: Rev. Mod. Phys. 55, 837 (1983)] doi:10.1103/RevModPhys.54.729

    work page doi:10.1103/revmodphys.54.729 1982

  12. [12]

    Asymptotic freedom in higher derivative quantum gravity,

    I. G. A vramidi and A. O. Barvinsky, “Asymptotic freedom in higher derivative quantum gravity,” Phys. Lett. B 159, 269-274 (1985) doi:10.1016/0370-2693(85)90248-5

    work page doi:10.1016/0370-2693(85)90248-5 1985

  13. [14]

    R. M. Wald, General Relativ- ity, Chicago University Press, 1984, doi:10.7208/chicago/9780226870373.001.0001

    work page doi:10.7208/chicago/9780226870373.001.0001 1984

  14. [15]

    Inflation in scale-invariant theories of gravity

    M. Rinaldi, G. Cognola, L. Vanzo and S. Zerbini, “Inflation in scale-invariant theories of grav- ity,” Phys. Rev. D 91, no.12, 123527 (2015) doi:10.1103/PhysRevD.91.123527 [arXiv:1410.0631 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.91.123527 2015

  15. [16]

    Inflation and reheating in theories with spontaneous scale invariance symmetry breaking

    M. Rinaldi and L. Vanzo, “Inflation and reheating in theories with spontaneous scale invariance symme- try breaking,” Phys. Rev. D 94, no.2, 024009 (2016) doi:10.1103/PhysRevD.94.024009 [arXiv:1512.07186 [gr- qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.94.024009 2016

  16. [17]

    Inflation and reheating in scale-invariant scalar-tensor gravity

    G. Tambalo and M. Rinaldi, “Inflation and reheat- ing in scale-invariant scalar-tensor gravity,” Gen. Rel. Grav. 49, no.4, 52 (2017) doi:10.1007/s10714-017-2217- 8 [arXiv:1610.06478 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/s10714-017-2217- 2017

  17. [18]

    Scale-independent R2 inflation,

    P. G. Ferreira, C. T. Hill, J. Noller and G. G. Ross, “Scale-independent R2 inflation,” Phys. Rev. D 100, no.12, 123516 (2019) doi:10.1103/PhysRevD.100.123516 [arXiv:1906.03415 [gr-qc]]

    work page doi:10.1103/physrevd.100.123516 2019

  18. [19]

    Scale-invariant inflation with one-loop quantum corrections

    S. Vicentini, L. Vanzo and M. Rinaldi, “Scale- invariant inflation with one-loop quantum correc- tions,” Phys. Rev. D 99, no.10, 103516 (2019) doi:10.1103/PhysRevD.99.103516 [arXiv:1902.04434 [gr- qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.99.103516 2019

  19. [20]

    In- flation and primordial gravitational waves in scale- invariant quadratic gravity with Higgs,

    A. Ghoshal, D. Mukherjee and M. Rinaldi, “In- flation and primordial gravitational waves in scale- invariant quadratic gravity with Higgs,” JHEP 05, 023 (2023) doi:10.1007/JHEP05(2023)023 [arXiv:2205.06475 [gr-qc]]

    work page doi:10.1007/jhep05(2023)023 2023

  20. [21]

    Scale-invariant inflation,

    M. Rinaldi, C. Cecchini, A. Ghoshal and D. Mukherjee, “Scale-invariant inflation,” J. Phys. Conf. Ser. 2531, no.1, 012012 (2023) doi:10.1088/1742-6596/2531/1/012012 [arXiv:2303.16107 [gr-qc]]

    work page doi:10.1088/1742-6596/2531/1/012012 2023

  21. [22]

    Tracing cos- mic stretch marks: probing scale invariance in the early Universe,

    M. De Angelis, C. Cecchini and M. Rinaldi, “Tracing cos- mic stretch marks: probing scale invariance in the early Universe,” [arXiv:2410.05977 [hep-th]]

    arXiv

  22. [23]

    Testing scale-invariant inflation against co s- mological data,

    C. Cecchini, M. De Angelis, W. Giarè, M. Rinaldi and S. Vagnozzi, “Testing scale-invariant inflation against co s- mological data,” JCAP 07, 058 (2024) doi:10.1088/1475- 7516/2024/07/058 [arXiv:2403.04316 [astro-ph.CO]]

    work page doi:10.1088/1475- 2024

  23. [24]

    On quadratic lagrangians in General Relativity,

    E. Pechlaner and R. Sexl, “On quadratic lagrangians in General Relativity,” Commun. Math. Phys. 2, no.1, 165- 175 (1966) doi:10.1007/BF01773351

    work page doi:10.1007/bf01773351 1966

  24. [25]

    Emerging Newtonian potential in pure R2 gravity on a de Sitter background,

    H. K. Nguyen, “Emerging Newtonian potential in pure R2 gravity on a de Sitter background,” JHEP 08, 127 (2023) doi:10.1007/JHEP08(2023)127 [arXiv:2306.03790 [gr-qc]]

    work page doi:10.1007/jhep08(2023)127 2023

  25. [26]

    Solar System constraints to general f(R) gravity

    T. Chiba, T. L. Smith and A. L. Erickcek, “Solar Sys- tem constraints to general f(R) gravity,” Phys. Rev. D 75, 124014 (2007) doi:10.1103/PhysRevD.75.124014 [arXiv:astro-ph/0611867 [astro-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.75.124014 2007

  26. [27]

    Limit to General Relativity in f(R) theories of gravity

    G. J. Olmo, “Limit to general relativity in f(R) the- ories of gravity,” Phys. Rev. D 75, 023511 (2007) doi:10.1103/PhysRevD.75.023511 [arXiv:gr-qc/0612047 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.75.023511 2007

  27. [28]

    Spherically symmetric spacetimes in f(R) gravity theories

    K. Kainulainen, J. Piilonen, V. Reijonen and D. Sun- hede, “Spherically symmetric spacetimes in f(R) grav- 9 ity theories,” Phys. Rev. D 76, 024020 (2007) doi:10.1103/PhysRevD.76.024020 [arXiv:0704.2729 [gr- qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.76.024020 2007

  28. [29]

    A test of general relativity using radio links with the Cassini spacecraft,

    B. Bertotti, L. Iess and P. Tortora, “A test of general relativity using radio links with the Cassini spacecraft,” Nature 425, 374-376 (2003) doi:10.1038/nature01997

    work page doi:10.1038/nature01997 2003

  29. [30]

    The Stability of General Relativistic Cosmological Theory,

    J. D. Barrow and A. C. Ottewill, “The Stability of General Relativistic Cosmological Theory,” J. Phys. A 16, 2757 (1983) doi:10.1088/0305-4470/16/12/022

    work page doi:10.1088/0305-4470/16/12/022 1983

  30. [31]

    de Sitter space and the equivalence between f(R) and scalar-tensor gravity

    V. Faraoni, “de Sitter space and the equivalence be- tween f(R) and scalar-tensor gravity,” Phys. Rev. D 75, 067302 (2007) doi:10.1103/PhysRevD.75.067302 [arXiv:gr-qc/0703044 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.75.067302 2007

  31. [32]

    Physical nonviability of a wide class of f (R) models and their constant-curvature so- lutions,

    A. Casado-Turrión, Á. de la Cruz-Dombriz and A. Dobado, “Physical nonviability of a wide class of f (R) models and their constant-curvature so- lutions,” Phys. Rev. D 108, no.6, 064006 (2023) doi:10.1103/PhysRevD.108.064006 [arXiv:2303.02103 [gr-qc]]

    work page doi:10.1103/physrevd.108.064006 2023

  32. [33]

    Propagating degrees of freedom on maximally symmetric backgrounds in f(R) theories of gravity,

    A. Casado-Turrión, Á. de la Cruz-Dombriz and A. Dobado, “Propagating degrees of freedom on maximally symmetric backgrounds in f(R) theories of gravity,” Phys. Rev. D 111, no.4, 044030 (2025) doi:10.1103/PhysRevD.111.044030 [arXiv:2412.09366 [gr-qc]]

    work page doi:10.1103/physrevd.111.044030 2025

  33. [34]

    Probing the f(R) formalism through gravitational wave polarizations

    M. E. S. Alves, O. D. Miranda and J. C. N. de Araujo, “Probing the f(R) formalism through gravitational wave polarizations,” Phys. Lett. B 679, 401-406 (2009) doi:10.1016/j.physletb.2009.08.005 [arXiv:0908.0861 [ gr- qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.physletb.2009.08.005 2009

  34. [36]

    Gravitational Wave Polarization Modes in $f(R)$ Theories

    H. Rizwana Kausar, L. Philippoz and P. Jetzer, “Gravitational Wave Polarization Modes in f (R) The- ories,” Phys. Rev. D 93, no.12, 124071 (2016) doi:10.1103/PhysRevD.93.124071 [arXiv:1606.07000 [gr- qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.93.124071 2016

  35. [37]

    Polarizations of gravitational waves in $f(R)$ gravity

    D. Liang, Y. Gong, S. Hou and Y. Liu, “Polarizations of gravitational waves in f (R) gravity,” Phys. Rev. D 95, no.10, 104034 (2017) doi:10.1103/PhysRevD.95.104034 [arXiv:1701.05998 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.95.104034 2017

  36. [38]

    Gauge invariant formulation of metric f (R) gravity for gravi- tational waves,

    F. Moretti, F. Bombacigno and G. Montani, “Gauge invariant formulation of metric f (R) gravity for gravi- tational waves,” Phys. Rev. D 100, no.8, 084014 (2019) doi:10.1103/PhysRevD.100.084014 [arXiv:1906.01899 [gr-qc]]

    work page doi:10.1103/physrevd.100.084014 2019

  37. [39]

    Aspects of Quadratic Gravity

    L. Alvarez-Gaume, A. Kehagias, C. Kounnas, D. Lüst and A. Riotto, “Aspects of Quadratic Gravity,” Fortsch. Phys. 64, no.2-3, 176-189 (2016) doi:10.1002/prop.201500100 [arXiv:1505.07657 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1002/prop.201500100 2016

  38. [40]

    Black Hole Solutions in $R^2$ Gravity

    A. Kehagias, C. Kounnas, D. Lüst and A. Riotto, “Black Hole Solutions in R 2 Gravity,” JHEP 05, 143 (2015) doi:10.1007/JHEP05(2015)143 [arXiv:1502.04192 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/jhep05(2015)143 2015

  39. [41]

    On the degrees of freedom of R 2 gravity in flat spacetime,

    A. Hell, D. Lüst and G. Zoupanos, “On the degrees of freedom of R 2 gravity in flat spacetime,” JHEP 02, 039 (2024) doi:10.1007/JHEP02(2024)039 [arXiv:2311.08216 [hep-th]]

    work page doi:10.1007/jhep02(2024)039 2024

  40. [42]

    On the Degrees of Freedom Count on Singular Phase Space Submanifolds,

    A. Golovnev, “On the Degrees of Freedom Count on Singular Phase Space Submanifolds,” Int. J. Theor. Phys. 63, no.8, 212 (2024) doi:10.1007/s10773-024-05741- 5 [arXiv:2311.10690 [hep-th]]

    work page doi:10.1007/s10773-024-05741- 2024

  41. [43]

    Particle content of (scalar curvature)2 gravities revisited,

    G. K. Karananas, “Particle content of (scalar curvature)2 gravities revisited,” Phys. Rev. D 111, no.4, 044068 (2025) doi:10.1103/PhysRevD.111.044068 [arXiv:2407.09598 [hep-th]]

    work page doi:10.1103/physrevd.111.044068 2025

  42. [44]

    Conformal and pure scale- invariant gravities in d dimensions,

    A. Hell and D. Lüst, “Conformal and pure scale- invariant gravities in d dimensions,” JHEP 09, 202 (2025) doi:10.1007/JHEP09(2025)202 [arXiv:2506.18775 [hep-th]]

    work page doi:10.1007/jhep09(2025)202 2025

  43. [45]

    Aspects of non-minimally coupled curvature with power laws,

    A. Hell and D. Lüst, “Aspects of non-minimally coupled curvature with power laws,” [arXiv:2509.20217 [hep-th]]

    arXiv

  44. [46]

    Spectrum of pure R2 gravity: full Hamiltonian analysis,

    W. Barker and D. Glavan, “Spectrum of pure R2 gravity: full Hamiltonian analysis,” [arXiv:2510.08201 [gr-qc]]

    Pith/arXiv arXiv

  45. [47]

    Matos, F.S

    I. L. Buchbinder and S. L. Lyakhovich, “Canonical Quan- tization and Local Measure of R**2 Gravity,” Class. Quant. Grav. 4 (1987), 1487-1501 doi:10.1088/0264- 9381/4/6/008

    work page doi:10.1088/0264- 1987

  46. [48]

    Imperfect fluid description of modified gravities

    V. Faraoni and J. Côté, “Imperfect fluid description of modified gravities,” Phys. Rev. D 98 no. 8, 084019 (2018) doi:10.1103/PhysRevD.98.084019 [arXiv:1808.02427 [gr- qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.98.084019 2018

  47. [49]

    Thermodynamics of scalar- tensor gravity,

    V. Faraoni and A. Giusti, “Thermodynamics of scalar- tensor gravity,” Phys. Rev. D 103, no.12, L121501 (2021) doi:10.1103/PhysRevD.103.L121501 [arXiv:2103.05389 [gr-qc]]

    work page doi:10.1103/physrevd.103.l121501 2021

  48. [50]

    New ap- proach to the thermodynamics of scalar-tensor gravity,

    V. Faraoni, A. Giusti and A. Mentrelli, “New ap- proach to the thermodynamics of scalar-tensor gravity,” Phys. Rev. D 104, no.12, 124031 (2021) doi:10.1103/PhysRevD.104.124031 [arXiv:2110.02368 [gr-qc]]

    work page doi:10.1103/physrevd.104.124031 2021

  49. [51]

    First-order thermodynamics of Horndeski cos- mology,

    M. Miranda, S. Giardino, A. Giusti and L. Heisen- berg, “First-order thermodynamics of Horndeski cos- mology,” Phys. Rev. D 109, no.12, 124033 (2024) doi:10.1103/PhysRevD.109.124033 [arXiv:2401.10351 [gr-qc]]

    work page doi:10.1103/physrevd.109.124033 2024

  50. [52]

    Einstein gravity as the thermal equilibrium state of a nonminimally coupled scalar field geometry,

    N. Karolinski and V. Faraoni, “Einstein gravity as the thermal equilibrium state of a nonminimally coupled scalar field geometry,” Phys. Rev. D 109, no.8, 084042 (2024) doi:10.1103/PhysRevD.109.084042 [arXiv:2401.04877 [gr-qc]]

    work page doi:10.1103/physrevd.109.084042 2024

  51. [53]

    Scalar field as a perfect fluid: thermodynamics of minimally coupled scalars and Einstein frame scalar- tensor gravity,

    V. Faraoni, S. Giardino, A. Giusti and R. Vander- wee, “Scalar field as a perfect fluid: thermodynamics of minimally coupled scalars and Einstein frame scalar- tensor gravity,” Eur. Phys. J. C 83, no.1, 24 (2023) doi:10.1140/epjc/s10052-023-11186-7 [arXiv:2208.0405 1 [gr-qc]]

    work page doi:10.1140/epjc/s10052-023-11186-7 2023

  52. [54]

    First-order thermodynamics of scalar-tensor cosmology,

    S. Giardino, V. Faraoni and A. Giusti, “First-order thermodynamics of scalar-tensor cosmology,” JCAP 04, no.04, 053 (2022) doi:10.1088/1475-7516/2022/04/053 [arXiv:2202.07393 [gr-qc]]

    work page doi:10.1088/1475-7516/2022/04/053 2022

  53. [55]

    Thermal sta- bility of stealth and de Sitter spacetimes in scalar- tensor gravity,

    S. Giardino, A. Giusti and V. Faraoni, “Thermal sta- bility of stealth and de Sitter spacetimes in scalar- tensor gravity,” Eur. Phys. J. C 83, no.7, 621 (2023) doi:10.1140/epjc/s10052-023-11697-3 [arXiv:2302.0855 0 [gr-qc]]

    work page doi:10.1140/epjc/s10052-023-11697-3 2023

  54. [56]

    Alternative formulations of the thermodynam- ics of scalar-tensor theories,

    L. Gallerani, M. Miranda, A. Giusti and A. Men- trelli, “Alternative formulations of the thermodynam- ics of scalar-tensor theories,” Phys. Rev. D 110, no.6, 064087 (2024) doi:10.1103/PhysRevD.110.064087 [arXiv:2405.20865 [gr-qc]]

    work page doi:10.1103/physrevd.110.064087 2024

  55. [57]

    Effective fluid mixture of tensor-multi-scalar gravity,

    M. Miranda, P. A. Graham and V. Faraoni, “Effective fluid mixture of tensor-multi-scalar gravity,” Eur. Phys. J. Plus 138, no.5, 387 (2023) doi:10.1140/epjp/s13360- 023-03984-5 [arXiv:2211.03958 [gr-qc]]

    work page doi:10.1140/epjp/s13360- 2023

  56. [58]

    Can modified gravity explain accelerated cosmic expansion?

    A. D. Dolgov and M. Kawasaki, “Can modified grav- ity explain accelerated cosmic expansion?,” Phys. Lett. B 573, 1-4 (2003) doi:10.1016/j.physletb.2003.08.039 [arXiv:astro-ph/0307285 [astro-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.physletb.2003.08.039 2003

  57. [59]

    Fluid nature constrains Horndeski gravity,

    M. Miranda, D. Vernieri, S. Capozziello and V. Faraoni,“Fluid nature constrains Horndeski gravity,”Gen. Rel. Grav. 55 (2023) no.7, 84 doi:10.1007/s10714-023-03128-1 [arXiv:2209.02727 [gr-qc]]

    work page doi:10.1007/s10714-023-03128-1 2023

  58. [60]

    Pecu- liar thermal states in the first-order thermodynamics of gravity,

    V. Faraoni, A. Giusti, S. Jose and S. Giardino, “Pecu- liar thermal states in the first-order thermodynamics of gravity,” Phys. Rev. D 106, no.2, 024049 (2022) doi:10.1103/PhysRevD.106.024049 [arXiv:2206.02046 [gr-qc]]

    work page doi:10.1103/physrevd.106.024049 2022

  59. [61]

    Crit- ical solutions of nonminimally coupled scalar field 10 theory and first-order thermodynamics of grav- ity,

    V. Faraoni, P. A. Graham and A. Leblanc, “Crit- ical solutions of nonminimally coupled scalar field 10 theory and first-order thermodynamics of grav- ity,” Phys. Rev. D 106, no.8, 084008 (2022) doi:10.1103/PhysRevD.106.084008 [arXiv:2207.03841 [gr-qc]]

    work page doi:10.1103/physrevd.106.084008 2022

  60. [62]

    Stealth metastable state of scalar-tensor thermodynam- ics,

    V. Faraoni and T. B. Françonnet, “Stealth metastable state of scalar-tensor thermodynam- ics,” Phys. Rev. D 105, no.10, 104006 (2022) doi:10.1103/PhysRevD.105.104006 [arXiv:2203.14934 [gr-qc]]

    work page doi:10.1103/physrevd.105.104006 2022

  61. [63]

    Gyroscopic Precession in the vicinity of Static Blackhole’s Event Horizon

    A. Giusti, S. Giardino and V. Faraoni, “Past-directed scalar field gradients and scalar-tensor thermodynamics,” Gen. Rel. Grav. 55, no.3, 47 (2023) doi:10.1007/s10714- 023-03095-7 [arXiv:2210.15348 [gr-qc]]

    work page doi:10.1007/s10714- 2023

  62. [64]

    First-order thermodynam- ics of scalar-tensor gravity,

    S. Giardino and A. Giusti,“First-order thermodynam- ics of scalar-tensor gravity,” Ric. Mat. 74 (2025) no.1, 43-59 doi:10.1007/s11587-023-00801-0 [arXiv:2306.0158 0 [gr-qc]]

    work page doi:10.1007/s11587-023-00801-0 2025

  63. [65]

    More on the first-order ther- modynamics of scalar-tensor and Horndeski gravity,

    V. Faraoni and J. Houle, “More on the first-order ther- modynamics of scalar-tensor and Horndeski gravity,” Eur. Phys. J. C 83, no.6, 521 (2023) doi:10.1140/epjc/s10052- 023-11712-7 [arXiv:2302.01442 [gr-qc]]

    work page doi:10.1140/epjc/s10052- 2023

  64. [66]

    New phenomenology in the first-order thermodynamics of scalar-tensor grav- ity for Bianchi universes,

    J. Houle and V. Faraoni, “New phenomenology in the first-order thermodynamics of scalar-tensor grav- ity for Bianchi universes,” Phys. Rev. D 110, no.2, 024067 (2024) doi:10.1103/PhysRevD.110.024067 [arXiv:2404.19470 [gr-qc]]

    work page doi:10.1103/physrevd.110.024067 2024

  65. [67]

    The thermal view of singularity-free scalar-tensor spacetimes,

    V. Faraoni and N. Veilleux, “The thermal view of singularity-free scalar-tensor spacetimes,” [arXiv:2511.04941 [gr-qc]]

    arXiv

  66. [68]

    Thermal view of f(R) cosmology,

    V. Faraoni and S. N. Cattivelli,“Thermal view of f(R) cosmology,” Phys. Rev. D 113 (2026) no.4, 044034 doi:10.1103/y86x-18t8 [arXiv:2511.00347 [gr-qc]]

    work page doi:10.1103/y86x-18t8 2026

  67. [69]

    Thermal Origin of the Attractor-to-General-Relativity in Scalar-Tensor Grav- ity,

    V. Faraoni and A. Giusti, “Thermal Origin of the Attractor-to-General-Relativity in Scalar-Tensor Grav- ity,” Phys. Rev. Lett. 134, no.21, 211406 (2025) doi:10.1103/22w4-v2xn [arXiv:2502.18272 [gr-qc]]

    work page doi:10.1103/22w4-v2xn 2025

  68. [70]

    Black hole interiors in the thermal view of scalar-tensor gravity,

    V. Faraoni, “Black hole interiors in the thermal view of scalar-tensor gravity,” Phys. Rev. D 112, no.2, L021504 (2025) doi:10.1103/mk89-hjkn [arXiv:2505.08322 [gr-qc] ]

    work page doi:10.1103/mk89-hjkn 2025

  69. [71]

    Thermal description of braneworld effective theories,

    S. Bhattacharyya and S. SenGupta, “Thermal description of braneworld effective theories,” Phys. Rev. D 113, no.6, 064019 (2026) doi:10.1103/dyf3-h6gb [arXiv:2508.14228 [hep-th]]

    work page doi:10.1103/dyf3-h6gb 2026

  70. [72]

    Matter instability in modified gravity,

    V. Faraoni, “Matter instability in modified gravity,” Phys. Rev. D 74, 104017 (2006) doi:10.1103/PhysRevD.74.104017 [arXiv:astro- ph/0610734 [astro-ph]]

    work page doi:10.1103/physrevd.74.104017 2006

  71. [73]

    Eckart heat-flux appli- cability in F (Φ , X )R theories and the existence of tem- perature gradients,

    D. S. Pereira and J. P. Mimoso, “Eckart heat-flux appli- cability in F (Φ , X )R theories and the existence of tem- perature gradients,” [arXiv:2512.20553 [gr-qc]]

    Pith/arXiv arXiv

  72. [74]

    Revisiting induced gravity in scalar-tensor thermodynamics,

    A. Giusti,“Revisiting induced gravity in scalar-tensor thermodynamics,” Phys. Rev. D 113 (2026) no.6, 064032 doi:10.1103/ml3t-nrn5 [arXiv:2601.17398 [gr-qc]]

    work page doi:10.1103/ml3t-nrn5 2026

  73. [75]

    First-order thermodynamics of multi- scalar-tensor gravity,

    D. S. Pereira, “First-order thermodynamics of multi- scalar-tensor gravity,” [arXiv:2604.16907 [gr-qc]]

    Pith/arXiv arXiv

  74. [76]

    Ther- mal channels of scalar and tensor waves in Jordan-frame scalar–tensor gravity,

    D. S. Pereira, F. S. N. Lobo and J. P. Mimoso, “Ther- mal channels of scalar and tensor waves in Jordan-frame scalar–tensor gravity,” [arXiv:2603.27386 [gr-qc]]

    Pith/arXiv arXiv

  75. [77]

    Frame invariant diffusive for- mulation of scalar-tensor gravity,

    L. Järv and S. Karamitsos, “Frame invariant diffusive for- mulation of scalar-tensor gravity,” [arXiv:2604.16094 [g r- qc]]

    Pith/arXiv arXiv

  76. [78]

    First-order thermodynamics of Horndeski grav- ity,

    A. Giusti, S. Zentarra, L. Heisenberg and V. Faraoni, “First-order thermodynamics of Horndeski grav- ity,” Phys. Rev. D 105, no.12, 124011 (2022) doi:10.1103/PhysRevD.105.124011 [arXiv:2108.10706 [gr-qc]]

    work page doi:10.1103/physrevd.105.124011 2022

  77. [79]

    The phase space view of f(R) gravity

    J. C. C. de Souza and V. Faraoni, “The Phase space view of f(R) gravity,” Class. Quant. Grav. 24, 3637-3648 (2007) doi:10.1088/0264-9381/24/14/006 [arXiv:0706.1223 [gr- qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0264-9381/24/14/006 2007

  78. [80]

    Equivalence between Horn- deski and beyond Horndeski theories and imper- fect fluids,

    U. Nucamendi, R. De Arcia, T. Gonzalez, F. A. Horta- Rangel and I. Quiros, “Equivalence between Horn- deski and beyond Horndeski theories and imper- fect fluids,” Phys. Rev. D 102, no.8, 084054 (2020) doi:10.1103/PhysRevD.102.084054 [arXiv:1910.13026 [gr-qc]]

    work page doi:10.1103/physrevd.102.084054 2020

  79. [81]

    Phase space geometry in scalar-tensor cosmology

    V. Faraoni, “Phase space geometry in scalar-tensor cosmology,” Annals Phys. 317, 366-382 (2005) doi:10.1016/j.aop.2004.11.009 [arXiv:gr-qc/0502015 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.aop.2004.11.009 2005

  80. [82]

    The Thermodynamics of irreversible pro- cesses. 3. Relativistic theory of the simple fluid,

    C. Eckart, “The Thermodynamics of irreversible pro- cesses. 3. Relativistic theory of the simple fluid,” Phys. Rev. 58, 919-924 (1940)

    1940

Showing first 80 references.