Pith. sign in

REVIEW 1 major objections 1 cited by

In the frame-invariant formulation of scalar-tensor gravity the effective fluid is perfect with identically zero temperature.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Download PDF Read on arXiv ↗

T0 review · grok-4.3

2026-05-10 07:48 UTC

load-bearing objection The effective temperature in scalar-tensor gravity is frame-dependent, and the invariant formulation gives a perfect fluid with zero temperature instead. the 1 major comments →

arxiv 2604.16094 v1 submitted 2026-04-17 gr-qc hep-th

Frame invariant diffusive formulation of scalar-tensor gravity

Laur J\"arv , Sotirios Karamitsos This is my paper
classification gr-qc hep-th
keywords scalar-tensor gravityconformal frameseffective fluidframe invariancechemical potentialthermodynamicsgeneral relativitydiffusive equilibrium
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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 effective temperature previously assigned to nonminimally coupled scalar fields depends on the choice of conformal frame and can be tuned away. When the theory is rewritten using only frame-invariant quantities, the effective fluid becomes perfect and its temperature vanishes. The departure from general relativity is then carried instead by a frame-invariant chemical potential, exactly as in minimally coupled theories. This construction lets general relativity be interpreted as the state of diffusive equilibrium for scalar-tensor gravity regardless of whether the coupling is minimal or nonminimal.

Core claim

The originally proposed effective temperature of the imperfect fluid in scalar-tensor gravity is not frame invariant. In the frame-invariant formulation the effective fluid is perfect with vanishing temperature; the non-general-relativistic sector is governed by a frame-invariant chemical potential. General relativity therefore appears as the diffusive equilibrium state for any scalar-tensor theory.

What carries the argument

The frame-invariant effective fluid, whose thermodynamic description replaces temperature with a chemical potential to encode departures from general relativity.

Load-bearing premise

The thermodynamic identification of the effective fluid continues to hold when only frame-invariant quantities are retained and no new frame-dependent artifacts are introduced.

What would settle it

An explicit calculation for a concrete model (such as Brans-Dicke) in which the frame-invariant effective fluid is shown to be imperfect or to possess a non-zero temperature would falsify the central claim.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • General relativity is diffusive equilibrium for both minimal and nonminimal scalar-tensor theories.
  • Temperature is not an intrinsic property of a scalar-tensor theory but a frame-dependent representation.
  • The chemical potential becomes the universal quantity controlling deviations from general relativity.
  • Thermodynamic interpretations of scalar-tensor gravity must be reformulated in frame-invariant variables.

Where Pith is reading between the lines

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

  • The result suggests that any thermodynamic description of modified gravity should be checked for frame invariance before assigning physical meaning to temperature.
  • It opens the possibility of searching for chemical-potential signatures in cosmological or astrophysical observables that are independent of conformal frame choice.
  • The same logic could be applied to other conformal-frame ambiguities in modified gravity, such as those appearing in f(R) or other higher-order theories.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

1 major / 0 minor

Summary. The manuscript claims that the effective temperature in the thermodynamic interpretation of nonminimally coupled scalar-tensor gravity is frame-dependent and can be arbitrarily tuned via conformal transformations. Reformulating the theory in frame-invariant variables yields an effective stress-energy tensor that is exactly that of a perfect fluid with identically vanishing temperature; the departure from general relativity is then carried by a frame-invariant chemical potential, allowing the interpretation that general relativity corresponds to a state of diffusive equilibrium for any scalar-tensor theory.

Significance. If substantiated, the result would establish that temperature is not an intrinsic property of scalar-tensor theories but a frame-dependent artifact, while providing a robust invariant description in which deviations from GR are governed by chemical potential. This strengthens the diffusive thermodynamic analogy by eliminating frame dependence and aligns the nonminimal case with minimal theories, representing a useful clarification in the literature on frame-invariant formulations.

major comments (1)
  1. The central derivation of the frame-invariant effective fluid (following the re-expression of the stress-energy tensor in invariant variables): the claim that this fluid is perfect with vanishing temperature rests on the assumption that the original thermodynamic dictionary (temperature, heat flux, etc.) carries over unchanged without introducing new frame-dependent artifacts. Because the non-invariant temperature was shown to be frame-dependent, explicit verification is required that the invariantization procedure does not alter the fluid type or the vanishing of temperature by construction; without this step-by-step check, the conclusion that the departure from GR is governed solely by the chemical potential remains load-bearing and unverified.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for identifying a point that merits additional clarification. We address the major comment below and will incorporate the requested verification into the revised version.

read point-by-point responses

  1. Referee: The central derivation of the frame-invariant effective fluid (following the re-expression of the stress-energy tensor in invariant variables): the claim that this fluid is perfect with vanishing temperature rests on the assumption that the original thermodynamic dictionary (temperature, heat flux, etc.) carries over unchanged without introducing new frame-dependent artifacts. Because the non-invariant temperature was shown to be frame-dependent, explicit verification is required that the invariantization procedure does not alter the fluid type or the vanishing of temperature by construction; without this step-by-step check, the conclusion that the departure from GR is governed solely by the chemical potential remains load-bearing and unverified.

    Authors: We agree that an explicit step-by-step verification of the thermodynamic dictionary in the invariant variables strengthens the argument. In the derivation, the stress-energy tensor is first rewritten using the frame-invariant combinations (the invariant metric and the invariant scalar-field gradient). The fluid four-velocity is likewise defined invariantly as the normalized timelike eigenvector of this tensor. Projecting the invariant tensor onto this velocity and its orthogonal complement yields vanishing heat flux and anisotropic stress by direct algebraic cancellation; the effective temperature, identified as the coefficient multiplying the dissipative terms in the standard decomposition, is identically zero. These cancellations occur because the nonminimal coupling contributions are entirely absorbed into the invariant redefinitions, leaving no residual frame-dependent dissipation. We will add a dedicated subsection that recomputes each thermodynamic quantity (energy density, pressure, heat flux, temperature, and chemical potential) from the invariant tensor, confirming that the dictionary carries over without introducing new artifacts and that the departure from GR is carried exclusively by the invariant chemical potential. revision: yes

Circularity Check

0 steps flagged

Minor self-citation to prior thermodynamic construction but central invariance result is independently derived

full rationale

The paper starts from the established effective fluid description in scalar-tensor theories and applies standard conformal rescalings to identify which thermodynamic quantities remain invariant. The demonstration that the original temperature is frame-dependent follows directly from the transformation rules applied to the stress-energy tensor components. The subsequent construction of the frame-invariant formulation then yields a perfect fluid with vanishing temperature as a direct algebraic consequence of retaining only invariant combinations, without any parameter fitting or redefinition that presupposes the final result. Self-citation to the authors' earlier work supplies the initial thermodynamic dictionary but does not carry the load of the new invariance analysis, which stands on explicit re-expressions of the fluid variables.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper relies on the standard properties of conformal transformations in scalar-tensor gravity and on the thermodynamic identification of the effective fluid; no free parameters or new entities are introduced.

axioms (1)
  • domain assumption Conformal transformations preserve the physical content of the theory
    Invoked when re-expressing the effective fluid in frame-invariant variables.

pith-pipeline@v0.9.0 · 5480 in / 1095 out tokens · 64798 ms · 2026-05-10T07:48:07.160016+00:00 · methodology

0 comments
read the original abstract

Thermodynamics provides a useful interpretation of scalar-tensor gravity, in which the effective imperfect fluid admitted by the nonminimal coupling features a temperature that is associated with the departure from general relativity. However, in this construction, certain thermodynamical quantities are defined with respect to a particular conformal frame. In the present work, we show that the originally proposed effective temperature assigned to nonminimally coupled scalar field theories is not frame invariant, and can thus be arbitrarily tuned by a change of frame. This raises the question of whether temperature can be viewed as an intrinsic property of a scalar-tensor theory rather than a particular representation of it. Working instead with the frame invariant formulation of scalar-tensor gravity, we find that the frame invariant effective fluid is perfect with identically vanishing temperature. The departure from general relativity is then governed not by temperature, but rather by a frame invariant chemical potential, similar to minimal theories. Therefore, general relativity can be interpreted as a state of diffusive equilibrium for any scalar-tensor theory, regardless of whether it is minimal or nonminimal.

discussion (0)

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

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. New interpretation of the Minkowski limit of $R^2$ gravity

    gr-qc 2026-06 unverdicted novelty 5.0

    The Minkowski limit of pure R² gravity is reinterpreted as a thermal singularity via scalar-tensor to Eckart fluid analogy, showing infinite departure from GR rather than recovery.

Reference graph

Works this paper leans on

86 extracted references · 86 canonical work pages · cited by 1 Pith paper · 24 internal anchors

  1. [1]

    The Thermodynamics of Black Holes

    R. M. Wald, “The thermodynamics of black holes,”Living Rev. Rel.4(2001) 6,arXiv:gr-qc/9912119

    work page Pith review arXiv 2001

  2. [2]

    Thermodynamical Aspects of Gravity: New insights

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

    work page Pith review arXiv 2010

  3. [3]

    A Survey of Black Hole Thermodynamics

    A. C. Wall, “A Survey of Black Hole Thermodynamics,”arXiv:1804.10610 [gr-qc]

    work page Pith review arXiv

  4. [4]

    Witten, Introduction to black hole thermodynamics, Eur

    E. Witten, “Introduction to black hole thermodynamics,”Eur. Phys. J. Plus140(2025) no. 5, 430,arXiv:2412.16795 [hep-th]

    work page arXiv 2025

  5. [5]

    Thermodynamics of Spacetime: The Einstein Equation of State

    T. Jacobson, “Thermodynamics of space-time: The Einstein equation of state,”Phys. Rev. Lett.75(1995) 1260–1263, arXiv:gr-qc/9504004

    work page Pith review arXiv 1995

  6. [6]

    Black Hole Thermodynamics: General Relativity and Beyond,

    S. Sarkar, “Black Hole Thermodynamics: General Relativity and Beyond,”Gen. Rel. Grav.51(2019) no. 5, 63, arXiv:1905.04466 [hep-th]

    work page internal anchor Pith review arXiv 2019

  7. [7]

    Non-equilibrium Thermodynamics of Spacetime

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

    work page Pith review arXiv 2006

  8. [8]

    A systematic approach to generalisations of General Relativity and their cosmological implications

    L. Heisenberg, “A systematic approach to generalisations of General Relativity and their cosmological implications,” Phys. Rept.796(2019) 1–113,arXiv:1807.01725 [gr-qc]. [9]CosmoVerse NetworkCollaboration, E. Di Valentinoet al., “The CosmoVerse White Paper: Addressing observational tensions in cosmology with systematics and fundamental physics,”Phys. Dark...

    work page Pith review arXiv 2019

  9. [9]

    Jordan,Schwerkraft und Weltall: Grundlagen der theoretischen Kosmologie

    P. Jordan,Schwerkraft und Weltall: Grundlagen der theoretischen Kosmologie. Die Wissenschaft. Vieweg, Braunschweig, 2., erw. aufl. ed., 1955. Mit 13 Abb

    work page 1955

  10. [10]

    On the physical interpretation of P.Jordan’s extended theory of gravitation,

    M. Fierz, “On the physical interpretation of P.Jordan’s extended theory of gravitation,”Helv. Phys. Acta29(1956) 128–134

    work page 1956

  11. [11]

    Mach’s principle and a relativistic theory of gravitation,

    C. Brans and R. H. Dicke, “Mach’s principle and a relativistic theory of gravitation,”Phys. Rev.124(1961) 925–935

    work page 1961

  12. [12]

    Horndeski theory and beyond: a review

    T. Kobayashi, “Horndeski theory and beyond: a review,”Rept. Prog. Phys.82(2019) no. 8, 086901,arXiv:1901.07183 [gr-qc]

    work page Pith review arXiv 2019

  13. [13]

    Extended Theories of Gravity

    S. Capozziello and M. De Laurentis, “Extended Theories of Gravity,”Phys. Rept.509(2011) 167–321,arXiv:1108.6266 [gr-qc]

    work page Pith review arXiv 2011

  14. [14]

    Energy conditions in modified gravity

    S. Capozziello, F. S. N. Lobo, and J. P. Mimoso, “Energy conditions in modified gravity,”Phys. Lett. B730(2014) 280–283,arXiv:1312.0784 [gr-qc]

    work page Pith review arXiv 2014

  15. [15]

    Energy Momentum Tensor in the General Scalar - Tensor Theory,

    L. O. Pimentel, “Energy Momentum Tensor in the General Scalar - Tensor Theory,”Class. Quant. Grav.6(1989) L263–L265

    work page 1989

  16. [16]

    The Energy-Momentum Tensor for a Dissipative Fluid in General Relativity,

    O. M. Pimentel, G. A. González, and F. D. Lora-Clavijo, “The Energy-Momentum Tensor for a Dissipative Fluid in General Relativity,”Gen. Rel. Grav.48(2016) no. 10, 124,arXiv:1604.01318 [gr-qc]. 17

    work page internal anchor Pith review arXiv 2016

  17. [17]

    Thermodynamics of scalar-tensor gravity,

    V. Faraoni and A. Giusti, “Thermodynamics of scalar-tensor gravity,”Phys. Rev. D103(2021) no. 12, L121501, arXiv:2103.05389 [gr-qc]

    work page arXiv 2021

  18. [18]

    First-order thermodynamics of Horndeski gravity,

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

    work page arXiv 2022

  19. [19]

    New approach to the thermodynamics of scalar-tensor gravity,

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

    work page arXiv 2021

  20. [20]

    First-order thermodynamics of scalar-tensor cosmology,

    S. Giardino, V. Faraoni, and A. Giusti, “First-order thermodynamics of scalar-tensor cosmology,”JCAP04(2022) no. 04, 053,arXiv:2202.07393 [gr-qc]

    work page arXiv 2022

  21. [21]

    Faraoni, S

    V. Faraoni, S. Giardino, A. Giusti, and R. Vanderwee, “Scalar field as a perfect fluid: thermodynamics of minimally coupled scalars and Einstein frame scalar-tensor gravity,”Eur. Phys. J. C83(2023) no. 1, 24,arXiv:2208.04051 [gr-qc]

    work page arXiv 2023

  22. [22]

    Alternative formulations of the thermodynamics of scalar-tensor theories,

    L. Gallerani, M. Miranda, A. Giusti, and A. Mentrelli, “Alternative formulations of the thermodynamics of scalar-tensor theories,”Phys. Rev. D110(2024) no. 6, 064087,arXiv:2405.20865 [gr-qc]

    work page arXiv 2024

  23. [23]

    Gallerani, A

    L. Gallerani, A. Giusti, A. Mentrelli, and V. Faraoni, “Thermal aspects of the anomalousω→ ∞limit of Brans-Dicke gravity,”arXiv:2508.00498 [gr-qc]

    work page arXiv

  24. [24]

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

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

    work page arXiv 2025

  25. [25]

    The Thermodynamics of irreversible processes. 3.. Relativistic theory of the simple fluid,

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

    work page 1940

  26. [26]

    Einstein frame or Jordan frame ?

    V. Faraoni and E. Gunzig, “Einstein frame or Jordan frame?,”Int. J. Theor. Phys.38(1999) 217–225, arXiv:astro-ph/9910176

    work page internal anchor Pith review arXiv 1999

  27. [27]

    Cosmological viability of f(R)-gravity as an ideal fluid and its compatibility with a matter dominated phase

    S. Capozziello, S. Nojiri, S. D. Odintsov, and A. Troisi, “Cosmological viability of f(R)-gravity as an ideal fluid and its compatibility with a matter dominated phase,”Phys. Lett. B639(2006) 135–143,arXiv:astro-ph/0604431

    work page Pith review arXiv 2006

  28. [28]

    Einstein and Jordan frames reconciled: a frame-invariant approach to scalar-tensor cosmology

    R. Catena, M. Pietroni, and L. Scarabello, “Einstein and Jordan reconciled: a frame-invariant approach to scalar-tensor cosmology,”Phys. Rev. D76(2007) 084039,arXiv:astro-ph/0604492

    work page Pith review arXiv 2007

  29. [29]

    The (pseudo)issue of the conformal frame revisited

    V. Faraoni and S. Nadeau, “The (pseudo)issue of the conformal frame revisited,”Phys. Rev. D75(2007) 023501, arXiv:gr-qc/0612075

    work page Pith review arXiv 2007

  30. [30]

    Physical non-equivalence of the Jordan and Einstein frames,

    S. Capozziello, P. Martin-Moruno, and C. Rubano, “Physical non-equivalence of the Jordan and Einstein frames,”Phys. Lett. B689(2010) 117–121,arXiv:1003.5394 [gr-qc]

    work page internal anchor Pith review arXiv 2010

  31. [31]

    Gauge invariant cosmological perturbations for the nonminimally coupled inflaton field,

    J. Weenink and T. Prokopec, “Gauge invariant cosmological perturbations for the nonminimally coupled inflaton field,” Phys. Rev. D82(2010) 123510,arXiv:1007.2133 [hep-th]

    work page internal anchor Pith review arXiv 2010

  32. [32]

    Conformal invariance of curvature perturbation,

    J.-O. Gong, J.-c. Hwang, W.-I. Park, M. Sasaki, and Y.-S. Song, “Conformal invariance of curvature perturbation,” JCAP09(2011) 023,arXiv:1107.1840 [gr-qc]

    work page internal anchor Pith review arXiv 2011

  33. [33]

    Conformal transformations and the conformal equivalence principle,

    I. Quiros, R. Garcia-Salcedo, and J. E. Madriz Aguilar, “Conformal transformations and the conformal equivalence principle,”arXiv:1108.2911 [gr-qc]

    work page internal anchor Pith review arXiv

  34. [34]

    The Conformal Transformation in General Single Field Inflation with Non-Minimal Coupling

    T. Kubota, N. Misumi, W. Naylor, and N. Okuda, “The Conformal Transformation in General Single Field Inflation with Non-Minimal Coupling,”JCAP02(2012) 034,arXiv:1112.5233 [gr-qc]

    work page Pith review arXiv 2012

  35. [35]

    Curvature perturbation in multi-field inflation with non-minimal coupling

    J. White, M. Minamitsuji, and M. Sasaki, “Curvature perturbation in multi-field inflation with non-minimal coupling,” JCAP07(2012) 039,arXiv:1205.0656 [astro-ph.CO]

    work page Pith review arXiv 2012

  36. [36]

    The conformal transformation's controversy: what are we missing?

    I. Quiros, R. Garcia-Salcedo, J. E. Madriz Aguilar, and T. Matos, “The conformal transformation’s controversy: what are we missing?,”Gen. Rel. Grav.45(2013) 489–518,arXiv:1108.5857 [gr-qc]

    work page Pith review arXiv 2013

  37. [37]

    Frame Transformations of Gravitational Theories,

    X. Calmet and T.-C. Yang, “Frame Transformations of Gravitational Theories,”Int. J. Mod. Phys. A28(2013) 1350042, arXiv:1211.4217 [gr-qc]

    work page internal anchor Pith review arXiv 2013

  38. [38]

    Frame independent cosmological perturbations,

    T. Prokopec and J. Weenink, “Frame independent cosmological perturbations,”JCAP09(2013) 027,arXiv:1304.6737 [gr-qc]

    work page internal anchor Pith review arXiv 2013

  39. [39]

    Non-linear curvature perturbation in multi-field inflation models with non-minimal coupling,

    J. White, M. Minamitsuji, and M. Sasaki, “Non-linear curvature perturbation in multi-field inflation models with non-minimal coupling,”JCAP09(2013) 015,arXiv:1306.6186 [astro-ph.CO]

    work page internal anchor Pith review arXiv 2013

  40. [40]

    Quantum equivalence off(R)gravity and scalar-tensor theories,

    M. S. Ruf and C. F. Steinwachs, “Quantum equivalence off(R)gravity and scalar-tensor theories,”Phys. Rev. D97 (2018) no. 4, 044050,arXiv:1711.07486 [gr-qc]

    work page internal anchor Pith review arXiv 2018

  41. [41]

    Frame (In)equivalence in Quantum Field Theory and Cosmology,

    K. Falls and M. Herrero-Valea, “Frame (In)equivalence in Quantum Field Theory and Cosmology,”Eur. Phys. J. C79 (2019) no. 7, 595,arXiv:1812.08187 [hep-th]

    work page arXiv 2019

  42. [42]

    Frame-dependence of inflationary observables in scalar-tensor gravity,

    A. Karam, T. Pappas, and K. Tamvakis, “Frame-dependence of inflationary observables in scalar-tensor gravity,”PoS CORFU2018(2019) 064,arXiv:1903.03548 [gr-qc]

    work page internal anchor Pith review arXiv 2019

  43. [43]

    Reheating after Starobinsky Inflation in the Jordan Frame,

    G. C. Dorsch, L. C. Miranda, and N. Yokomizo, “Reheating after Starobinsky Inflation in the Jordan Frame,” arXiv:2603.04497 [gr-qc]

    work page arXiv

  44. [44]

    Non-minimal Higgs Inflation and Frame Dependence in Cosmology

    C. F. Steinwachs and A. Y. Kamenshchik, “Non-minimal Higgs Inflation and Frame Dependence in Cosmology,”AIP Conf. Proc.1514(2013) no. 1, 161–164,arXiv:1301.5543 [gr-qc]

    work page Pith review arXiv 2013

  45. [45]

    Question of quantum equivalence between Jordan frame and Einstein frame

    A. Y. Kamenshchik and C. F. Steinwachs, “Question of quantum equivalence between Jordan frame and Einstein frame,” Phys. Rev. D91(2015) no. 8, 084033,arXiv:1408.5769 [gr-qc]

    work page Pith review arXiv 2015

  46. [46]

    Conformal Frame Dependence of Inflation,

    G. Domènech and M. Sasaki, “Conformal Frame Dependence of Inflation,”JCAP04(2015) 022,arXiv:1501.07699 [gr-qc]

    work page internal anchor Pith review arXiv 2015

  47. [47]

    Inflation, deflation, and frame independence in string cosmology,

    M. Gasperini and G. Veneziano, “Inflation, deflation, and frame independence in string cosmology,”Mod. Phys. Lett. A8 (1993) 3701–3714,arXiv:hep-th/9309023. 18

    work page internal anchor Pith review arXiv 1993

  48. [48]

    Frame Covariant Nonminimal Multifield Inflation

    S. Karamitsos and A. Pilaftsis, “Frame Covariant Nonminimal Multifield Inflation,”Nucl. Phys. B927(2018) 219–254, arXiv:1706.07011 [hep-ph]

    work page Pith review arXiv 2018

  49. [49]

    Quantum equivalence off(R)gravity and scalar–tensor theories in the Jordan and Einstein frames,

    N. Ohta, “Quantum equivalence off(R)gravity and scalar–tensor theories in the Jordan and Einstein frames,”PTEP 2018(2018) no. 3, 033B02,arXiv:1712.05175 [hep-th]

    work page arXiv 2018

  50. [50]

    The conformal frame freedom in theories of gravitation

    E. E. Flanagan, “The Conformal frame freedom in theories of gravitation,”Class. Quant. Grav.21(2004) 3817, arXiv:gr-qc/0403063

    work page Pith review arXiv 2004

  51. [51]

    Conformal-Frame (In)dependence of Cosmological Observations in Scalar-Tensor Theory

    T. Chiba and M. Yamaguchi, “Conformal-Frame (In)dependence of Cosmological Observations in Scalar-Tensor Theory,” JCAP10(2013) 040,arXiv:1308.1142 [gr-qc]

    work page Pith review arXiv 2013

  52. [52]

    Equivalence of the Einstein and Jordan frames

    M. Postma and M. Volponi, “Equivalence of the Einstein and Jordan frames,”Phys. Rev. D90(2014) no. 10, 103516, arXiv:1407.6874 [astro-ph.CO]

    work page internal anchor Pith review arXiv 2014

  53. [53]

    Invariant quantities in the scalar-tensor theories of gravitation

    L. Järv, P. Kuusk, M. Saal, and O. Vilson, “Invariant quantities in the scalar-tensor theories of gravitation,”Phys. Rev. D91(2015) no. 2, 024041,arXiv:1411.1947 [gr-qc]

    work page Pith review arXiv 2015

  54. [54]

    Frame-Covariant Formulation of Inflation in Scalar-Curvature Theories

    D. Burns, S. Karamitsos, and A. Pilaftsis, “Frame-Covariant Formulation of Inflation in Scalar-Curvature Theories,” Nucl. Phys. B907(2016) 785–819,arXiv:1603.03730 [hep-ph]

    work page Pith review arXiv 2016

  55. [55]

    Mach’s principle and invariance under transformation of units,

    R. H. Dicke, “Mach’s principle and invariance under transformation of units,”Phys. Rev.125(1962) 2163–2167

    work page 1962

  56. [56]

    Transformation properties and general relativity regime in scalar–tensor theories,

    L. Järv, P. Kuusk, M. Saal, and O. Vilson, “Transformation properties and general relativity regime in scalar–tensor theories,”Class. Quant. Grav.32(2015) 235013,arXiv:1504.02686 [gr-qc]

    work page internal anchor Pith review arXiv 2015

  57. [57]

    A frame independent classification of single field inflationary models

    L. Järv, K. Kannike, L. Marzola, A. Racioppi, M. Raidal, M. Rünkla, M. Saal, and H. Veermäe, “Frame-Independent Classification of Single-Field Inflationary Models,”Phys. Rev. Lett.118(2017) no. 15, 151302,arXiv:1612.06863 [hep-ph]

    work page Pith review arXiv 2017

  58. [58]

    Imperfect fluid description of modified gravities

    V. Faraoni and J. Coté, “Imperfect fluid description of modified gravities,”Phys. Rev. D98(2018) no. 8, 084019, arXiv:1808.02427 [gr-qc]

    work page Pith review arXiv 2018

  59. [59]

    First-order thermodynamics of scalar-tensor gravity,

    S. Giardino and A. Giusti, “First-order thermodynamics of scalar-tensor gravity,”Ric. Mat.74(2025) no. 1, 43–59, arXiv:2306.01580 [gr-qc]

    work page arXiv 2025

  60. [62]

    Quantum theory of nonequilib- rium processes, i.Annals of Physics, 152(2):239– 304, 1984

    W. Israel, “Nonstationary irreversible thermodynamics: A causal relativistic theory,”Annals of Physics100(1976) no. 1, 310–331.https://www.sciencedirect.com/science/article/pii/0003491676900646

    work page arXiv 1976

  61. [63]

    Note on the thermodynamics and the speed of sound of a scalar field,

    O. F. Piattella, J. C. Fabris, and N. Bilić, “Note on the thermodynamics and the speed of sound of a scalar field,”Class. Quant. Grav.31(2014) 055006,arXiv:1309.4282 [gr-qc]

    work page internal anchor Pith review arXiv 2014

  62. [64]

    Diffusion of relativistic gas mixtures in gravitational fields,

    G. M. Kremer, “Diffusion of relativistic gas mixtures in gravitational fields,”Physica A393(2014) 76–85, arXiv:1303.6463 [gr-qc]

    work page internal anchor Pith review arXiv 2014

  63. [65]

    From Frame Covariance to the Swampland Distance Conjecture,

    S. Karamitsos and B. Muntz, “From Frame Covariance to the Swampland Distance Conjecture,”arXiv:2512.07929 [hep-th]

    work page arXiv

  64. [66]

    Beyond the Poles in Attractor Models of Inflation,

    S. Karamitsos, “Beyond the Poles in Attractor Models of Inflation,”JCAP09(2019) 022,arXiv:1903.03707 [hep-th]

    work page arXiv 2019

  65. [67]

    Frame Covariance in Quantum Gravity,

    K. Finn, S. Karamitsos, and A. Pilaftsis, “Frame Covariance in Quantum Gravity,”Phys. Rev. D102(2020) no. 4, 045014,arXiv:1910.06661 [hep-th]

    work page arXiv 2020

  66. [68]

    Frame covariant formalism for fermionic theories,

    K. Finn, S. Karamitsos, and A. Pilaftsis, “Frame covariant formalism for fermionic theories,”Eur. Phys. J. C81(2021) no. 7, 572,arXiv:2006.05831 [hep-th]

    work page arXiv 2021

  67. [69]

    Quasi-Palatini formulation of scalar-tensor gravity,

    S. Karamitsos, “Quasi-Palatini formulation of scalar-tensor gravity,”JCAP09(2025) 022,arXiv:2503.06886 [gr-qc]

    work page arXiv 2025

  68. [70]

    What is the temperature of a moving body?,

    C. Farías, V. A. Pinto, and P. S. Moya, “What is the temperature of a moving body?,”Sci. Rep.7(2017) no. 1, 17657

    work page 2017

  69. [71]

    About the temperature of moving bodies,

    T. S. Biro and P. Van, “About the temperature of moving bodies,”EPL89(2010) no. 3, 30001,arXiv:0905.1650 [physics.class-ph]

    work page internal anchor Pith review arXiv 2010

  70. [72]

    Invariant quantities in the multiscalar-tensor theories of gravitation,

    P. Kuusk, L. Jarv, and O. Vilson, “Invariant quantities in the multiscalar-tensor theories of gravitation,”Int. J. Mod. Phys. A31(2016) no. 02n03, 1641003,arXiv:1509.02903 [gr-qc]

    work page internal anchor Pith review arXiv 2016

  71. [73]

    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,arXiv:2209.02727 [gr-qc]

    work page arXiv 2023

  72. [74]

    Faraoni and J

    V. Faraoni and J. Houle, “More on the first-order thermodynamics of scalar-tensor and Horndeski gravity,”Eur. Phys. J. C83(2023) no. 6, 521,arXiv:2302.01442 [gr-qc]

    work page arXiv 2023

  73. [75]

    Miranda, S

    M. Miranda, S. Giardino, A. Giusti, and L. Heisenberg, “First-order thermodynamics of Horndeski cosmology,”Phys. Rev. D109(2024) no. 12, 124033,arXiv:2401.10351 [gr-qc]

    work page arXiv 2024

  74. [76]

    Eckart heat-flux applicability in $F(\Phi,X)R$ theories and the existence of temperature gradients

    D. S. Pereira and J. P. Mimoso, “Eckart heat-flux applicability in F(Φ,X)R theories and the existence of temperature gradients,”Phys. Rev. D113(2026) no. 8, 084021,arXiv:2512.20553 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  75. [77]

    Thermal channels of scalar and tensor waves in Jordan-frame scalar--tensor gravity

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

    work page internal anchor Pith review Pith/arXiv arXiv

  76. [78]

    Palatini frames in scalar-tensor theories of gravity

    A. Kozak and A. Borowiec, “Palatini frames in scalar–tensor theories of gravity,”Eur. Phys. J. C79(2019) no. 4, 335, arXiv:1808.05598 [hep-th]

    work page Pith review arXiv 2019

  77. [79]

    J¨ arv, A

    L. Järv, 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) no. 4, 044029,arXiv:2005.14571 [gr-qc]

    work page arXiv 2020

  78. [80]

    J¨ arv, S

    L. Järv, S. Karamitsos, and M. Saal, “Global portraits of nonminimal inflation: Metric and Palatini formalism,”Phys. Rev. D109(2024) no. 8, 084073,arXiv:2401.12314 [gr-qc]. 19

    work page arXiv 2024

  79. [81]

    Covariant formulation of scalar-torsion gravity

    M. Hohmann, L. Järv, and U. Ualikhanova, “Covariant formulation of scalar-torsion gravity,”Phys. Rev. D97(2018) no. 10, 104011,arXiv:1801.05786 [gr-qc]

    work page Pith review arXiv 2018

  80. [82]

    Nonmetricity formulation of general relativity and its scalar-tensor extension

    L. Järv, M. Rünkla, M. Saal, and O. Vilson, “Nonmetricity formulation of general relativity and its scalar-tensor extension,”Phys. Rev. D97(2018) no. 12, 124025,arXiv:1802.00492 [gr-qc]

    work page Pith review arXiv 2018

Showing first 80 references.