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REVIEW 3 major objections 3 minor 1 cited by

Correspondence between Myrzakulov $F(R,Q)$ gravity and Tsallis cosmology

T0 review · 3 major / 3 minor · reviewed 2026-08-08 · deepseek-v4-flash

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Pith's one-line read This paper claims that two otherwise different cosmological frameworks—Myrzakulov F(R,Q) gravity and Tsallis entropy cosmology—can be tuned to share one expansion history while still predicting different structure growth.

desk verdict A background-level correspondence between F(R,Q) gravity and Tsallis cosmology that only works after correcting a central parameter typo, while the claimed perturbation-level difference rests on an unvalidated mini-superspace shortcut. read the letter →

arxiv 2502.04462 v1 pith:GI3DFMOY submitted 2025-02-06 gr-qc astro-ph.CO

Andreas Lymperis , Gulgassyl Nugmanova , Almira Sergazina This is my paper · ORCID
classification gr-qcastro-ph.CO PACS 04.50.Kd98.80.-k
keywords MyrzakulovF(RQ)gravityTsalliscosmologymetric-affinegravity-thermodynamicsconjecturenonmetricitydarkenergydensityperturbationsfσ8
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper claims that Myrzakulov $F(R,Q)$ gravity—a modified theory built from both curvature and nonmetricity—can be made to reproduce exactly the background expansion of Tsallis cosmology, a framework that obtains modified Friedmann equations from the gravity–thermodynamics conjecture with Tsallis entropy. The match is achieved for the simple model $F=R+\lambda Q+\tilde{\Lambda}$ by choosing specific power-law forms for the connection-dependent functions $u$ and $w$, and by identifying $\lambda=3$, $\tilde{\Lambda}=2\Lambda$, and the remaining parameters in terms of the Tsallis entropy index $\delta$. The paper then argues that the two frameworks nevertheless differ at the level of linear matter perturbations: the friction terms coincide, but the effective Newton constant in the growth equation does not, so the growth of structure and $f\sigma_8$ can in principle discriminate between them. If true, this gives a concrete dictionary between a metric-affine modification of gravity and a thermodynamic modification of cosmology, while making perturbation datasets the decisive tests.

What carries the argument

The central object is the mini-superspace Lagrangian (2.18) for $F(R,Q)$ gravity, where $u=R-\hat{R}$ and $w=Q-\breve{Q}$ are treated as free functions of the scale factor, its derivatives, and the connection. Inserting $F=R+\lambda Q+\tilde{\Lambda}$ turns this Lagrangian into effective Friedmann equations whose dark-energy density and pressure are given by (2.24)–(2.25). The background correspondence is carried by the power-law ansatz $u=\epsilon H^{\zeta}+\eta H^{\theta}$, $w=\xi H$ with $H=\dot{a}/a$, whose exponents and coefficients are fixed by matching the Tsallis dark-energy sector (3.10)–(3.11). The perturbation comparison is carried by the linearized matter-overdensity equation (4.8), obtained by perturbing the same mini-superspace action in the Newtonian gauge; its last term, containing the effective Newton constant, is the specific place where the two frameworks diverge.

What would settle it

Compute the linear scalar perturbation equations of the full metric-affine $F(R,Q)$ theory for the same background-matching parameters and compare the matter-growth equation with (4.5); if the effective Newton constant becomes equal to the Tsallis one, the claimed discriminator disappears. On the observational side, measuring $f\sigma_8$ with errors smaller than the separation between the two curves in Fig. 3 over the plotted redshift range would decide which perturbation prescription is realized.

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Extended reading notes

Core claim

On the background level, the paper finds that the Myrzakulov $F(R,Q)$ field equations reduce to effective Friedmann equations whose dark-energy sector is expressed through the connection-dependent functions $u$ and $w$, the parameter $\lambda$, and the constant $\tilde{\Lambda}$. Requiring this dark-energy sector to coincide with the one that arises from applying the first law of thermodynamics at the apparent horizon with Tsallis entropy, for the ansatz $u=\epsilon(\dot{a}/a)^{\zeta}+\eta(\dot{a}/a)^{\theta}$ and $w=\xi(\dot{a}/a)$, leads to the identifications $\lambda=3$, $\tilde{\Lambda}=2\Lambda$, $\eta=-12$, $\theta=2$, $\xi=10$, $\zeta=4-2\delta$, and $\epsilon=\frac{6\alpha\delta}{(2-\delta)(3-2\delta)}$. Under these identifications the two frameworks are reported to give identical background evolution, reproducing the matter and dark-energy sequence and a dark-energy equation of state that can cross into the phantom regime. Moving to linear scalar perturbations in the Newtonian gauge, the paper derives a matter-overdensity equation for Myrzakulov gravity from the same mini-superspace action and compares it with the Tsallis growth equation: the friction terms agree, but the coefficient multiplying $\delta_m$, i.e. the effective Newton constant, differs, so the growth of matter fluctuations and the $f\sigma_8$ curves separate. The paper therefore claims that structure-growth and weak-lensing observables can distinguish the two theories even when their expansion histories coincide.

Load-bearing premise

The main distinguishing result rests on treating the mini-superspace action (2.18) as the correct source of linear scalar perturbations in the Newtonian gauge, since the full metric-affine perturbation analysis is explicitly left beyond the paper's scope.

Editorial extensions

If this is right

  • Under the identified parameter map, background observables such as $H(z)$, $\Omega_m(z)$, and $w_{DE}(z)$ are identical in the two frameworks, so expansion-history data alone cannot separate them.
  • The linear growth of matter overdensities differs because the effective Newton constant in the Myrzakulov perturbation equation (4.8) is not the same as in the Tsallis equation (4.5), making redshift-space-distortion measurements a potential discriminator.
  • Weak-lensing observables, which depend on the matter power spectrum, inherit this growth difference and can in principle distinguish the two theories even at fixed background evolution.
  • The reconstruction maps the Tsallis entropy parameters $\alpha$ and $\delta$ directly to the connection-function coefficients $\epsilon$ and $\zeta$ of $F(R,Q)$ gravity, providing a translation between a thermodynamic and a geometric description of dark energy.
  • In the limit $\delta=1$, Tsallis cosmology reduces to $\Lambda$CDM, and the matched Myrzakulov model is constructed to fall back to the same background behavior, so standard cosmology is recovered as a special case.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Because the perturbation equation (4.8) is obtained from the mini-superspace action rather than from the full metric-affine perturbation theory, the quantitative separation of the $f\sigma_8$ curves in Fig. 3 should be treated as indicative until the full treatment, which the paper postpones, is carried out.
  • The same reconstruction strategy could be applied to other extended entropies, such as Barrow or Kaniadakis entropy, by inserting their effective dark-energy sectors into the $u,w$ ansatz; the resulting growth equations would then provide a family of perturbation-level tests of the gravity–thermodynamics correspondence.
  • A sharper forecast could be made by computing the growth index $\gamma(z)$ and the linear matter power spectrum from (4.8) and comparing with current and future survey error bars, which would indicate how much data a discriminating measurement requires.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 3 minor

Summary. The paper investigates whether Myrzakulov F(R,Q) gravity, a metric-affine theory involving both curvature and nonmetricity, can reproduce the background cosmology of Tsallis cosmology, and claims that despite this background degeneracy the two frameworks differ in linear density perturbations and effective Newton constant, so that structure-growth and weak-lensing observables could distinguish them. The authors choose the model F(R,Q)=R+lambda Q+\tilde{\Lambda}, impose the ansatze u=epsilon(a_dot/a)^zeta+eta(a_dot/a)^theta and w=xi(a_dot/a), and give a parameter identification list that allegedly matches the effective dark-energy density and pressure of Myrzakulov gravity, Eqs. (2.24)-(2.25), to the Tsallis expressions, Eqs. (3.10)-(3.11). They then present a perturbation equation (4.8), obtained by insertion of the Newtonian-gauge metric into the mini-superspace Lagrangian, and plot f-sigma_8 in Fig. 3 to argue that the two scenarios are observationally distinguishable.

Significance. If established, the claimed result would be of moderate interest to the modified-gravity and cosmology communities: it would provide an explicit example of two very different frameworks that are background-degenerate yet perturbatively distinguishable. The paper is clearly organized, the reconstruction strategy is transparent, and the authors explicitly acknowledge that their perturbation treatment is approximate. However, the two load-bearing claims are not currently supported. The background matching contains an arithmetic inconsistency in the printed parameter list, and the perturbation equation (4.8) is asserted from a mini-superspace Lagrangian without a derivation from the full field equations. The scientific value of the paper therefore depends on corrections that go beyond its stated scope.

major comments (3)
  1. [Sec. 4.1, Eqs. (2.24) and (3.10)] The identification list after Eq. (4.2) contains lambda=3, but direct substitution of the ansatze (4.1)-(4.2) with the printed values eta=-12, theta=2, zeta=4-2delta, epsilon=6 alpha delta/[(2-delta)(3-2delta)] into (2.24) yields an H^2 coefficient 6-3lambda. With lambda=3 this equals -3, whereas the Tsallis dark-energy density (3.10) requires the coefficient +3; the matching forces lambda=1, not lambda=3. As printed, the background correspondence used in Figs. 1 and 2 therefore does not hold, and the central claim of identical background evolution is not demonstrated.
  2. [Sec. 4.2, Eqs. (4.7)-(4.8) and Fig. 3] Equation (4.8) is the entire basis for the claimed perturbative distinguishability, but it is not derived from the field equations (2.10)-(2.13) of Myrzakulov gravity. The text states that inserting the Newtonian-gauge metric (4.7) into the mini-superspace Lagrangian (2.18) yields (4.8), yet (2.18) was constructed for homogeneous backgrounds with u=u(a,a_dot,a_ddot) and w=w(a,a_dot) and does not incorporate the connection-field equations (2.13) at linear order. The authors themselves state that the full metric-affine perturbation analysis lies beyond the present work. Consequently (4.8), the effective Newton constant it contains, and the f-sigma_8 curves in Fig. 3 cannot be regarded as predictions of Myrzakulov F(R,Q) gravity; the main distinguishing message of the paper is unestablished.
  3. [Sec. 4.2, Eq. (4.8)] Even taken on its own terms, Eq. (4.8) is not reproducible as written: the quantities u_a, u_a_dot, w_a, and w_a_dot are not evaluated for the background-matched ansatz, the role of the Newton constant G in the coefficient G(1+lambda(w_a+w_a_dot)/2+u_a+u_a_dot/2)/(1+lambda) in relation to the G in Eqs. (2.24)-(2.25) is not defined, and the equation contains no scale dependence, leaving unclear which perturbative regime (e.g., long-wavelength limit) is being considered. These omissions prevent the reader from verifying the plotted f-sigma_8 results.
minor comments (3)
  1. [Abstract, Sec. 1] There are several typographical issues: 'Beken stein-Hawking' in the Abstract, 'de-Sitter' in Sec. 4.1, and 'of of f-sigma_8' in the caption of Fig. 3.
  2. [Sec. 4.2, Eq. (4.5)] Equation (4.5) has unbalanced parentheses and inconsistent notation for derivatives with respect to redshift; please clarify the expression so that it can be checked against the cited reference [65].
  3. [Sec. 4.1, after Eq. (4.2)] The identifications are presented without derivation; providing an explicit step-by-step match of (2.24)-(2.25) to (3.10)-(3.11) would make the reconstruction verifiable and would have exposed the lambda discrepancy.

Circularity Check

1 steps flagged · score 2.0 of 10

Background correspondence is imposed by construction, but the perturbative distinguishability claim is an independent calculation; self-citation is non-load-bearing.

  1. self definitional [Section 4.1, Eqs. (4.1)-(4.2) and parameter identifications; Fig. 1 caption]
    "To make the two theories coincide at the background level, we appropriately choose the functions u(a, ȧ, ä) and w(a, ȧ) in such a way that the modified Friedmann equations in both scenarios become identical. Observing the forms (2.24),(2.25) as well as (3.10),(3.11) we impose the ansatz"

    The free functions u and w are chosen so that the Myrzakulov effective dark-energy density (2.24) reproduces the Tsallis dark-energy density (3.10) term by term; the stated parameter identifications are the solution of that matching condition. The subsequent conclusion that both frameworks give identical background evolution is therefore a restatement of the imposed condition, not an independent prediction. The paper itself concedes this in the Fig. 1 caption: 'since they were reconstructed to coincide at the background level.' This is a mild, transparent by-construction step; it does not affect the perturbation comparison, which takes these functions as inputs and computes a new output.

full rationale

The paper's background-level 'correspondence' in Sec. 4.1 is a by-construction step: u(a,ȧ,ä) and w(a,ȧ) are free functions of the mini-superspace model, and they are explicitly chosen (Eqs. 4.1-4.2) so that the effective dark-energy density (2.24) matches the Tsallis expression (3.10); the paper acknowledges in the Fig. 1 caption that the two scenarios 'were reconstructed to coincide at the background level.' This makes the background equivalence an identity relative to the ansatz, rather than an empirical prediction. However, this is not the paper's distinguishing claim. The perturbative analysis (Sec. 4.2) uses the background-fitted functions as inputs and computes a new quantity, the growth equation (4.8), which is not used to choose u,w; the difference from the Tsallis perturbation equation (4.5) is an independent output. The only self-citation, Ref. [44], appears in a general list of applications and is not load-bearing. The skeptic's concerns — that (4.8) is obtained from the mini-superspace Lagrangian rather than the full metric-affine equations, and that the printed λ=3 would not match (3.10) (direct substitution requires λ=1 for the H^2 term) — are correctness and validity issues, not circularity. Overall circularity is low.

Assumptions & free parameters 9 free parameters · 5 assumptions · 0 invented entities

The free parameters are mostly reconstruction parameters chosen by hand to reproduce the Tsallis dark energy sector; alpha and delta are inherited from Tsallis entropy. No new particles or forces are introduced. The axioms are background framework assumptions, a borrowed perturbation equation, and an unverified mini-superspace treatment of perturbations.

free parameters (9)
  • lambda (Q-coupling) = 3 (stated); algebra requires 1
    Sets the F(R,Q)=R+lambda Q+Lambda_tilde coupling; chosen to match the Tsallis dark energy sector. The printed value is inconsistent with the matching; direct substitution requires lambda=1.
  • Lambda_tilde (or Lambda) = set by Omega_m0 approx 0.31
    Cosmological constant tuned to fix the present matter density parameter to the Planck value.
  • eta = -12
    Coefficient in the u ansatz, chosen to produce the H^2 contribution that cancels part of the -3 lambda H^2 term.
  • theta = 2
    Exponent in the u ansatz; combined with eta=-12 it gives a +12 H^2 contribution.
  • xi = 10
    Coefficient in the w ansatz; the w - a_dot w_a_dot combination vanishes identically for this linear form.
  • zeta = 4 - 2 delta
    Exponent in the u ansatz, tied to the Tsallis index delta so that H^zeta matches H^{4-2 delta} in the Tsallis dark energy.
  • epsilon = 6 alpha delta / ((2-delta)(3-2 delta))
    Coefficient derived from matching the H^{4-2 delta} term of Tsallis dark energy; it is a function of the free Tsallis parameters alpha and delta.
  • alpha = 1
    Set to its standard value without loss of generality, as stated in Section 4.1.
  • delta = varied: 0.9, 1, 1.1, 1.2, 1.3
    Tsallis entropic index, an input from Tsallis cosmology; the paper varies it to show the evolution of the equation-of-state parameter.
assumptions (5)
  • domain assumption Mini-superspace Lagrangian variation yields the correct full Friedmann equations.
    Used in Section 2 to extract (2.19)-(2.20). This is standard in the cited program [30] but not proved in the paper.
  • domain assumption The gravity-thermodynamics conjecture applied to the apparent horizon is valid.
    Underpins the Tsallis cosmology equations (3.6)-(3.11), inherited from references [45-49,59].
  • domain assumption Tsallis entropy for black holes has the form S_T = (alpha_tilde/4G) A^delta.
    Input from reference [87]; not derived or justified in this paper.
  • domain assumption The Tsallis perturbation equation (4.5) taken from reference [65] is correct.
    Equation (4.5) is imported directly from Sheykhi and Farsi [65] without re-derivation.
  • ad hoc to paper The mini-superspace action (2.18) describes linear scalar perturbations in the Newtonian gauge.
    Assumed in Section 4.2 to derive (4.8). The authors admit the full metric-affine perturbation analysis is beyond the scope of the work.

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Pith. "Pith review of Correspondence between Myrzakulov $F(R,Q)$ gravity and Tsallis cosmology." pith.science (2026). https://pith.science/paper/GI3DFMOY

@misc{pith2026250204462,
  author       = {Pith},
  title        = {Pith review of: Correspondence between Myrzakulov $F(R,Q)$ gravity and Tsallis cosmology},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GI3DFMOY}},
  note         = {Machine review of arXiv:2502.04462}
}
abstract

We investigate the correspondence between Myrzakulov $F(R,Q)$ gravity and Tsallis cosmology. The former is a modified gravity that uses both curvature and nonmetricity, while the latter is a modified cosmology arising from the gravity-thermodynamics conjecture, employing Tsallis entropy instead of the Bekenstein-Hawking one. By appropriately identifying the functional dependencies and the model parameters, we demonstrate that both frameworks can give identical background evolution, reproducing the standard cosmological sequence of matter and dark energy domination. However, their perturbation behavior exhibits differences, since the growth of density fluctuations and the effective Newton constant deviate between the two scenarios, indicating that perturbative observables, such as structure formation and weak-lensing ones, could serve as distinguishing factors between them.

Discussion (0). Continue with ORCID to comment.

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  1. Effective matter sectors from modified entropies

    gr-qc 2025-11 conditional novelty 4.0 of 10

    Choosing a modified entropy S(r) fixes a metric f(r)=1-4πM/S'(r), and the Einstein tensor of that metric acts as an anisotropic effective fluid.

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