REVIEW 3 major objections 4 minor 2 cited by
Weak Gravity Limit in Newer General Relativity
T0 review · 3 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash
Pith's one-line read STEGR with a determinant-gradient term has 1.5 new dynamical modes, not the 1 previously claimed.
desk verdict Careful weak-field analysis of Newer GR with a real correction to the mode count, but the extra half degree of freedom hangs on an interpretive choice about the flat connection, not on a first-principles derivation. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The load-bearing object is the flat symmetric connection in the coincident gauge, where connection coefficients vanish and partial derivatives of the metric play the role of nonmetricity. In the linearized scalar sector the decisive identity is chi equal to log of minus g, equation (40), which ties the would-be pure-gauge determinant mode to the preferred coordinates; together with the reduced linearised equations (35) through (37), this constraint leaves only volume-preserving coordinate changes as gauge and produces the extra half degree of freedom. The kinetic matrix and its principal-minor positivity analysis carry the no-ghost and no-full-dynamics result.
What would settle it
Perform a full Dirac-Bergmann constraint analysis of the model with a1 equal to a2, a4, and a5 but a3 different from a1, treating the flat connection components as independent variables; if the number of physical initial data per point is three rather than three and a half, the linearised counting is an artifact.
Extended reading notes
Core claim
The paper's central claim is that the popular STEGR extension obtained by adding the square of the gradient of the metric determinant carries one and a half new dynamical degrees of freedom in its weak-field limit, not the single new mode attributed to it in the earlier literature. The counting is performed from the teleparallel viewpoint: the flat symmetric connection is an objective structure, so only coordinate changes with determinant equal to one are gauge once the field chi equal to log of minus the metric determinant is fixed. That reduces the kinematical gauge group from four diffeomorphism freedoms to three, and the remaining combination becomes a half-dynamical mode on top of the single scalar from chi. The paper also establishes that a fully dynamical, ghost-free Newer GR model is impossible and that in the linearized theory only the parameter combinations a1, a2 minus a4, a3, and a5 matter.
Load-bearing premise
The whole argument rests on treating the flat connection and its coincident-gauge coordinates as physical structure, so that only determinant-one coordinate changes count as gauge; drop that assumption and the extra half mode disappears.
Editorial extensions
If this is right
- If the central claim is right, the STEGR plus determinant-gradient model must be treated as a three-and-a-half-degree-of-freedom theory in every subsequent application, including cosmology and gravitational-wave analysis.
- The linearized theory depends on only four parameter combinations, with a2 and a4 entering only through their difference, so any observational distinction between those two coefficients must come from nonlinear effects.
- A fully dynamical ghost-free Newer GR model is impossible, so a healthy theory must leave some metric components constrained exactly as in GR.
- Within the viable scalar sector, deviations controlled by a3 or a5 both produce half-integer numbers of new modes, so the two deformations are not distinguished by the mode count alone.
- Setting a1 to zero removes the standard tensor gravitational-wave polarisations, making such models unsuitable as theories of gravity.
Reading between the lines
- Editorial inference: if the flat connection really carries a half degree, viable Newer GR models should exhibit a scalar or preferred-frame gravitational signature controlled by the determinant-gradient term; computing that observable would be a natural next step beyond this paper.
- Editorial inference: the same determinant-condition mechanism should apply to any symmetric-teleparallel action that breaks diffeomorphisms only through the metric determinant, so half-integer mode counts may be generic in that class.
- Editorial inference: a full nonlinear Hamiltonian analysis of the a5-modified model would test whether the linearised half mode survives away from Minkowski spacetime or is removed by strong-coupling constraints.
- Editorial inference: comparing scalar propagation speeds in the a3- and a5-modified models against gravitational-wave or pulsar-timing observations could distinguish the two viable deformations, which are degenerate in the mode count alone.
Signed reviews
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper studies the linearised weak-field limit of Newer GR, the most general parity-even quadratic action in the nonmetricity tensor (action (3)). It parametrises metric perturbations into scalar, vector, and tensor sectors, derives the linearised equations (22)-(25), and uses them to constrain the parameter space and count degrees of freedom. The central claim, stated in the abstract and Section 7.1, is that the STEGR-plus-(gradient of the metric determinant)² model has one and a half new dynamical scalar modes rather than one as previously claimed in Ref. [40], provided the flat connection is treated as an objective physical structure so that only volume-preserving coordinate changes are gauge (Eq. (40), χ = ln(−g)).
Significance. If the mode count is accepted, the paper corrects a previous result and maps out the viable parameter region of Newer GR in a transparent way. Its strengths are that the linearised equations, the kinetic matrix (17), and its determinant (18) are given explicitly, making the algebraic core checkable, and that the comparison with Ref. [40] is addressed directly. The main claim, however, is conditional on an interpretive assumption about the flat connection, and the paper does not provide an independent first-principles count that would settle whether the extra half mode is physical.
major comments (3)
- [Section 7.1, Eq. (40)] The claim of one and a half new modes is not derived from the action (3) alone; it presupposes that the flat connection is an objective physical field, so that only volume-preserving coordinate changes (det ∂ζ/∂x = 1) are gauge and χ = ln(−g) is a constraint. In the standard covariant symmetric-teleparallel formulation, the flat connection is a pure-gauge variable and the same linearised system reduces to the one-mode count of Ref. [40]. Since the paper does not give an independent first-principles count (for example, a covariant Hamiltonian or symplectic analysis) that selects the objective-connection interpretation, the headline three-halves claim remains conditional. The authors should either supply such a count or explicitly present the result as specific to the coincident-gauge teleparallel interpretation rather than as a definitive correction.
- [Section 7.1, after Eq. (39)] The text first says that the previous claim [40] 'is wrong' and then says 'we do agree with the scalar-tensor representation' and 'their analysis is also correct.' These statements are compatible only under the interpretive assumption discussed above; without it, Ref. [40]'s one-mode count is the correct result in the covariant formulation. The authors should remove the apparent contradiction by stating that the two counts apply to different frameworks, and by not calling the earlier count wrong without specifying that the disagreement concerns the physical status of the flat connection.
- [Section 3 and Section 7] The derivations repeatedly use the rule that an equation of the form Δ f = 0 is solved as f = 0, effectively treating Δ as an invertible operator and discarding harmonic and constant modes. Since the degree-of-freedom count in Section 7 depends on the number of initial data in this perturbative system, the authors should justify why the discarded modes cannot alter the count, or state explicitly that the result concerns only local modes with non-zero spatial momentum.
minor comments (4)
- [Abstract and Section 7.1] The phrase 'three halves new dynamical modes' is unusual; 'one and a half new dynamical degrees of freedom' would be less ambiguous, especially because the paper also speaks of 'three halves constrained and three halves dynamical modes.'
- [Eq. (17)] The grouping of fields in the kinetic matrix is indicated with braces in a way that is difficult to read; a table listing the fields and the corresponding blocks would improve clarity.
- [Section 7.1] The variable χ = ln(−g) is introduced both as a field and as a condition (40); the paper should state explicitly that this is an identity for the metric determinant rather than an independent constraint imposed by hand.
- [Footnote in Section 7.1] The remark about the notation in Ref. [40] being 'strange' is not needed for the technical argument and could be moved to a separate remark or omitted.
Circularity Check
No significant circularity: the 1.5-mode count is an explicit linearized calculation under a stated teleparallel gauge interpretation.
full rationale
The linearized analysis is self-contained: the quadratic action (3) is expanded around Minkowski in Section 3, the scalar equations (22)-(25) are derived explicitly from the linearized tensor (15), and the special case a1 = tilde-a2 = a5 with a3 != a1 is reduced in Section 7.1 to the system (39), from which the count of three scalar initial data (one for V and two for the phi/psi combination) follows by direct algebra. The comparison with Ref. [40] is an external benchmark: the paper reproduces the scalar-tensor equation square-chi = lambda0 e^{chi/2} and then disagrees only about whether the residual volume-preserving coordinate freedom should be counted as a gauge symmetry. That disagreement rests on the explicitly stated teleparallel interpretation, 'As long as we take the flat connection as something objective and sensical,' which is a physical assumption, not a hidden circular input. Self-citations to the authors' previous New GR papers and to Ref. [7] are methodological or geometric background and do not supply the degree-of-freedom count; no fitted parameter is renamed as a prediction, and no uniqueness theorem is imported to forbid alternatives. The claim is therefore conditional on the teleparallel viewpoint, but it is not circular.
Assumptions & free parameters
free parameters (5)
- a1
- a2
- a3
- a4
- a5
assumptions (5)
- domain assumption A global coincident gauge exists for the flat symmetric connection, so Q_alpha_mu_nu = partial_alpha g_mu_nu (Section 2, Eq. (1)).
- ad hoc to paper Equations of the form Delta f = 0 are solved as f = 0, and Delta is treated as a nonzero number in perturbation theory (Sections 3 and 5).
- domain assumption The flat connection is objective and physical, so only volume-preserving diffeomorphisms are gauge, enforced by chi = ln(-g) in the coincident gauge (Section 7.1, Eq. (40)).
- standard math Sylvester's criterion characterizes positive definiteness of the kinetic matrix K (Section 4, Eq. (17)).
- domain assumption The action (3) is the most general parity-preserving quadratic Newer GR action, taken from Ref. [3].
Cite this review
Pith. "Pith review of Weak Gravity Limit in Newer General Relativity." pith.science (2026). https://pith.science/paper/V7KJE6U7
@misc{pith2026250100376,
author = {Pith},
title = {Pith review of: Weak Gravity Limit in Newer General Relativity},
year = {2026},
howpublished = {\url{https://pith.science/paper/V7KJE6U7}},
note = {Machine review of arXiv:2501.00376}
}
read the original abstract
We analyse linearised field equations around the Minkowski metric with its standard flat parallel transport in models of Newer GR, that is quadratic actions in terms of nonmetricity tensor. We show that half of the freedom in choosing the model parameters is immediately fixed by asking for reasonable properties of tensors and vectors, defined with respect to spatial rotations, and accurately describe the much more complicated sector of scalars. In particular, we show that, from the teleparallel viewpoint, the model of STEGR with addition of a gradient squared of the metric determinant exhibits three halves new dynamical modes, and not just one like it was previously claimed.
Forward citations
Cited by 2 Pith papers
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Degrees of freedom of a quadratic scalar-nonmetricity theory
In quadratic scalar-nonmetricity gravity, Hamiltonian analysis shows 10, 8, and 8 degrees of freedom for cases II, V, and VI, while linear cosmological perturbation theory sees only 10, 6, and 5, indicating hidden str...
-
Dynamical systems approach and cosmological attractors in newer general relativity
In vacuum flat cosmology, type 1 newer general relativity cannot drive late-time acceleration, while type 2 theories produce either phantom or non-phantom dark energy depending on the sign of one free parameter.
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