{"id":"84885f69-1c67-4e65-bb19-18872e988f5b","arxiv_id":"2505.13298","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"In the most general symmetric teleparallel gravity, gravitational waves always include tensor modes, and with hypermomentum-carrying test particles they always include extra shear and longitudinal modes traveling at light speed.","lead":"This paper derives which gravitational wave polarization modes appear in the most general symmetric teleparallel gravity. It finds that if test particles carry hypermomentum, extra shear and longitudinal modes always appear, giving a potential observational test that distinguishes this gravity framework from general relativity.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Universal shear/longitudinal mode predictions hinge on an unproven detector model: Eq. (29) is imported from Ref. [29], and a different hypermomentum-matter coupling would change P7/P8 and the f(Q) pathology claim.","rationale":"The reader's weakest assumption is exactly the detector model of Eq. (29), and this is the most load-bearing concern because it connects the field-equation computation to every new physical prediction. The paper's own statements in Sec. IV.B and V.A show that the 'unconstrained Ki' becomes pathological only because Eq. (32) declares Ki observable through P7/P8, and Eq. (32) follows from Eq. (29). Without a derivation of Eq. (29) from a matter action, the universality claim is conditional on a specific, and possibly non-unique, test-particle model. The manuscript deserves credit for the explicit linearized field equations and the careful tensor/vector/scalar decomposition, and I do not see an internal algebraic contradiction that would justify rejection. But the hypermomentum observability claim is not fully self-contained. The additional concerns raised by the reader, such as the unverified longitudinal-mode solution and the lack of a dispersion analysis, are secondary but reinforce the same conditional status. Therefore the correct verdict remains conditional, and the existing reader verdict needs no adjustment.","tokens_in":15575,"tokens_out":9879,"duration_ms":97999,"concrete_test":"Derive the deviation equation for two nearby test particles from an explicit hypermomentum matter action, e.g., a Dirac fermion minimally coupled to the connection or a spinning-particle worldline action, in the same linearized symmetric-teleparallel background. Compare the resulting A_ij with Eq. (29). If additional terms such as ∂0 N^i_j0 or Σ^i_0j appear, recompute P7/P8 and the f(Q) unconstrained-mode conclusion; if the result matches Eq. (29) for a broad class of couplings, the concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central observable claim is that hypermomentum-carrying test particles always see shear modes P7/P8 and a longitudinal mode, and that f(Q) gravity becomes pathological if matter couples to the connection. All of these conclusions are read off from the deviation equation d2ηi/dt2 = -R^i_0j0 ηj - ∂j N^i_00 ηj in Eq. (29). The paper does not derive Eq. (29) from a matter action, nor does it show that this detector response is unique for matter carrying hypermomentum. Eq. (30) defines N only; it does not fix how a specific hypermomentum coupling enters the worldline or the relative acceleration. In metric-affine theories, the matter action can couple to the connection in many ways, and the equation of motion for a particle with intrinsic hypermomentum is model-dependent. If the correct deviation equation contains additional terms, the shear-mode formulas P7/P8 in Eq. (32), the claimed universal longitudinal mode read from P1, and the Sec. V.A conclusion that connection-dependent matter leads to unconstrained pathological modes all change. The field-equation analysis in Secs. IV.A-IV.C may be correct, but the mapping from field degrees of freedom to observable polarization modes is not established for the hypermomentum case. At minimum, the manuscript should specify the matter action that defines the hypermomentum charge and derive Eq. (29) from it, rather than importing it from a companion paper.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies gravitational-wave polarization modes in the most general symmetric teleparallel gravity action that yields second-order field equations, using a gauge-invariant decomposition. It claims that, when test particles carry hypermomentum, two shear modes and a longitudinal mode are universally present and propagate at the speed of light, while vector-x/y modes exist only in a special parameter region. The paper also analyzes f(Q) gravity and quadratic non-metricity gravity as concrete examples, concluding that f(Q) gravity is physically unreasonable if matter couples to the connection, and that in the parameter conditions considered both theories only have tensor modes in the absence of hypermomentum.","tokens_in":15840,"tokens_out":4174,"duration_ms":40150,"significance":"If the results hold, the paper provides a concrete, falsifiable distinction between symmetric teleparallel gravity and Riemannian theories: the universal presence of shear and longitudinal modes for hypermomentum-charged test particles. The field-equation analysis is explicit and checkable, and the parameter mappings for f(Q) and quadratic non-metricity gravity are clearly stated, which is useful for the community. However, the observable predictions rest on a detector model that is imported from a companion paper without derivation, and one of the two universal scalar-mode conclusions is asserted rather than demonstrated against the six scalar equations in Appendix A. The significance is therefore conditional on closing these gaps.","major_comments":[{"comment":"The central observable claims for the hypermomentum case depend on the relative-acceleration equation d^2 eta^i/dt^2 = -R^hat_i_0j0 eta^j - partial_j N^i_00 eta^j, which is imported from Ref. [29] without derivation. The paper does not specify the matter action that defines the hypermomentum charge, nor does it show that Eq. (29) is the unique or correct detector response for matter coupled to the connection. Since the definitions of P7/P8 in Eq. (32), the identification of the longitudinal mode P1, and the f(Q) pathology conclusion in Sec. V.A all read off from this equation, a different hypermomentum-matter coupling could change which field perturbations are observable. The authors should derive Eq. (29) from a concrete action, or state explicitly the minimal assumptions under which it holds.","section":"Sec. III, Eq. (29)"},{"comment":"The claim that there always exists a plane-wave solution L+K=0, phi=Theta=0 propagating at the speed of light is asserted but not verified against the six scalar equations (A1)-(A6). These equations are coupled and contain non-standard terms such as Delta/partial_0 and partial_0^3/Delta; the proposed ansatz should be substituted explicitly or shown by a linear-algebra argument to solve the full system for all allowed parameters. Without this, the universal existence of the longitudinal mode is not established. The companion claim that all scalar modes propagate at light speed also needs a concrete derivation from the scalar equations, since the stated reasons of homogeneity and formal Lorentz symmetry are not self-evident for these momentum-space equations.","section":"Sec. IV.C and Appendix A"},{"comment":"The vector-mode analysis states, after Eqs. (35)-(37), that when C(1)+E(1) is nonzero there exists a solution for K_i propagating at the speed of light, and that when C(1)+E(1)=0 the K_i are unconstrained. The latter is evident, but the former propagation claim is not demonstrated from the given equations. This is load-bearing for the conclusion that shear modes always exist (either as physical modes or as unconstrained pathological modes). The authors should show the elimination of Xi_i and the resulting dispersion relation for K_i, or provide the algebraic step that leads to this conclusion.","section":"Sec. IV.B, Eqs. (35)-(37)"}],"minor_comments":[{"comment":"There are several typos and OCR-like artifacts: 'carameter' in Sec. V.B should be 'parameter'; Eq. (A5) contains '1/2 C(1) 1/partial_0 K' and similar expressions that appear to be incorrect typesetting; and the second sentence of the abstract is missing a period after 'field equations'.","section":"Global"},{"comment":"The sentence 'this implies that symmetric teleparallel gravity necessarily requires A(2) != 0' is unclear: if A(2)=0, Eq. (34) imposes no constraint on hTT_ij, so the tensor modes would be unconstrained rather than nonexistent. The phrasing should be sharpened to say that a well-defined propagation of tensor modes requires A(2) != 0.","section":"Sec. IV.A, Eq. (34)"},{"comment":"The expression for P1 changes between the no-hypermomentum case and the hypermomentum case, with additional terms involving Pi, Pi-bar, and L appearing in Eq. (32). The text should explain how these terms arise from the connection contributions in Eq. (29), since P1 is read off from the same A_ij matrix.","section":"Sec. III, Eqs. (28) and (32)"},{"comment":"Figure 2, which illustrates the shear modes, is referenced but does not appear to be included in the manuscript text; please ensure the figure is present or remove the reference.","section":"Sec. III, Fig. 2"},{"comment":"The statement that conditions (a) and (b) endow the second-order action with 'the gauge symmetry and the Weyl Transverse Diffeomorphism (WTDiff) symmetry' is vague; the specific gauge symmetry should be named.","section":"Sec. V.B"}],"recommendation":"major_revision","confidential_remarks":"The paper's load-bearing claims depend on Ref. [29], a companion preprint by the same authors, for both the deviation equation and the shear-mode formalism. Since that reference is not yet published, the authors should either include a self-contained derivation of Eq. (29) or make the connection to the companion paper sufficiently explicit that the referee and readers can check it. The scalar universal-longitudinal-mode claim in Sec. IV.C is also currently unsupported by the appendix equations; this is a fixable gap if the authors supply the demonstration."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Read this one with the detector model in Eq. (29) in mind. The paper's headline claims—universal shear and longitudinal modes in the presence of hypermomentum, and the f(Q) no-go for matter-connection coupling—all hang on that equation, which is taken from the authors' companion paper rather than derived from a matter action. That is the main thing to check before trusting the results.\n\nWhat is genuinely new: they extend the polarization analysis of symmetric teleparallel gravity to the most general second-order action, including hypermomentum, and they give explicit parameter mappings for f(Q) and quadratic non-metricity gravity. The tensor and vector sectors are worked through in detail, with momentum-space equations that are transparent enough to verify. The observation that quadratic non-metricity gravity cannot cover all six linear parameters, and that adding an R term can, is a useful structural point.\n\nThe soft spots are proportional. First, Eq. (29) is the only bridge from connection perturbations to observed particle motion for hypermomentum-carrying particles. If the matter action couples to the connection differently, the P7/P8 shear formulas and the claimed longitudinal mode could change. The authors should either derive Eq. (29) from a concrete matter action or state clearly that it is an assumption. Second, the universal longitudinal solution L+K=0, phi=Theta=0 is asserted but not demonstrated against the six scalar equations in Appendix A; it needs a short derivation. Third, the claim that all scalar modes propagate at light speed is justified by a homogeneity/symmetry argument rather than a dispersion analysis—plausible but not fully argued. The f(Q) pathology result inherits the first two concerns: the 'unconstrained' modes are unconstrained in the field equations, but whether they are observable is still tied to Eq. (29).\n\nWho this is for: people working on symmetric teleparallel gravity and gravitational-wave polarizations. The paper is a legitimate extension of a line the authors have been developing, and the citation pattern is appropriate—they rely heavily on their own framework, but that is a real framework, not an argument by citation. It deserves a serious referee, but the referee should push on Eq. (29) and on the scalar-sector claims.\n\nRecommendation: send to peer review with a request for a derivation of the detector model and an explicit check of the longitudinal-mode solution. It is not ready as is, but it is worth engaging.","headline":"A useful but incomplete polarization-mode catalog for general symmetric teleparallel gravity; the universal-mode and f(Q) pathology claims rest on an imported detector equation the paper does not derive.","tokens_in":16409,"tokens_out":2065,"would_cite":false,"duration_ms":19244,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["04.30.-w","04.50.Kd"],"model":"deepseek-v4-flash","headline":"In the most general symmetric teleparallel gravity, gravitational waves always include two shear modes and a longitudinal mode, all travelling at light speed, when test particles carry hypermomentum — a polarization signature absent from…","keywords":["gravitational waves","polarization modes","symmetric teleparallel gravity","hypermomentum","non-metricity","f(Q) gravity","shear modes","longitudinal mode"],"falsifier":"For the universality claim, substitute the plane-wave branch $L+K=0$, $\\varphi=\\Theta=0$ into the six scalar equations (A1)–(A6) at a generic parameter point and inspect the dispersion relation: a parameter choice for which this branch fails to solve all six equations, or for which some other scalar mode acquires a non-lightlike speed, would refute the claim that the longitudinal mode is universal. For the detector model, deriving Eq. (29) from an explicit hypermomentum matter action and comparing the resulting deviation equation would settle whether the shear modes are the modes such matter actually exhibits.","tokens_in":15338,"feed_emoji":"🌊","tokens_out":20181,"duration_ms":179183,"temperature":0.7,"pith_summary":"This paper maps out the complete set of gravitational-wave polarization modes allowed by the most general symmetric teleparallel gravity — the family of theories that attributes gravity to non-metricity of the connection rather than to spacetime curvature — and treats that set as a fingerprint for distinguishing the family from general relativity. Its central statement is parameter-independent: when test particles carry hypermomentum, a charge that couples them to the connection, two shear modes and one longitudinal mode are always present and always travel at the speed of light, regardless of the values of the theory's coefficients. Without hypermomentum the generic prediction is just the two tensor modes, with light-speed vector modes appearing only on a finely tuned parameter surface. The same analysis shows that the two most studied special theories, f(Q) gravity and quadratic non-metricity gravity, cannot admit connection-coupled matter without producing unconstrained, physically unreasonable modes. Since polarization is read directly from the motion of test particles, a universal shear-plus-longitudinal pattern would be an observational discriminator between symmetric teleparallel gravity and the Riemannian framework.","feed_headline":"Two shear modes always ride waves carrying hypermomentum","feed_subtitle":"In symmetric teleparallel gravity a longitudinal mode travels with them — a fingerprint general relativity lacks.","key_machinery":"Three pieces of machinery carry the argument. A gauge-invariant decomposition of the metric and connection perturbations on a flat background separates the fields into transverse-traceless tensors $h^{TT}_{ij}$, transverse vectors $\\Xi_i$ and $K_i$, and scalars $\\Theta$, $\\phi$, $K$, $L$, which decouples the linearized field equations sector by sector. The symmetric-teleparallel constraint of zero curvature, written linearly as $\\partial_\\rho\\Sigma^\\mu_{\\nu\\lambda}=\\partial_\\lambda\\Sigma^\\mu_{\\nu\\rho}$, forces every gauge-invariant perturbation built purely from the connection to vanish, leaving only $h^{TT}_{ij}$, $\\Xi_i$, $K_i$, $\\Theta$, $\\phi$, $K$, and $L$ as possible carriers of radiation. The observable modes are then read off from the test-particle deviation equation: the metric part $\\hat{R}^i_{0j0}$ gives the six standard modes P1–P6, while the hypermomentum term $-\\partial_j N^i_{00}$ makes the deviation matrix asymmetric and generates the shear modes P7 and P8 from the transverse vector $K_i$; the longitudinal mode P1 is sourced by the scalar $L$ through the solution $L+K=0$, $\\varphi=\\Theta=0$. All of the parameter dependence sits in a six-coefficient quadratic action whose coefficients $A^{(1)}$, $B^{(1)}$, $C^{(1)}$, $D^{(1)}$, $E^{(1)}$, and $A^{(2)}$ decide which sectors propagate.","core_discovery":"The paper claims that in the most general symmetric teleparallel gravity theory with second-order field equations, the gravitational-wave polarization content is nearly rigid. The tensor sector always produces the + and $\\times$ modes at light speed, and a viable theory must have $A^{(2)}\\neq 0$ so these modes actually propagate. When test particles carry hypermomentum, the connection perturbation enters the particle-deviation equation, the deviation matrix becomes asymmetric, and two shear modes, P7 and P8, appear; they propagate at light speed whenever $C^{(1)}+E^{(1)}\\neq 0$, while in the degenerate case $C^{(1)}+E^{(1)}=0$ they are left unconstrained by the field equations, which the paper counts as a pathology. A longitudinal mode at light speed always exists as well, carried by the scalar-sector solution $L+K=0$, $\\varphi=\\Theta=0$. The paper further argues that f(Q) gravity is viable only if matter is independent of the connection, since any hypermomentum coupling yields unconstrained shear and longitudinal modes, and that the standard parameter conditions of quadratic non-metricity gravity likewise force the no-hypermomentum choice, leaving only tensor modes. The distinguishing claim is universality: with hypermomentum, shear and longitudinal modes are unavoidable companions of any gravitational wave, a pattern absent from Riemannian gravity.","pith_inferences":["Reading the paper's formulas literally, the universal longitudinal branch ($L+K=0$, $\\varphi=\\Theta=0$) has vanishing metric scalars: a detector following metric geodesics sees no scalar radiation, while a hypermomentum-charged detector sees a pure longitudinal signal carried entirely by the connection scalar $L$. The discriminating observation therefore needs purpose-built detectors with connecti","The paper's criterion for health — no polarization mode may be left unconstrained by the field equations — singles out the subspace $C^{(1)}+E^{(1)}\\neq 0$ and rules out hypermomentum in f(Q) and quadratic non-metricity gravity. The same criterion could serve as a general diagnostic for strong coupling in other metric-affine theories: an unconstrained field appearing in the observable modes is a s","The six-versus-five parameter gap implies that results obtained within quadratic non-metricity gravity, for example in cosmological perturbation theory, need not represent the full symmetric teleparallel landscape even at linear order; revisiting those results in the Ricci-scalar-extended action (49) would show which conclusions survive.","A testable extension would be to model a concrete hypermomentum-carrying test particle, such as matter with intrinsic spin probing a torsion-free connection background, and compute its response to the predicted plane waves; if the response differs from Eq. (29), the shear modes would be modified or absent, giving a laboratory-scale check of the paper's detector model."],"forward_implications":["A detector whose test masses carry hypermomentum should see two shear modes (P7 and P8) and a longitudinal mode arriving at light speed in every symmetric teleparallel theory, a pattern no Riemannian theory predicts; observing that pattern would select this family over general relativity.","f(Q) gravity cannot admit any coupling of matter to the connection: any such coupling produces unconstrained shear and longitudinal modes, a loss of predictability. This closes off connection–matter coupling as a cure for the ghost and strong-coupling problems found in cosmological f(Q) perturbations.","In the generic theory, vector-x and vector-y modes exist only under the fine-tuned condition $4A^{(2)}+C^{(1)}+E^{(1)}=0$, so a detection of light-speed vector modes would constrain the theory's parameter space rather than generically confirm the framework.","f(Q) gravity with metric-only matter and quadratic non-metricity gravity under its two standard parameter conditions both predict only the + and $\\times$ tensor modes at light speed, so polarization alone cannot distinguish those versions from general relativity without hypermomentum-sensitive detectors.","The most general linear field equations contain six free coefficients while quadratic non-metricity gravity has only five, so analyses restricted to that theory miss part of the symmetric teleparallel landscape; adding a Ricci-scalar term restores full linear coverage."],"supporting_citations":[{"why":"Supplies the most general second-order perturbation action, the gauge-invariant decomposition, the hypermomentum deviation equation (29), and the definition of the shear modes on which the paper's results are built.","marker":"[29]"},{"why":"Establishes the six standard Riemannian polarization modes that serve as the baseline the shear modes and the hypermomentum modifications extend.","marker":"[28]"},{"why":"Gives the prior f(Q) geodesic-deviation result that only tensor modes propagate, which the paper reproduces for metric-only matter and extends to the hypermomentum case.","marker":"[44]"},{"why":"Provides the earlier polarization analysis of symmetric teleparallel theories that the quadratic non-metricity section builds on and contrasts with.","marker":"[49]"},{"why":"Supplies the companion propagation analysis of gravitational waves in symmetric teleparallel gravity, used as context for the mode-speed results.","marker":"[50]"},{"why":"Reports the cosmological ghosts and strong coupling in f(Q) that motivated connection–matter coupling as a fix, which the paper's f(Q) analysis rules out.","marker":"[58]"},{"why":"Defines the geometrical trinity and the non-metricity framework, including the parameter conditions (a) and (b) whose gauge and WTDiff symmetries the paper analyzes.","marker":"[2]"}],"fun_headline_variants":["Hypermomentum forces shear and longitudinal gravitational-wave modes","Gravitational waves with hypermomentum always carry shear and longitudinal modes","Shear and longitudinal modes: hypermomentum's gravitational-wave fingerprint","Hypermomentum's waves never lack shear and longitudinal modes","Hypermomentum guarantees shear and longitudinal modes in every wave"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is the detector model of Eq. (29), adopted from the authors' earlier work rather than derived from a matter action: a hypermomentum-charged test particle is assumed to respond to a wave through $d^2\\eta^i/dt^2=-\\hat{R}^i_{0j0}\\eta^j-\\partial_j N^i_{00}\\eta^j$, and this specific response rule is what makes the connection scalar $L$ and the transverse vector $K_i$ show up as shear and longitudinal modes; a different coupling between matter and the connection would change which modes are observable even if the gravitational field equations stay the same.","fun_headline_variants_meta":{"raw":{"variants":["Hypermomentum forces shear and longitudinal gravitational-wave modes","Gravitational waves with hypermomentum always carry shear and longitudinal modes","Shear and longitudinal modes: hypermomentum's gravitational-wave fingerprint","Hypermomentum's waves never lack shear and longitudinal modes","Hypermomentum guarantees shear and longitudinal modes in every wave"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001873,"raw_usage":{"total_tokens":7413,"prompt_tokens":1074,"completion_tokens":6339,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":690,"completion_tokens_details":{"reasoning_tokens":6251}},"tokens_in":690,"tokens_out":6339,"duration_ms":47208,"temperature":1.0,"reasoning_tokens":6251,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T20:16:32.268214+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"For the universality claim, substitute the plane-wave branch $L+K=0$, $\\varphi=\\Theta=0$ into the six scalar equations (A1)–(A6) at a generic parameter point and inspect the dispersion relation: a parameter choice for which this branch fails to solve all six equations, or for which some other scalar mode acquires a non-lightlike speed, would refute the claim that the longitudinal mode is universal. For the detector model, deriving Eq. (29) from an explicit hypermomentum matter action and comparing the resulting deviation equation would settle whether the shear modes are the modes such matter actually exhibits.","supporting_citations":[{"cited_title":"New gravitational wave polarization modes in the torsionless spacetime","cited_arxiv_id":null,"evidence_quote":"Supplies the most general second-order perturbation action, the gauge-invariant decomposition, the hypermomentum deviation equation (29), and the definition of the shear modes on which the paper's results are built."},{"cited_title":"Gravitational-wave observations as a tool for testing relativistic gravity","cited_arxiv_id":null,"evidence_quote":"Establishes the six standard Riemannian polarization modes that serve as the baseline the shear modes and the hypermomentum modifications extend."},{"cited_title":"Gravitational waves in f(Q) non-metric gravity via geodesic deviation","cited_arxiv_id":null,"evidence_quote":"Gives the prior f(Q) geodesic-deviation result that only tensor modes propagate, which the paper reproduces for metric-only matter and extends to the hypermomentum case."},{"cited_title":"Polarization of gravitational waves in symmetric teleparallel theories of gravity and their modifications","cited_arxiv_id":null,"evidence_quote":"Provides the earlier polarization analysis of symmetric teleparallel theories that the quadratic non-metricity section builds on and contrasts with."},{"cited_title":"Propagation of gravitational waves in symmetric teleparallel gravity theories","cited_arxiv_id":null,"evidence_quote":"Supplies the companion propagation analysis of gravitational waves in symmetric teleparallel gravity, used as context for the mode-speed results."},{"cited_title":"Pathological Character of Modifications to Coincident General Relativity: Cosmological Strong Coupling and Ghosts in f(Q) Theories","cited_arxiv_id":null,"evidence_quote":"Reports the cosmological ghosts and strong coupling in f(Q) that motivated connection–matter coupling as a fix, which the paper's f(Q) analysis rules out."},{"cited_title":"The Geometrical Trinity of Gravity","cited_arxiv_id":null,"evidence_quote":"Defines the geometrical trinity and the non-metricity framework, including the parameter conditions (a) and (b) whose gauge and WTDiff symmetries the paper analyzes."}],"review_version":1}