{"id":"21ded89e-3935-4387-9487-dbed8e0a7ac0","arxiv_id":"2607.17431","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"In the leading Horava-Lifshitz truncation, gravitational waves acquire amplitude corrections proportional to alpha f^2, propagation phases proportional to alpha f^3 r, and chirp corrections proportional to alpha f^2, with GWTC-4.0 bounding -620 eV^-2 < alpha < 190 eV^-2.","lead":"This paper works out how gravitational waves change in Horava-Lifshitz gravity, where frequency and wavelength are related by omega^2 = k^2 + alpha k^4 instead of omega^2 = k^2. It finds small frequency-dependent amplitude and phase shifts, and translates LIGO/Virgo/KAGRA data into a bound on alpha.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"GW energy flux and chirp rate in Eqs. (96)-(99) are imported from GR without deriving them from the Horava-Lifshitz action; the alpha(nabla^2 h)^2 term likely adds same-order contributions.","rationale":"The propagation phase and amplitude corrections to the waveform are derived consistently from the modified Green function and appear internally sound. The mapping to the LVK beta=4 posterior is straightforward and the resulting constraint on alpha follows from the propagation phase alone. The weakest point is indeed the energy flux and chirp calculation: Eq. (96) is the GR quadrupole flux formula, imported without a derivation from the Horava-Lifshitz action. Because the action (10) contains a higher-derivative term that contributes to the energy-momentum at the same fractional order as the claimed corrections, the luminosity and chirp rate (Eqs. 98-99) may be incomplete. This concern is load-bearing for the paper's claims about Delta P/P and Delta f_dot/f_dot, though not for the main propagation-phase bound. The reader's weakest_assumption identifies exactly this, so I agree. A concrete derivation of the energy flux from the action would settle whether the omission is real. Since this concern does not invalidate the propagation-phase result, the CONDITIONAL verdict remains appropriate; no verdict change is needed.","tokens_in":23889,"tokens_out":11656,"duration_ms":100901,"concrete_test":"Compute the gravitational-wave energy flux from the quadratic action (10) using, e.g., the Noether current for time translations or the effective stress tensor obtained by varying the action around a flat background. Evaluate this on the phase-resummed waveform (84) in the radiation zone and integrate over the sphere to obtain the total luminosity. Compare the result with Eq. (98). If there is a difference at O(alpha omega^2), then Eq. (99) and the associated chirp corrections are incorrect. A complementary check is to reproduce the tensor-sector luminosity from Blas & Sanctuary (Phys. Rev. D 84, 064004 (2011)) in the same truncation and compare the coefficient of the alpha correction.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's derivation of the luminosity and adiabatic chirp evolution (Section V.B-C, Eqs. 96-99) relies on the standard GR energy flux formula dP/dOmega = r^2/(16 pi G) < h_dot_+^2 + h_dot_x^2 >, taken directly from Maggiore's textbook, and on the energy balance P = -dE_orb/dt. This is not derived from the Horava-Lifshitz action (Eq. 10). The quadratic action contains a term alpha (nabla^2 h_ij)^2, which modifies the canonical energy-momentum tensor (or pseudotensor) for gravitational waves. For a wave of frequency omega, each extra spatial derivative brings a factor k ~ omega, so this term contributes to the energy flux at relative order alpha omega^2—the same order as the claimed corrections Delta P/P = -16 pi^2 alpha f^2 and Delta f_dot/f_dot = -16 pi^2 alpha f^2. Therefore, Eqs. (98)-(99) may miss a same-order contribution from the higher-derivative part of the action. The propagation phase and amplitude corrections (Eqs. 68-69, 109) are derived from the retarded Green function and appear sound, so the main LVK constraint from the propagation phase is unaffected. But the chirp evolution and the associated 'generation phase' (Eq. 140) are central to part of the paper's claims and are not secure.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper studies linearized tensor gravitational waves in the leading parity-even infrared truncation of Hořava–Lifshitz gravity, characterized by the modified wave equation (∂_t² − ∇² + α∇⁴) h_ij = 0. The authors construct the retarded Green function (Sec. IV.A), derive the radiation-zone waveform to first order in α (Sec. IV.B), and obtain the phase-resummed frequency-domain form h̃_A(f,r) ≃ h̃_A^GR(f,r) (1 − 8π²α f²) exp(−4iπ³α f³ r). They apply this to a circular binary, give polarization waveforms for arbitrary inclination, compute luminosity and adiabatic chirp corrections ΔP/P_GR = Δḟ/ḟ_GR = −16π²α f², and map α to the LVK β = 4 modified-dispersion parameter, obtaining −6.2×10² eV⁻² < α < 1.9×10² eV⁻² at 90% credibility from GWTC-4.0. The paper also discusses amplitude, chirp, and generation-phase constraints and their limitations.","tokens_in":24304,"tokens_out":31243,"duration_ms":273819,"significance":"Section IV is the strongest part of the manuscript: the Green-function computation is explicit, the distributional identities check, and the phase-resummed representation correctly avoids expanding the accumulated propagation phase. The mapping to the LVK dispersion framework (Sec. VI.A-B) is straightforward and yields a clean constraint on the Hořava–Lifshitz coefficient. The paper is also appropriately cautious in Sec. VI.E about not converting the amplitude and chirp relations directly into catalog bounds. However, the luminosity and chirp results (Sec. V.B-C) are not yet on the same footing: they import the GR energy-flux formula without deriving it from the Hořava–Lifshitz action, and the printed energy-balance chain contains inconsistencies. If those derivations are repaired, the paper would be a solid contribution to the gravitational-wave phenomenology of Hořava–Lifshitz gravity.","major_comments":[{"comment":"The luminosity is obtained by substituting the modified waveform into the standard GR flux formula dP/dΩ = r²/(16πG)⟨ḣ_+² + ḣ_ײ⟩ (Maggiore). This formula is not derived from the Hořava–Lifshitz action (10). The quadratic action contains a term α(∇²h_ij)²; for a mode of frequency f each extra spatial derivative brings a factor k ∼ 2πf, so the energy-momentum/flux current receives contributions at relative order αω² — the same order as the claimed ΔP/P = −16π²αf². Without an explicit derivation of the energy flux from the action, Eqs. (97)-(99) are not established. The propagation-phase results in Eqs. (68)-(69) and (109) are unaffected, but the abstract's luminosity/chirp claims require either a proper flux derivation or an explicit statement that these results are heuristic under the GR flux prescription.","section":"Section V.B, Eq. (96)"},{"comment":"The energy-balance chain as printed is internally inconsistent. Integrating Eq. (97) over solid angle yields a factor π^{10/3}, so Eq. (98) is missing π^{10/3} in (GM_c f_gw)^{10/3}. Moreover, the displayed orbital energy E_orb = −(G² M_c^5 ω_gw)^{1/3} has the wrong scaling: for a circular orbit the binding energy scales as ω_gw^{2/3}, not ω_gw^{1/3}, up to numerical factors. Starting from the printed P and E does not produce the quoted chirp equation (99). The standard form of Eq. (99) suggests the preceding factors are typographical, but as printed the derivation is not reproducible. Please correct the factors and show the full derivation, including the α correction, so that Eq. (99) actually follows.","section":"Section V.C, Eqs. (98)-(99)"},{"comment":"The 'generation phase' correction δΨ_gen and the ppE coefficient β_ppE are obtained by applying the stationary-phase approximation to Eq. (134), which inherits both the unverified luminosity derivation and the inconsistencies of Eqs. (98)-(99). Until the chirp equation is re-derived from the action, the numerical coefficient and the claimed 3PN relative scaling in Eq. (142) should be regarded as provisional. The propagation-phase constraint (Eq. 144) is independent and can stand, but the generation-phase channel should be presented only after the energy-flux issue is resolved.","section":"Section VI.E, Eqs. (140)-(142)"}],"minor_comments":[{"comment":"Sections V.A and V.B both carry the title 'Polarization waveforms for an arbitrary observation direction'. The second should be retitled (e.g., 'Energy flux and luminosity').","section":"Section V headings"},{"comment":"The phrase 'after accounting conservatively for the possible' is duplicated in the sentence preceding Eq. (127).","section":"Section VI.D"},{"comment":"Typo: 'first=-order' should be 'first-order'.","section":"Section VI.A"},{"comment":"Once Eq. (99) is re-derived consistently, the sign and coefficient of the α correction in the solution (100) should be rechecked; the solution is quoted without derivation.","section":"Section V.C, Eq. (100)"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know. The Green-function and radiation-zone waveform derivation in Section IV is careful, and the resulting amplitude and phase corrections match the known LVK beta=4 mapping. But the luminosity and chirp results in Section V are built on the GR energy-flux formula taken from Maggiore without deriving it from the HL action (Eq. 10). Since that action contains an alpha (nabla^2 h)^2 term, the gravitational-wave energy flux picks up a same-order alpha omega^2 correction that the paper does not compute. That is a real gap, not a nitpick.\n\nWhat is actually new: the explicit retarded Green function, the radiation-zone waveform including the fifth-derivative term and its resummation into the exponential phase, and the binary waveform for arbitrary inclination. These are done carefully; the distributional identities check out and the phase-resummed form is sensible. The propagation-phase part, however, substantially overlaps with earlier work (Mirshekari-Yunes-Will, Gong et al., and the authors' own ref. [51]). The genuinely new pieces are the waveform package and the GWTC-4.0 bound, which is a straightforward mapping of an external posterior onto alpha.\n\nThe soft spot is the flux. The paper replaces h with the corrected waveform in the GR formula dP/dOmega = r^2/(16 pi G) <hdot_+^2 + hdot_x^2> and obtains -16 pi^2 alpha f^2, but the action's higher-derivative term contributes to the energy-momentum at that same order. Without computing the relevant current or pseudotensor for the HL truncation, Eqs. (98)-(99) and the generation-phase result (140) are not secure. This does not affect the propagation phase or the LVK bound, so the central observable claim stands. It does affect the chirp and generation-phase claims, which are part of the paper's advertised results. Secondary: the paper does not clearly delineate which parts of the waveform already appear in refs. [49,51]; a careful reader has to cross-check. The TT-sector restriction is stated clearly, so that is not a problem.\n\nWho this is for: people working on Horava-Lifshitz phenomenology or modified dispersion in gravitational waves. The propagation result is a clean confirmation of known physics; the flux result needs a proper derivation from the action. With that fixed, this could be a solid paper. As is, it deserves peer review rather than desk rejection, but the referee should push specifically on the energy-flux question and the novelty relative to the earlier literature.","headline":"The propagation waveform is derived cleanly and the LVK bound is a fair translation, but the luminosity/chirp section imports GR flux without justification and likely misses same-order corrections, so the paper needs revision before it is fully reliable.","tokens_in":24764,"tokens_out":2644,"would_cite":false,"duration_ms":26935,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["83C35","83D05","83C45"],"pacs":["04.30.-w","04.60.-m"],"model":"deepseek-v4-flash","headline":"Horava-Lifshitz gravity predicts that gravitational waves acquire a frequency-dependent amplitude correction and a phase that grows with distance, while the polarization content remains identical to general relativity.","keywords":["Horava-Lifshitz gravity","gravitational waves","modified dispersion relation","dispersive phase","chirp evolution","GWTC-4.0","Lorentz violation","Green function"],"falsifier":"Derive the gravitational-wave energy-momentum tensor directly from the quadratic action (Eq. 10) to first order in α and compute the total luminosity for a quasi-circular binary. If the resulting chirp rate differs from f_dot = (96/5)π^{8/3}(GM_c)^{5/3} f^{11/3}(1 − 16π²αf²) by a term of order αω², the paper's luminosity and chirp predictions are incomplete. Alternatively, a numerical relativity simulation of a binary inspiral with the modified action that measures the phase evolution to order α would settle whether the propagation-phase formula is the whole story.","tokens_in":23817,"feed_emoji":"📡","tokens_out":6060,"duration_ms":59264,"temperature":0.7,"pith_summary":"This paper tries to establish what the leading parity-even higher-derivative correction of Horava-Lifshitz gravity does to observable gravitational waves. It shows that the modified dispersion relation ω² = k² + αk⁴, with α a length-squared parameter, preserves the standard plus and cross polarizations and introduces no birefringence or polarization mixing. The radiation-zone waveform picks up a frequency-dependent amplitude factor (1 − 8π²αf²) and a dispersive phase −4π³αf³r that grows linearly with source distance. Applying the result to binary black holes, the paper derives corrections to luminosity and chirp evolution and maps the coefficient to the LIGO-Virgo-KAGRA dispersion parametrization, obtaining −6.2×10² eV⁻² < α < 1.9×10² eV⁻² at 90% credibility. If correct, this turns existing gravitational-wave catalogs into a probe of the Horava-Lifshitz ultraviolet scale through accumulated propagation phase rather than local waveform changes.","feed_headline":"Horava-Lifshitz gravity predicts a distance-growing f³ phase","feed_subtitle":"Each Fourier component of a binary merger accumulates a phase shift −4π³αf³r; GWTC-4.0 data bind α to less than ~10² eV⁻².","key_machinery":"The key object is the retarded Green function of the modified wave operator ∂_t² − ∇² + α∇⁴. Expanding the dispersion frequency Ω_k = k√(1+αk²) to first order in α, the Green function becomes a local combination of δ(t−r), δ″(t−r), and δ‴(t−r) supported on the GR light cone; convolving with the source produces the amplitude renormalization and the fifth-derivative term that, once resummed into an exponential, yields the accumulated phase −½αω³r. This phase resummation is what preserves the 1/r falloff and makes the propagation effect distinct from a local radiative contribution.","core_discovery":"The central result is a one-parameter modification of the gravitational-wave waveform in the radiation zone: h̃_A(f,r) ≈ h̃_A^GR(f,r) (1 − 8π²αf²) exp(−4iπ³αf³r), where α is the coefficient of the k⁴ term in the tensor dispersion relation. The phase accumulates over the source–observer distance, while the amplitude correction is local and frequency dependent. For a quasi-circular binary, the fractional corrections to the luminosity and chirp rate are both −16π²αf², and the accumulated generation phase behaves like a relative third post-Newtonian contribution. The paper also shows that the correction acts diagonally on the two tensor polarizations, so it does not produce polarization mixing,","pith_inferences":["The paper imports the general-relativistic quadrupole energy-flux formula to compute luminosity and chirp. A first-principles derivation of the flux from the action (Eq. 10) would likely add a same-order αω² contribution to the energy-momentum tensor, so Eq. (99) may not be the complete leading-order chirp correction.","The parity-odd k⁵ term, which the paper leaves to future work, would break the +/× degeneracy and produce helicity-dependent phase; the framework developed here can be extended to constrain that term separately in the same LVK parametrization.","Because the phase shift grows linearly with distance, a single loud, high-redshift binary at high frequency could rival the combined bound of many nearby events; targeted searches for dephasing in far sources are a natural follow-up."],"forward_implications":["Every compact-binary signal in Horava-Lifshitz gravity carries a phase shift −4π³αf³r, so distant high-frequency sources are the most sensitive probes: the bound improves with both catalog size and source distance.","The polarization content stays identical to general relativity, so current tests of polarization and birefringence cannot discriminate this truncation; only amplitude, phase, and chirp measurements can.","The derived GWTC-4.0 interval translates to a characteristic length scale ℓ_α = √|α| ≲ 4.9×10⁻⁶ m and energy scale Λ_α ≳ 4.0×10⁻² eV, which is far below the Planck scale but within reach of accumulated-phase measurements.","In the LVK band the local expansion parameter |α|(2πf)² is below 10⁻²⁰, so the only observable effect is the distance-accumulated phase; local corrections are negligible.","If the chirp correction −16π²αf² is confirmed, the inspiral rate itself carries the signature, providing a consistency check across independent channels."],"fun_headline_variants":["Horava-Lifshitz gravity predicts f³ phase in gravitational waves","Distance-dependent phase from modified dispersion in Horava-Lifshitz gravity","GWTC-4.0 constrains Horava-Lifshitz gravity to new limits","Horava-Lifshitz gravity modifies chirp without birefringence","f³ dispersion phase in GWs: a test of Horava-Lifshitz gravity"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The luminosity and chirp results assume that the gravitational-wave energy flux is given by the GR formula dP/dΩ = r²/(16πG)⟨ḣ₊² + ḣₓ²⟩ and that energy balance P = −dE_orb/dt holds, without deriving the flux from the Horava-Lifshitz action; the α(∇²h)² term contributes to the energy-momentum tensor at the same fractional order αω² as the claimed corrections, so the chirp evolution may be missing a same-order term.","fun_headline_variants_meta":{"raw":{"variants":["Horava-Lifshitz gravity predicts f³ phase in gravitational waves","Distance-dependent phase from modified dispersion in Horava-Lifshitz gravity","GWTC-4.0 constrains Horava-Lifshitz gravity to new limits","Horava-Lifshitz gravity modifies chirp without birefringence","f³ dispersion phase in GWs: a test of Horava-Lifshitz gravity"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000418,"raw_usage":{"total_tokens":2075,"prompt_tokens":913,"completion_tokens":1162,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":657,"completion_tokens_details":{"reasoning_tokens":1056}},"tokens_in":657,"tokens_out":1162,"duration_ms":10526,"temperature":1.0,"reasoning_tokens":1056,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-01T17:58:33.883398+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Derive the gravitational-wave energy-momentum tensor directly from the quadratic action (Eq. 10) to first order in α and compute the total luminosity for a quasi-circular binary. If the resulting chirp rate differs from f_dot = (96/5)π^{8/3}(GM_c)^{5/3} f^{11/3}(1 − 16π²αf²) by a term of order αω², the paper's luminosity and chirp predictions are incomplete. Alternatively, a numerical relativity simulation of a binary inspiral with the modified action that measures the phase evolution to order α would settle whether the propagation-phase formula is the whole story.","supporting_citations":[],"review_version":1}