{"id":"36838990-4406-4976-be67-28f1eadb4691","arxiv_id":"2608.12456","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":9,"one_line_summary":"A scale-invariant quadratic gravity plus hidden QCD-like sector can generate the Planck and electroweak scales, realize Starobinsky inflation, and produce dark matter from scalaron decay, with candidate masses around 10^8 to 10^11 GeV.","lead":"This paper proposes that inflation, the Planck and electroweak scales, and dark matter all come from one scale-invariant theory in which a hidden confining sector replaces the Higgs mass mechanism. A generalist reader might care because the scheme yields specific dark matter masses and a dark radiation signal that future cosmological data can test.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Central scale-generation step rests on an assumed sign dominance of the hidden gluon condensate over the chiral condensate; the paper offers motivation but no derivation, so the Planck scale and all downstream predictions are conditional on an untested assumption.","rationale":"I read the paper's central argument as: hidden confinement produces M_Pl and a Higgs mass via the gravitational portal (Eq. 2.8), the R^2 term gives Starobinsky inflation (Eq. 3.27), and scalaron decays produce DM (Eq. 4.8). The weakest load-bearing step is the sign and magnitude of the induced Einstein-Hilbert term, because without a positive M_Pl^2 there is no gravitational sector to build anything on. The paper explicitly flags this as an assumption in Sec. 2.1, which is honest, but it is not derived or tested. The motivation from asymptotic freedom (negative beta function) does not translate into a sign statement about the curved-space <F^2> matrix element relative to <psi-bar psi>; Refs. [54-56] indicate the chiral contribution has the wrong sign, so the two contributions could partially cancel. This matters because Models I-III all include fermions. The semi-conformal limit and unknown C (Eqs. 2.8, 3.34) are parameter choices, acknowledged by the authors, and reduce predictive sharpness but do not invalidate the framework. Footnote 7's unresolved valley-stability condition is a second concern, but it can be checked within the model; the gluon-dominance issue is more fundamental. I therefore agree substantially with the reader's weakest-assumption identification and see no reason to change the CONDITIONAL verdict. The proposed effective-action and lattice-based computation would settle the concern; until then, the central claim remains conditional.","tokens_in":27707,"tokens_out":11902,"duration_ms":104908,"concrete_test":"Compute the coefficient of the Ricci scalar in the one-loop effective action of the hidden SU(N_c) gauge theory with N_f fundamental Dirac fermions on a constant-curvature background, including both the gluon-condensate and chiral-condensate contributions following the curved-space NJL formalism of Refs. [54-56] and the lattice-supported method of Ref. [53]. Evaluate this for Model I (N_c=3, N_f=1) and Models II/III (N_c=4 with a fermion doublet). If the total induced Einstein-Hilbert coefficient is negative or the gluonic contribution does not dominate, the Planck-scale generation in Sec. 2.1 fails, and the DM and inflation predictions should not be trusted.","verdict_should_be":"UNCHANGED","load_bearing_attack":"In Sec. 2.1 the authors state that the hidden chiral condensate induces an Einstein-Hilbert term with sign opposite to the required positive Newton constant, so 'one must assume that the gluon contribution dominates.' This assumption is load-bearing: all three dark matter models in Sec. 5 contain hidden fermions, so both condensates are present. If the gluonic term does not dominate, the induced M_Pl^2 could have the wrong sign or the wrong magnitude; then the Einstein-Hilbert rewriting (2.4), the induced Higgs mass (2.8), the value of kappa (3.34), and the dark matter abundance formula (4.8) all lose their basis. The paper's motivation from the negative beta function does not determine the sign of the curved-space matrix element of <F^2> relative to <psi-bar psi>. Lattice support cited (Ref. [53]) is for pure Yang-Mills, not for theories with chiral fermions. A secondary unresolved point is footnote 7: the reduction to single-field Starobinsky inflation requires m^2_{sigma,perp} >> H^2 and negligible turning rate, which is asserted but not verified in the parameter region generating the DM mass windows. The gluon-dominance issue is the more fundamental, since it underpins the very existence of the induced Planck scale.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript proposes a classically scale-invariant framework in which quadratic gravity plus a hidden confining SU(N_c) gauge sector generates the Planck and electroweak scales via hidden condensates, realizes Starobinsky inflation through the R^2 scalaron, and reheats both the visible and hidden sectors through scalaron decay. The central result is the gravitational freeze-in formula in Eq. (4.8), which relates the present dark matter abundance to the scalaron branching ratio, the dark matter mass, and the visible reheating temperature. Three hidden-sector dark matter realizations are studied: a hidden eta-prime meson (Model I), hidden vector bosons from a gauged SU(2)_L (Model II), and charged hidden pions together with massless dark radiation (Model III). The authors derive dark matter and dark radiation relic abundances and quote viable composite dark matter masses in the range 10^8 to 10^11 GeV for Models I and III, together with constraints on hidden gauge couplings and on Delta N_eff.","tokens_in":28068,"tokens_out":7556,"duration_ms":72804,"significance":"If the underlying scale-generation premises can be substantiated, the framework would be a noteworthy unification of the hierarchy problem, inflation, dark matter, and dark radiation in a single classically scale-invariant structure. The paper's strengths are its careful derivation of the freeze-in abundance and its agreement with Ref. [92], its explicit acknowledgment of the conditions needed for single-field inflation in footnote 7, and its treatment of three qualitatively different dark matter stability mechanisms. The analysis is nonetheless conditional on two unproven premises: the dominance and sign of the hidden gluon condensate over the chiral condensate in inducing the Einstein-Hilbert term, and the validity of the single-field reduction in the parameter regions used for the dark matter mass windows. Because these premises support the central claim, the manuscript needs substantive revision rather than minor polish.","major_comments":[{"comment":"The induced Planck scale is assumed, not derived. Equations (2.4), (2.8), and the subsequent determination of kappa in Eq. (3.34) rely on the hidden gluon condensate inducing an Einstein-Hilbert term with the correct sign and dominating the chiral condensate. The paper states, in Sec. 2.1, that 'one must assume that the gluon contribution dominates.' The supporting beta-function argument controls asymptotic freedom, not the curved-space matrix element of <F^2> relative to <psi-bar psi>; moreover, Ref. [53] is a lattice computation for pure Yang-Mills, whereas all models in Sec. 5 contain chiral fermions so that both condensates are present. Please provide a computation or a lattice-motivated estimate of the two contributions to the induced R coefficient for N_f > 0 and demonstrate the required sign and magnitude. Without this, the Planck scale, the induced Higgs mass, and every abundance computed from Eq. (4.8) rest on an untested premise.","section":"Sec. 2.1"},{"comment":"The reduction to single-field Starobinsky inflation is asserted rather than verified in the regions of parameter space used for the dark matter predictions. The valley condition gives the location sigma_v(phi) = v_sigma, but as footnote 7 correctly notes, single-field dynamics also requires m^2_{sigma,perp} >> H^2 and a negligible turning rate in field space. These conditions are not demonstrated for the parameter points that produce the mass windows in Figs. 5, 7, and 8. Figure 3 is only a representative illustration. In regions where the hidden condensate is shallow or the trajectory bends, Eq. (3.27) and the reheating relation (3.48) would not apply. Please compute the orthogonal mass and the turning rate from the NJL potential and state the allowed ranges of the hidden-sector parameters in which the single-field approximation is valid.","section":"Sec. 3.1, footnote 7"},{"comment":"The quoted 'viable composite dark matter masses' are not predictions in the usual sense. In Model I the text says, 'Since m_eta' is not calculable, we regard it as a free parameter,' and in Model III the charged pion mass is fixed by inverting Eq. (4.8) while Delta in Eq. (5.30) is treated as an independent parameter. The mass windows are therefore the values required to reproduce Omega_DM h^2 = 0.12 for a chosen reheating history, not independent outputs of the framework. The summary in Sec. 6 should distinguish 'required mass' from 'predicted mass' and should state the number of free parameters in each model before the relic abundance is imposed.","section":"Secs. 5.1, 5.3, and 6"}],"minor_comments":[{"comment":"The axis labels in the left panel are ambiguous; the sigma/v_sigma and phi/M_Pl axes appear to be interchanged or incompletely labelled, which makes it hard to verify the claimed valley behaviour.","section":"Fig. 3"},{"comment":"The caption and surrounding text contain notation slips such as m'_eta for m_eta' and f_eta for f_eta'; the ratio being plotted should also be defined explicitly.","section":"Fig. 5 caption"},{"comment":"The displayed factor contains a repeated polarization index, epsilon^{(s)*}_mu(k1) epsilon^{(s)*}_mu(k1), which is inconsistent with the subsequent helicity sum; please correct the index structure.","section":"Appendix B, Eq. (B.7)"},{"comment":"The symbol for the mean equation of state is written as \\(\\bar\\omega\\) after Eq. (3.43) but as \\(\\bar w\\) in Eq. (3.40); use one notation consistently.","section":"Sec. 3.3"},{"comment":"Reference [31] is cited as a 2025 manuscript without journal information, yet it appears to contain several ingredients of the scale-generation argument; its status should be clarified or updated.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The paper is within the scope of JCAP and does not contain an internal inconsistency that would force rejection. The central issue is that the Planck-scale generation step is an assumption, and the inflationary reduction is asserted rather than checked in the parameter regions used. Both are fixable by adding the missing analysis or by explicitly reframing the paper as a conditional construction. I would also ask the authors to clarify the relation to the companion work Ref. [31]."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Read this one if you care about the scale-invariant gravity + hidden strong dynamics program. The genuinely new piece is the systematic treatment of three composite dark matter realizations: hidden eta', hidden vector, and hidden charged pions, with gravitational freeze-in relic abundances computed from the same scalaron-decay machinery. The DM stability arguments are concrete and useful, especially the gravitational anomaly decay of eta' giving a real upper bound on its mass, and the custodial/U(1) mechanisms for the vector and pion are clean. Eq. (4.8) matches Allahverdi-Drees, and the paper is unusually honest about its own conditions: footnote 7 concedes that the reduction to single-field Starobinsky inflation requires m_perp^2 >> H^2 and negligible turning, which is not demonstrated; footnote 8 brackets the ghost issue; Sec. 2.1 explicitly says one must assume the gluon condensate dominates the chiral condensate to get the correct sign of the induced Planck mass.\n\nThat last assumption is the load-bearing one. The entire scale-generation chain—induced Einstein-Hilbert term, induced Higgs mass, kappa from Eq. (3.34), and therefore the DM abundance—starts from M_Pl^2 being positive and dominated by <F^2>. The paper motivates this via the beta function, but as the stress-test note points out, the sign of the curved-space matrix element of <F^2> relative to <psi-bar psi> is not determined by asymptotic freedom. The cited lattice support is for pure Yang-Mills, not for a theory with chiral fermions. The central claim is therefore conditional, and the paper says so, but the abstract and summary don't carry the caveat with enough weight.\n\nThe advertised DM mass windows 10^8 to 10^11 GeV are also less predictive than they look. They follow from inverting Eq. (4.8) with Omega h^2 fixed to 0.12 and with free parameters m_eta', Delta, and the unknown coefficient C. That is fitting the observed abundance, not predicting a mass. The range is more a statement of the available parameter space. That said, the framework does make falsifiable cosmological connections: r is suppressed by the Weyl ghost, Delta_Neff is bounded, and the eta' lifetime bound is a genuine handle. Those are the parts that deserve referee time.\n\nOverall: a solid, clear framework paper in an already-established program. Not a breakthrough, but a legitimate advance in mapping the model space. The soft spots are real but mostly acknowledged. I'd send it to peer review; the referee should ask whether the gluon-dominance assumption can be supported or softened, and should push the authors to be sharper about what is predicted versus fit.","headline":"Same-group extension with a systematic three-model DM study; the Planck-mass sign assumption is openly admitted but load-bearing, and the DM masses are fits, not predictions.","tokens_in":28735,"tokens_out":3154,"would_cite":true,"duration_ms":29123,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A classically scale-invariant quadratic gravity with a hidden confining sector can generate the Planck and electroweak scales, drive Starobinsky inflation, and produce the observed dark matter via scalaron decays, all without input mass…","keywords":["classical scale invariance","quadratic gravity","hidden strong dynamics","dimensional transmutation","Starobinsky inflation","induced electroweak scale","gravitational freeze-in","composite dark matter"],"falsifier":"A lattice computation of the induced Einstein-Hilbert term in the hidden SU(Nc) theory with one fundamental Dirac fermion would settle the matter: if the chiral-condensate contribution has the wrong sign or cancels the gluon contribution, Planck-mass generation fails. Observationally, a tensor-to-scalar ratio that is not suppressed as strongly as predicted by the Weyl-squared ghost, or a dark radiation abundance $\\Delta N_{\\rm eff}$ incompatible with the model's predictions, would falsify the proposed models.","tokens_in":27396,"feed_emoji":"🌌","tokens_out":8931,"duration_ms":76258,"temperature":0.7,"pith_summary":"This paper seeks to show that four long-standing puzzles—the size of the electroweak scale, the existence of the Planck scale, cosmic inflation, and dark matter—can be accounted for by a single classically scale-invariant Lagrangian. A hidden QCD-like SU(Nc) sector confines and condenses, generating the Planck mass by dimensional transmutation; because the hidden and visible sectors are orthogonal, the breaking reaches the Standard Model only gravitationally and induces the Higgs mass. The scalar degree of freedom of the $R^{2}$ term acts as the Starobinsky inflaton and reheats both sectors through its universal coupling to the trace of the energy-momentum tensor, so hidden-sector relics are produced by gravitational freeze-in. The paper derives the relic formula (4.8) and, in three concrete hidden-sector models, finds viable dark matter masses.","feed_headline":"One hidden gauge sector yields Planck scale, Higgs mass, and dark matter","feed_subtitle":"Scale-invariant gravity with hidden confinement predicts Starobinsky inflation and dark matter at 10^8 to 10^11 GeV.","key_machinery":"The engine is the classically scale-invariant quadratic-gravity action with a dimensionless $R^2$ term, a Weyl-squared term, and a non-minimal Higgs-gravity coupling; the scalaron is the scalar degree of freedom hidden in the $R^2$ term and becomes the Starobinsky inflaton. The Planck mass is not put in by hand but appears from the hidden gluon condensate, while Eq. (2.8), obtained from the one-loop gravitational portal, converts that scale into the Higgs mass; in the semi-conformal limit $\\xi_H \\to -1/6$, the observed 125 GeV Higgs mass fixes $\\kappa \\simeq 5\\times10^{14} C^{1/2}$, with all non-perturbative corrections absorbed in an unknown coefficient $C$ of order 0.1 to 10. All subsequent abundance calculations rest on the trace-anomaly interaction $\\chi T^\\alpha{}_\\alpha/(\\sqrt{6}M_{\\rm Pl})$, which gives the scalaron partial widths into hidden states and, together with the Boltzmann system (4.1)–(4.3), yields the dark matter and dark radiation relic abundances and the key formula Eq. (4.8).","core_discovery":"On the paper's own terms, the central claim is that a single scale-invariant framework replaces the usual hierarchy of input scales with one dynamical sequence: hidden confinement generates the Planck mass; the same condensation, acting through the non-minimal term $\\xi_H H^\\dagger H R$, induces the electroweak scale; the $R^2$ term supplies Starobinsky inflation; and scalaron decays replenish the Universe, producing dark matter gravitationally. The operative formula is Eq. (4.8), $\\Omega_{\\rm DM}h^2 \\simeq 0.12\\, (m_{\\rm DM}/m_\\phi)(B_{\\rm DM}/2.9\\times10^{-10})(T_{\\rm RH}^{\\rm SM}/{\\rm GeV})$, which ties the relic abundance to the scalaron branching ratio, the dark matter mass, and the reheating temperature of the visible sector. Applied to a hidden $\\eta'$ meson, a hidden vector from a gauged SU(2)L, and hidden charged pions, the requirement $\\Omega h^2 = 0.12$ fixes the dark matter mass as a function of the inflationary e-folds; for the composite candidates of models I and III, viable masses lie in the range $10^8$ to $10^{11}$ GeV.","pith_inferences":["One step beyond the paper's claims, the universal trace coupling suggests that any hidden species with a small enough branching ratio inherits the same parametric abundance law as Eq. (4.8), so the observed dark matter density may constrain ratios of hidden masses and decay widths rather than any specific particle identity.","A nonperturbative computation fixing the unknown coefficient $C$ would convert the condition $\\kappa \\simeq 5\\times10^{14} C^{1/2}$ from a placeholder into a genuine prediction for the spin-two ghost mass and hence for the tensor-to-scalar ratio.","Because the hidden sector is gravitationally secluded, the model points toward cosmological rather than collider tests: a precise measurement of $\\Delta N_{\\rm eff}$ or of $r$ could discriminate among the three realizations even if no hidden particle is ever produced in the laboratory.","A lattice computation of the sign and size of the induced Einstein-Hilbert term in a hidden SU(Nc) gauge theory with chiral fermions would test the gluon-dominance premise directly, before any cosmological comparison is made."],"forward_implications":["If the framework is correct, no explicit mass terms are needed in the fundamental Lagrangian: the Planck scale appears as a hidden-sector condensate and the electroweak scale as its gravitational by-product.","Inflation is Starobinsky-like, with the spectral index and tensor-to-scalar ratio controlled by the number of e-folds; the Weyl-squared ghost suppresses the tensor ratio by orders of magnitude.","Dark matter is a gravitational freeze-in product of the same reheating phase, and for the composite hidden mesons of models I and III the required masses are $10^8$ to $10^{11}$ GeV.","Hidden radiation from massless states contributes $\\Delta N_{\\rm eff}$, and the current bound $\\Delta N_{\\rm eff} \\lesssim 0.12$ restricts the hidden gauge couplings, such as $e_{A'}$ in model III.","In model I, the hidden $\\eta'$ can decay into gravitons, so requiring its lifetime to exceed the age of the Universe places an upper bound on $m_{\\eta'}$ for each inflationary history."],"supporting_citations":[{"why":"provides the original mechanism by which a strongly coupled hidden sector breaks electroweak symmetry, which this paper couples to quadratic gravity.","marker":"[13]"},{"why":"establishes perturbative renormalizability of quadratic gravity and the necessity of the non-minimal Higgs-gravity coupling.","marker":"[20]"},{"why":"defines the Starobinsky inflation scenario whose potential and spectrum the single-field reduction reproduces.","marker":"[27]"},{"why":"supplies the multi-field to single-field inflation analysis and the scalaron-mediated dark matter freeze-in framework used in Sections 3 and 4.","marker":"[28]"},{"why":"contains the companion calculation of the gravity-mediated hierarchy, the NJL effective potential, and the semi-conformal limit used for the induced Higgs mass.","marker":"[31]"},{"why":"provides the one-loop beta-function of the induced portal coupling that underlies Eq. (2.8).","marker":"[57]"},{"why":"provides the inflaton-radiation-dark matter Boltzmann system whose solution gives the freeze-in abundance.","marker":"[90]"},{"why":"is the standard massive-particle production result that Eq. (4.8) matches.","marker":"[92]"}],"fun_headline_variants":["Hidden condensation sets Planck, Higgs, and dark matter scales","Scale-invariant gravity yields dark matter via gravitational freeze-in","One hidden gauge sector spawns inflation, Higgs, and dark matter","Dark matter from scalaron decay in scale-invariant gravity"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole chain of scale generation rests on the assumption that the hidden gluon condensate, not the chiral condensate, dominates the induced Einstein-Hilbert term with the correct sign, and that the Higgs-gravity coupling stays at the semi-conformal value $\\xi_H = -1/6$ with an unknown coefficient $C$ of order 0.1 to 10 absorbing all non-perturbative corrections.","fun_headline_variants_meta":{"raw":{"variants":["Hidden condensation sets Planck, Higgs, and dark matter scales","Scale-invariant gravity yields dark matter via gravitational freeze-in","One hidden gauge sector spawns inflation, Higgs, and dark matter","Dark matter from scalaron decay in scale-invariant gravity"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000258,"raw_usage":{"total_tokens":1603,"prompt_tokens":986,"completion_tokens":617,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":602,"completion_tokens_details":{"reasoning_tokens":548}},"tokens_in":602,"tokens_out":617,"duration_ms":5853,"temperature":1.0,"reasoning_tokens":548,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T00:09:12.031318+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A lattice computation of the induced Einstein-Hilbert term in the hidden SU(Nc) theory with one fundamental Dirac fermion would settle the matter: if the chiral-condensate contribution has the wrong sign or cancels the gluon contribution, Planck-mass generation fails. Observationally, a tensor-to-scalar ratio that is not suppressed as strongly as predicted by the Weyl-squared ghost, or a dark radiation abundance $\\Delta N_{\\rm eff}$ incompatible with the model's predictions, would falsify the proposed models.","supporting_citations":[],"review_version":1}