Quantum Omni–Synthesis as an Effective Field Theory: Phenomenological Completion, Cosmological Perturbations, and Constraints

Quantum Omni–Synthesis as an Effective Field Theory: Phenomenological Completion, Cosmological Perturbations, and Constraints Stefalo Acha1, 2 1North Carolina A&T State University, Greensboro, NC, USA 2[email protected]at.edu /[email protected] The Quantum Omni–Synthesis (QOS) framework organizes microphysical and cosmological phenomena as the balance of two orthogonal energy channels: implosive (gravitationally binding, inward) and explosive (kinetic/electromagnetic, outward). We present a phenomenological completion and EFT formalization of QOS that (i) provides the full scalar–tensor action with two scalars ψ, ς, (ii) derives field equations, modified Friedmann dynamics, and linear perturbations, (iii) gives quasi–static predictions for the effective Newton constant Geff (k, a) and slip η(k, a), and (iv) ensures luminal gravitational–wave speed (cT= 1) with modified damping. Stability, post–Newtonian limits, GW170817 bounds, cosmological and laboratory constraints are summarized. Distinct, testable predictions (growth fσ8, lensing slip, GW luminosity distance, expansion history, hydrogen spectral shifts) are highlighted with figures. All symbols are tabulated in Appendix C; derivation steps are in Appendix B. Keywords: Quantum Omni-Synthesis (QOS); effective field theory; scalar–tensor gravity; quasi-static limits; Geff (k, a); gravitational slip η; GW damping; PPN constraints; cosmology. 2 I. INTRODUCTION The Quantum Omni–Synthesis (QOS) model postulates that physical reality arises from the dynamic balance between two orthogonal energy channels: implosive energy, associated with inward contraction and gravitational binding, and explosive energy, associated with outward expansion, kinetic degrees of freedom, and electromagnetic excitations. Previous studies have developed the theoretical foundations of this idea, proposed a modified energy– momentum relation, and explored implications for quantum spin, quark dynamics, and observational consistency. In this study, we advance QOS into a phenomenological effective field theory (EFT). By embedding the implosive– explosive principle into a scalar–tensor framework, we provide a consistent action, field equations, cosmological perturbations, and empirical constraints. This treatment avoids duplication of earlier works by focusing exclusively on EFT formalization and data–oriented predictions. For conventional context, ΛCDM succeeds empirically yet leaves dark components unexplained [1,2]; scalar–tensor frameworks such as Brans–Dicke [3,4], Horndeski/beyond [5–7] and DHOST [8] provide flexible, testable baselines (see reviews [9–14]). II. ACTION (A1–A2): DEFINITIONS OF F, Kψ, Kς, U Scope and motivation. An EFT is defined by its degrees of freedom, symmetries, and operator hierarchy. QOS introduces two scalars: ψ(encoding energetic content in the implosive–explosive split) and ς(a quantized gravity– coupling that modulates the effective Planck mass). We work in the Jordan frame so matter follows geodesics of gµν. S=Zd4x√−gM2 Pl 2F(ς)R−1 2Kψ(ς)∇µψ∇µψ−1 2Kς∇µς∇µς−U(ψ, ς)+Sm[gµν ,Ψm] (A1) with baseline choices Kψ(ς)=1−ς2, Kς=κς>0 (constant), U(ψ, ς) = 1 2m2ψ2+1 2M2 ςς2+λcψ2ς2,(A2) and F(ς)>0 (GR recovered for F= 1). We restrict to the cT= 1 subset of Horndeski/DHOST. Baseline nonminimal coupling ansatz (unified across text and figures). F(ς) = 1 + α ς, F(a) = 1 + α ς0as, where sis the single exponent used in all figures; ς0≡ς(a=1). III. FIELD EQUATIONS (E1–E4) What is done here. We derive the dynamical equations so that the stress–energy content and nonminimal coupling are explicit. Varying (A1) with respect to gµν and the scalars gives: M2 PlF Gµν =T(m) µν +T(ψ,ς) µν +M2 Pl(∇µ∇νF−gµν□F),(E1) ∇µ(Kψ∇µψ)−U,ψ = 0,(E2) ∇µ(Kς∇µς)−U,ς +M2 Pl 2F,ς R= 0,(E3) with T(ψ,ς) µν =Kψ∇µψ∇νψ−1 2gµν∇αψ∇αψ+Kς∇µς∇νς−1 2gµν∇ας∇ας−gµν U. (E4) A line-by-line variation (including boundary terms) is provided in Appendix B. Kinetic dependences. With the baseline (A2): Kςis constant, so ˙ Kς= 0 and derivatives like Kς,ψ vanish; Kψdepends only on ς, hence ˙ Kψ=Kψ,ς ˙ςand Kψ,ψ = 0. 3 IV. BACKGROUND (B1–B4): FLRW, GR RECOVERY Goal. We now specialize to a spatially flat FLRW universe and derive the modified Friedmann system, demonstrating explicit recovery of GR+ΛCDM when ς→0. For ds2=−dt2+a2dx2and homogeneous fields: 3M2 PlFH2=ρm+ρr+ρQOS −3M2 PlH˙ F, (B1) −2M2 PlF˙ H= (ρm+pm)+(ρr+pr)+(ρQOS +pQOS) + M2 Pl(¨ F−H˙ F),(B2) with ρQOS =1 2Kψ˙ ψ2+1 2Kς˙ς2+U, pQOS =1 2Kψ˙ ψ2+1 2Kς˙ς2−U, (B0) and scalar backgrounds d dt(Kψ˙ ψ)+3HKψ˙ ψ+U,ψ = 0,(B3) d dt(Kς˙ς)+3HKς˙ς+U,ς −M2 Pl 2F,ς R= 0, R = 6(2H2+˙ H).(B4) GR limit: ς→0, F→1 ( ˙ F→0), Kψ→1, U→Λ⇒ΛCDM. V. PERTURBATIONS (P1–P3),(S1–S2) Purpose. Linear perturbations encode the testable fingerprints of QOS in CMB, LSS, and lensing. We work in Newtonian gauge, ds2=−(1 + 2Φ)dt2+a2(1 −2Ψ)dx2, with ψ=¯ ψ+δψ,ς= ¯ς+δς. Einstein constraints (explicit): −2M2 PlFk2 a2Ψ = δρm+δρr+δρQOS −3M2 PlH δ ˙ F+M2 Pl3H˙ FΦ + M2 Pl k2 a2δF, (P1) 2M2 PlF˙ Ψ + HΦ=−(ρm+pm)vm−(ρr+pr)vr−ΠQOS +1 2M2 Plδ˙ F−1 2M2 Pl ˙ FΦ,(P2) M2 PlF(Φ −Ψ) = Σ(m+r) aniso + Σ(QOS) aniso ,(P3) where δF =F′(¯ς)δς and ΠQOS, Σ(QOS) aniso follow from (E4). Scalar equations of motion (clean two-field form). Writing δϕI={δψ, δς}and using the baseline (A2) (so Kς=κς is constant and Kψ=Kψ(ς)), the linearized scalar equations are Kψδ¨ ψ+ (3HKψ+˙ Kψ)δ˙ ψ+Kψ k2 a2δψ +U,ψψ δψ +U,ψς δς =Sψ,(S1) κςδ¨ς+ 3Hκςδ˙ς+κς k2 a2δς +U,ςς −M2 Pl 2F,ςς Rδς +U,ψς δψ =Sς,(S2) where ˙ Kψ=Kψ,ς ˙ςand the source terms Sψ,ς collect the standard metric couplings ∝(Φ,Ψ) from (P1)–(P3). Cross terms proportional to Kς,ψ,Kς,ψψ, etc., vanish in the baseline because Kςis constant. 4 VI. QS LIMITS (QS0–QS2) AND GROWTH (G1) Rationale. On sub-horizon scales (k≫aH), time-derivatives of scalar perturbations are suppressed relative to spatial gradients. Eliminating (δψ, δς) algebraically in this limit yields closed forms for the modified Poisson law and slip, directly testable with LSS and lensing: Q(ς)≡MPl 2 F,ς F 1 √κς , m2 ς≡U,ςς κς ,(QS0) Geff (k, a) = GN F1 + 2Q2 1 + m2 ςa2/k2,(QS1) η(k, a) = Φ Ψ= 1−2Q2 1 + m2 ςa2/k2 1 + 2Q2 1 + m2 ςa2/k2 ,(QS2) ¨ δm+ 2H˙ δm−4πGeff (k, a)ρmδm= 0.(G1) Validity domain and interpolation. These quasi-static relations hold for k≫aH with neglected corrections of order O(aH/k)2. The limiting behavior interpolates as follows: for mςa/k ≪1 (light/long-range mode) the 2Q2 enhancement is unscreened, while for mςa/k ≫1 (heavy/short-range) the modification decouples and GR is recovered in practice. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Redshift z 0.44 0.46 0.48 0.50 0.52 f 8( z ) Growth f 8( z ) QOS (k=0.1 h/Mpc) CDM FIG. 1. Growth fσ8(z) for QOS (solid, k= 0.1hMpc−1) compared to ΛCDM (dashed). QOS uses (α, κς, ς0, s, mς, λc) = (0.05,1.0,0.02,0.5,0.1hMpc−1,10−4) and the quasi-static Geff (k, a) from (QS1) inside the growth ODE (G1). Figure 1(Growth fσ8). Within the quasi–static regime (k≫aH), the QOS model yields a modest enhancement in structure growth relative to ΛCDM at the benchmark scale k= 0.1hMpc−1. In the growth equation, the modification Geff (k, a) effectively rescales gravity, slightly increasing both the logarithmic growth rate fand the growth factor D, so the product fσ8(z) lies above the ΛCDM curve over the plotted redshift range (with the overall offset set by 5 the fσ8(0) calibration). The trend strengthens toward lower redshift as F(a) = 1 + α ς0asdeparts from unity and the coupling Q∝F,ς /F remains nonzero. When the Compton term m2 ςa2/k2is small (long–range regime), the 2Q2 contribution in Geff is less screened and the uplift is more visible; as m2 ςa2/k2grows (heavier/short–range mode or larger k), the modification decouples and the curve tends back to the ΛCDM limit. 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 Redshift z 0.99750 0.99775 0.99800 0.99825 0.99850 0.99875 0.99900 0.99925 0.99950 ( z ) = / Gravitational Slip ( z ) k = 0.05 h/Mpc k = 0.2 h/Mpc FIG. 2. Slip parameter η(z) = Φ/Ψ for two wavenumbers (k= 0.05,0.2hMpc−1) using (QS2). Benchmark parameters explicitly: (α, κς, ς0, s, mς, λc) = (0.05,1.0,0.02,0.5,0.1hMpc−1,10−4). Figure 2(Gravitational slip η). The slip parameter η(z) = Φ/Ψ remains very close to unity but shows the controlled, scale–dependent behavior characteristic of QOS in the quasi–static limit. For the chosen positive αand F,ς >0, (QS2) gives η≤1, so the deviation is a slight suppression below unity. At larger spatial scales (smaller k), screening is weaker and |η−1|is marginally larger; at smaller scales (larger k), the factor m2 ςa2/k2enhances screening and drives η→1. Together with the mild uplift of fσ8in Fig. 1, this yields a focused, falsifiable target for joint redshift–space distortion and weak–lensing analyses. VII. TENSOR SECTOR (T1–T2) Aim. Tensor perturbations probe the GW sector. From the quadratic action for transverse–traceless modes one finds equal kinetic and gradient prefactors ∝M2 PlF, ensuring luminal propagation and an extra friction term from ˙ F: ¨ hij + 3H+˙ F F!˙ hij +k2 a2hij = 0,(T1) c2 T= 1,(T2) consistent with GW170817 [17–19]. The friction ˙ F/F modifies dGW Lrelative to electromagnetic dEM L[13]. Figure 3(GW luminosity distance ratio). With luminal propagation (cT= 1) preserved, the QOS tensor sector modifies only the amplitude via an extra friction term ˙ F/F in the wave equation. This leads to a simple, model–independent relation for standard–siren distances, dGW L(z)/dEM L(z)≃pF(0)/F(z), where F(a) = 1 + α ς0as sets the evolving effective Planck mass. The plotted ratio deviates mildly from unity and grows with redshift as F(z) departs from its present–day value, providing a clean observational handle—independent of cT—to test QOS with siren Hubble diagrams and joint GW/EM standard–candle analyses. 6 0.0 0.5 1.0 1.5 2.0 Redshift z 0.00000 0.00005 0.00010 0.00015 0.00020 d GW L ( z )/ d EM L ( z ) +1 Figure 3: GW Luminosity Distance Ratio FIG. 3. Illustrative ratio dGW L(z)/dEM L(z)≈pF(0)/F(z) showing the friction effect from ˙ F/F implied by (T1) with cT= 1 (T2). All figures use the unified profile F(a) = 1 + α ς0aswith the same (α, ς0, s) as specified in Fig. 1. VIII. MAPPING TO EFT OF DARK ENERGY PARAMETERS Comparability with standard α-parameterization. Define the effective Planck mass M2 ∗≡M2 PlF(ς). Then αM≡dln M2 ∗ dln a=dln F dln a=F′(ς) F(ς) dς dln a, αT= 0,(1) and the kinetic mixing (“braiding”) is sourced by the nonminimal coupling together with the scalar kinetics; schematically one may write (schematic) αB∼F′(ς) F(ς) ˙ς HK−1,(2) where Kdenotes the appropriate combination of scalar kinetic prefactors after diagonalization. This map suffices for placing QOS on {αM, αB, αT}plots used in data analyses; the present model lives in the cT=1 subspace with αT= 0. IX. STABILITY & PPN (WITH (PPN1–PPN2)) Aim. We summarize theoretical consistency and Solar–System viability. Ghost/gradient absence follows from positivity of kinetic matrices; PPN parameters connect to Cavendish and Shapiro tests. Stability bullets: •No graviton ghost: F(ς)>0. •No scalar ghosts: Kψ>0, Kς>0. Domain note: with the baseline Kψ(ς) = 1 −ς2, the healthy domain is |ς|<1 (or else one must adjust Kψto ensure positivity). •No gradient instabilities: positive scalar sound speeds (quadratic action; Appendix B). 7 PPN: GCav ≃GN F01+2Q2 0,(PPN1) γ−1≃ − 4Q2 0 1+2Q2 0 ,(PPN2) with Solar–System limits Q2 0≪10−5unless ςis heavy [20–23]. Numerical cue: adopting |γ−1|≲2×10−5implies the explicit bound Q2 0≲5×10−6for the light-field case. X. CONSTRAINTS & VIABILITY GW170817: (T2) enforces cT=1; sirens constrain ˙ F/F [13,17]. Cosmology: CMB+BAO+SNe+fσ8test (QS1)–(G1) [1,24,25]. Laboratory/fifth–force: E¨ot–Wash, MICROSCOPE require screening or small Q0[21–23]. Parameter space: a practical benchmark is F= 1 + ας,Kς=κς, masses (m, Mς), portal λc(see figures for suggested posteriors). Cutoff and operator posture. We assume a cutoff ΛQOS high enough that higher-derivative operators are negligible on cosmological scales of interest (e.g. k≲0.2–0.3hMpc−1), ensuring that (A1)–(A2) dominate late-time dynamics. Laboratory applicability may require either (i) screening in dense environments or (ii) sufficiently small Q0and/or heavy Mςso that fifth-force effects remain below current bounds; this posture is consistent with the PPN discussion above. 0.0 0.5 1.0 1.5 2.0 Redshift z 80 100 120 140 160 180 200 H ( z ) [kms 1Mpc 1] Figure 4: Expansion History CDM QOS (illustrative) FIG. 4. Illustrative template. Expansion history comparison. ΛCDM uses (Ωm0,ΩΛ0) = (0.3,0.7). The QOS curve is a small illustrative deviation tied to F(a) (see text) to visualize potential background effects; full background fits follow from (B1)–(B4). Figure 4(Expansion history). The ΛCDM baseline adopts (Ωm0,ΩΛ0) = (0.3,0.7). The QOS curve is shown as an illustrative background deviation tied directly to the nonminimal coupling through F(a), using the minimal mapping 8 3M2 PlF(a)H2≈ρm0a−3+ρΛand hence HQOS(a)≈HΛCDM(a)/pF(a). This construction isolates the qualitative imprint of an evolving effective Planck mass on H(z) while avoiding model–dependent assumptions about additional sources or screening in the background sector; full fits follow from the complete set of background equations (B1)–(B4). 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.000000 0.000025 0.000050 0.000075 0.000100 0.000125 0.000150 0.000175 c Synthetic Posterior: ( , c ) 1 2 2 3 3 FIG. 5. Illustrative template. Synthetic 2D posterior density (contours) and samples (points) for (α, λc) centered on the benchmark (0.05,10−4). Intended as a visual template for a real MCMC; replace with data-driven contours in future work. Figure 5(Synthetic posterior). The two–dimensional posterior illustrates the expected degeneracy structure between the nonminimal–coupling amplitude αand the portal parameter λc, centered on the benchmark (0.05,10−4). Elliptical 1σ, 2σ, and 3σcontours reflect correlated constraints that typically arise when background and perturbation observables respond to both parameters in tandem. The overlaid samples are drawn from a Gaussian approximation to the likelihood and are included only as a visual template for a future data–driven MCMC; the location and widths of the contours in this figure are therefore illustrative, not derived from real datasets. Figure 6(Hydrogen–level shifts). In the small–ςregime, the fractional energy shift follows the quadratic scaling ∆En/En=C ς2with a dimensionless coefficient C=λc(1 + α/2)/p1+(Mς/m)2. For the benchmark (α, κς, λc) = (0.05,1.0,10−4) and Mς≪m, one finds C≃1.025 ×10−4, yielding a gently rising curve that quantifies the leading QOS imprint on atomic levels. This provides a clean, model–anchored scaling law to guide sensitivity estimates in precision–spectroscopy tests. 9 0.00 0.01 0.02 0.03 0.04 0.05 0.0 0.5 1.0 1.5 2.0 2.5 En / En 1e 7 Illustrative Hydrogen-Level Shifts vs. FIG. 6. Hydrogen-level fractional shift ∆En/Enin the small-ςregime for (α, κς, λc) = (0.05,1.0,10−4). We illustrate the scaling ∆En/En=C ς2with C=λc(1 + α/2)/p1 + (Mς/m)2(dimensionless; here Mς≪mso C≃1.025 ×10−4). XI. DISTINCT PREDICTIONS & TEST EQUATIONS (a) Growth fσ8:integrate (G1) for D(a) and f(a) = dln D/d ln a(Fig. 1). (b) Lensing slip: use (QS2) to forecast η(k, z) (Fig. 2). (c) GW amplitude/damping: from (T1), compare dGW Lvs. dEM L(Fig. 3). (d) Hydrogen spectral shifts: small–ςestimate ∆En/En∼C ς2+O(ς4) with model–dependent C(Appendix B; cf. [28]). (e) Spin–related hadron observables: proposed in prior QOS work (to be developed in a dedicated paper). XII. DISCUSSION Positioning and novelty. QOS, cast as an EFT, sits alongside GR+ΛCDM and scalar–tensor peers (Brans– Dicke, Horndeski, DHOST). Unlike those frameworks, the introduction of two scalars is energetically motivated by the implosive–explosive decomposition and a quantized gravitational coupling ςthat modulates the effective Planck mass while preserving cT= 1. What is testable now. The closed forms (QS1) and (QS2) enable immediate confrontation with redshift–space distortions (growth), galaxy–galaxy lensing (slip), and siren Hubble diagrams (GW damping). The background sector (B1)–(B4) permits fits to H(z) and dA(z) with Hubble–tension–sensitive forecasts (Fig. 4).