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

Quan um Omni–Syn hesis as an E ec i e Field Theo y:
Phenomenological Comple ion, Cosmological Pe u ba ions, and Cons ain s
S e alo Acha1, 2
1No h Ca olina A&T S a e Uni e si y, G eensbo o, NC, USA
2[email p o ec ed]a .edu /[email p o ec ed]
The Quan um Omni–Syn hesis (QOS) amewo k o ganizes mic ophysical and cosmological phe-
nomena as he balance o wo o hogonal ene gy channels: implosi e (g a i a ionally binding, in-
wa d) and explosi e (kine ic/elec omagne ic, ou wa d). We p esen a phenomenological comple ion
and EFT o maliza ion o QOS ha (i) p o ides he ull scala – enso ac ion wi h wo scala s
ψ, ς, (ii) de i es ield equa ions, modi ied F iedmann dynamics, and linea pe u ba ions, (iii) gi es
quasi–s a ic p edic ions o he e ec i e New on cons an Ge (k, a) and slip η(k, a), and (i ) ensu es
luminal g a i a ional–wa e speed (cT= 1) wi h modi ied damping. S abili y, pos –New onian lim-
i s, GW170817 bounds, cosmological and labo a o y cons ain s a e summa ized. Dis inc , es able
p edic ions (g ow h σ8, lensing slip, GW luminosi y dis ance, expansion his o y, hyd ogen spec al
shi s) a e highligh ed wi h igu es. All symbols a e abula ed in Appendix C; de i a ion s eps a e
in Appendix B.
Keywo ds: Quan um Omni-Syn hesis (QOS); e ec i e ield heo y; scala – enso g a i y; quasi-s a ic limi s;
Ge (k, a); g a i a ional slip η; GW damping; PPN cons ain s; cosmology.
2
I. INTRODUCTION
The Quan um Omni–Syn hesis (QOS) model pos ula es ha physical eali y a ises om he dynamic balance
be ween wo o hogonal ene gy channels: implosi e ene gy, associa ed wi h inwa d con ac ion and g a i a ional
binding, and explosi e ene gy, associa ed wi h ou wa d expansion, kine ic deg ees o eedom, and elec omagne ic
exci a ions. P e ious s udies ha e de eloped he heo e ical ounda ions o his idea, p oposed a modi ied ene gy–
momen um ela ion, and explo ed implica ions o quan um spin, qua k dynamics, and obse a ional consis ency.
In his s udy, we ad ance QOS in o a phenomenological e ec i e ield heo y (EFT). By embedding he implosi e–
explosi e p inciple in o a scala – enso amewo k, we p o ide a consis en ac ion, ield equa ions, cosmological pe -
u ba ions, and empi ical cons ain s. This ea men a oids duplica ion o ea lie wo ks by ocusing exclusi ely on
EFT o maliza ion and da a–o ien ed p edic ions. Fo con en ional con ex , ΛCDM succeeds empi ically ye lea es
da k componen s unexplained [1,2]; scala – enso amewo ks such as B ans–Dicke [3,4], Ho ndeski/beyond [5–7]
and DHOST [8] p o ide lexible, es able baselines (see e iews [9–14]).
II. ACTION (A1–A2): DEFINITIONS OF F, Kψ, Kς, U
Scope and mo i a ion. An EFT is de ined by i s deg ees o eedom, symme ies, and ope a o hie a chy. QOS
in oduces wo scala s: ψ(encoding ene ge ic con en in he implosi e–explosi e spli ) and ς(a quan ized g a i y–
coupling ha modula es he e ec i e Planck mass). We wo k in he Jo dan ame so ma e ollows geodesics o
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)
wi h baseline choices
Kψ(ς)=1−ς2, Kς=κς>0 (cons an ), U(ψ, ς) = 1
2m2ψ2+1
2M2
ςς2+λcψ2ς2,(A2)
and F(ς)>0 (GR eco e ed o F= 1). We es ic o he cT= 1 subse o Ho ndeski/DHOST.
Baseline nonminimal coupling ansa z (uni ied ac oss ex and igu es).
F(ς) = 1 + α ς, F(a) = 1 + α ς0as,
whe e sis he single exponen used in all igu es; ς0≡ς(a=1).
III. FIELD EQUATIONS (E1–E4)
Wha is done he e. We de i e he dynamical equa ions so ha he s ess–ene gy con en and nonminimal
coupling a e explici . Va ying (A1) wi h espec o gµν and he scala s gi es:
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)
wi h
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 a ia ion (including bounda y e ms) is p o ided in Appendix B.
Kine ic dependences. Wi h he baseline (A2): Kςis cons an , so ˙
Kς= 0 and de i a i es like Kς,ψ anish; Kψdepends
only on ς, hence ˙
Kψ=Kψ,ς ˙ςand Kψ,ψ = 0.
3
IV. BACKGROUND (B1–B4): FLRW, GR RECOVERY
Goal. We now specialize o a spa ially la FLRW uni e se and de i e he modi ied F iedmann sys em, demon-
s a ing explici eco e y o GR+ΛCDM when ς→0.
Fo ds2=−d 2+a2dx2and homogeneous ields:
3M2
PlFH2=ρm+ρ +ρQOS −3M2
PlH˙
F, (B1)
−2M2
PlF˙
H= (ρm+pm)+(ρ +p )+(ρQOS +pQOS) + M2
Pl(¨
F−H˙
F),(B2)
wi h
ρQOS =1
2Kψ˙
ψ2+1
2Kς˙ς2+U, pQOS =1
2Kψ˙
ψ2+1
2Kς˙ς2−U, (B0)
and scala backg ounds
d
d (Kψ˙
ψ)+3HKψ˙
ψ+U,ψ = 0,(B3)
d
d (Kς˙ς)+3HKς˙ς+U,ς −M2
Pl
2F,ς R= 0, R = 6(2H2+˙
H).(B4)
GR limi : ς→0, F→1 ( ˙
F→0), Kψ→1, U→Λ⇒ΛCDM.
V. PERTURBATIONS (P1–P3),(S1–S2)
Pu pose. Linea pe u ba ions encode he es able inge p in s o QOS in CMB, LSS, and lensing. We wo k in
New onian gauge, ds2=−(1 + 2Φ)d 2+a2(1 −2Ψ)dx2, wi h ψ=¯
ψ+δψ,ς= ¯ς+δς.
Eins ein cons ain s (explici ):
−2M2
PlFk2
a2Ψ = δρm+δρ +δρQOS −3M2
PlH δ ˙
F+M2
Pl3H˙
FΦ + M2
Pl
k2
a2δF, (P1)
2M2
PlF˙
Ψ + HΦ=−(ρm+pm) m−(ρ +p ) −ΠQOS +1
2M2
Plδ˙
F−1
2M2
Pl ˙
FΦ,(P2)
M2
PlF(Φ −Ψ) = Σ(m+ )
aniso + Σ(QOS)
aniso ,(P3)
whe e δF =F′(¯ς)δς and ΠQOS, Σ(QOS)
aniso ollow om (E4).
Scala equa ions o mo ion (clean wo- ield o m). W i ing δϕI={δψ, δς}and using he baseline (A2) (so Kς=κς
is cons an and Kψ=Kψ(ς)), he linea ized scala equa ions a e
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)
whe e ˙
Kψ=Kψ,ς ˙ςand he sou ce e ms Sψ,ς collec he s anda d me ic couplings ∝(Φ,Ψ) om (P1)–(P3). C oss
e ms p opo ional o Kς,ψ,Kς,ψψ, e c., anish in he baseline because Kςis cons an .
4
VI. QS LIMITS (QS0–QS2) AND GROWTH (G1)
Ra ionale. On sub-ho izon scales (k≫aH), ime-de i a i es o scala pe u ba ions a e supp essed ela i e o
spa ial g adien s. Elimina ing (δψ, δς) algeb aically in his limi yields closed o ms o he modi ied Poisson law and
slip, di ec ly es able wi h LSS and lensing:
Q(ς)≡MPl
2
F,ς
F
1
√κς
, m2
ς≡U,ςς
κς
,(QS0)
Ge (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−4πGe (k, a)ρmδm= 0.(G1)
Validi y domain and in e pola ion. These quasi-s a ic ela ions hold o k≫aH wi h neglec ed co ec ions o
o de O(aH/k)2. The limi ing beha io in e pola es as ollows: o mςa/k ≪1 (ligh /long- ange mode) he 2Q2
enhancemen is unsc eened, while o mςa/k ≫1 (hea y/sho - ange) he modi ica ion decouples and GR is eco e ed
in p ac ice.
0.0 0.1 0.2 0.3 0.4 0.5 0.6
Redshi z
0.44
0.46
0.48
0.50
0.52
8(
z
)
G ow h
8(
z
)
QOS (k=0.1 h/Mpc)
CDM
FIG. 1. G ow h σ8(z) o QOS (solid, k= 0.1hMpc−1) compa ed o ΛCDM (dashed). QOS uses (α, κς, ς0, s, mς, λc) =
(0.05,1.0,0.02,0.5,0.1hMpc−1,10−4) and he quasi-s a ic Ge (k, a) om (QS1) inside he g ow h ODE (G1).
Figu e 1(G ow h σ8). Wi hin he quasi–s a ic egime (k≫aH), he QOS model yields a modes enhancemen in
s uc u e g ow h ela i e o ΛCDM a he benchma k scale k= 0.1hMpc−1. In he g ow h equa ion, he modi ica ion
Ge (k, a) e ec i ely escales g a i y, sligh ly inc easing bo h he loga i hmic g ow h a e and he g ow h ac o D,
so he p oduc σ8(z) lies abo e he ΛCDM cu e o e he plo ed edshi ange (wi h he o e all o se se by
5
he σ8(0) calib a ion). The end s eng hens owa d lowe edshi as F(a) = 1 + α ς0asdepa s om uni y and
he coupling Q∝F,ς /F emains nonze o. When he Comp on e m m2
ςa2/k2is small (long– ange egime), he 2Q2
con ibu ion in Ge is less sc eened and he upli is mo e isible; as m2
ςa2/k2g ows (hea ie /sho – ange mode o
la ge k), he modi ica ion decouples and he cu e ends back o he ΛCDM limi .
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00
Redshi z
0.99750
0.99775
0.99800
0.99825
0.99850
0.99875
0.99900
0.99925
0.99950
(
z
) = /
G a i a ional Slip (
z
)
k = 0.05 h/Mpc
k = 0.2 h/Mpc
FIG. 2. Slip pa ame e η(z) = Φ/Ψ o wo wa enumbe s (k= 0.05,0.2hMpc−1) using (QS2). Benchma k pa ame e s
explici ly: (α, κς, ς0, s, mς, λc) = (0.05,1.0,0.02,0.5,0.1hMpc−1,10−4).
Figu e 2(G a i a ional slip η). The slip pa ame e η(z) = Φ/Ψ emains e y close o uni y bu shows he
con olled, scale–dependen beha io cha ac e is ic o QOS in he quasi–s a ic limi . Fo he chosen posi i e αand
F,ς >0, (QS2) gi es η≤1, so he de ia ion is a sligh supp ession below uni y. A la ge spa ial scales (smalle k),
sc eening is weake and |η−1|is ma ginally la ge ; a smalle scales (la ge k), he ac o m2
ςa2/k2enhances sc eening
and d i es η→1. Toge he wi h he mild upli o σ8in Fig. 1, his yields a ocused, alsi iable a ge o join
edshi –space dis o ion and weak–lensing analyses.
VII. TENSOR SECTOR (T1–T2)
Aim. Tenso pe u ba ions p obe he GW sec o . F om he quad a ic ac ion o ans e se– aceless modes one
inds equal kine ic and g adien p e ac o s ∝M2
PlF, ensu ing luminal p opaga ion and an ex a ic ion e m om ˙
F:
¨
hij + 3H+˙
F
F!˙
hij +k2
a2hij = 0,(T1)
c2
T= 1,(T2)
consis en wi h GW170817 [17–19]. The ic ion ˙
F/F modi ies dGW
L ela i e o elec omagne ic dEM
L[13].
Figu e 3(GW luminosi y dis ance a io). Wi h luminal p opaga ion (cT= 1) p ese ed, he QOS enso
sec o modi ies only he ampli ude ia an ex a ic ion e m ˙
F/F in he wa e equa ion. This leads o a simple,
model–independen ela ion o s anda d–si en dis ances, dGW
L(z)/dEM
L(z)≃pF(0)/F(z), whe e F(a) = 1 + α ς0as
se s he e ol ing e ec i e Planck mass. The plo ed a io de ia es mildly om uni y and g ows wi h edshi as F(z)
depa s om i s p esen –day alue, p o iding a clean obse a ional handle—independen o cT— o es QOS wi h
si en Hubble diag ams and join GW/EM s anda d–candle analyses.

6
0.0 0.5 1.0 1.5 2.0
Redshi
z
0.00000
0.00005
0.00010
0.00015
0.00020
d
GW
L
(
z
)/
d
EM
L
(
z
)
+1
Figu e 3: GW Luminosi y Dis ance Ra io
FIG. 3. Illus a i e a io dGW
L(z)/dEM
L(z)≈pF(0)/F(z) showing he ic ion e ec om ˙
F/F implied by (T1) wi h cT= 1
(T2). All igu es use he uni ied p o ile F(a) = 1 + α ς0aswi h he same (α, ς0, s) as speci ied in Fig. 1.
VIII. MAPPING TO EFT OF DARK ENERGY PARAMETERS
Compa abili y wi h s anda d α-pa ame e iza ion. De ine he e ec i e 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 he kine ic mixing (“b aiding”) is sou ced by he nonminimal coupling oge he wi h he scala kine ics; schema -
ically one may w i e
(schema ic) αB∼F′(ς)
F(ς)
˙ς
HK−1,(2)
whe e Kdeno es he app op ia e combina ion o scala kine ic p e ac o s a e diagonaliza ion. This map su ices o
placing QOS on {αM, αB, αT}plo s used in da a analyses; he p esen model li es in he cT=1 subspace wi h αT= 0.
IX. STABILITY & PPN (WITH (PPN1–PPN2))
Aim. We summa ize heo e ical consis ency and Sola –Sys em iabili y. Ghos /g adien absence ollows om
posi i i y o kine ic ma ices; PPN pa ame e s connec o Ca endish and Shapi o es s.
S abili y bulle s:
•No g a i on ghos : F(ς)>0.
•No scala ghos s: Kψ>0, Kς>0. Domain no e: wi h he baseline Kψ(ς) = 1 −ς2, he heal hy domain is |ς|<1
(o else one mus adjus Kψ o ensu e posi i i y).
•No g adien ins abili ies: posi i e scala sound speeds (quad a ic ac ion; Appendix B).
7
PPN:
GCa ≃GN
F01+2Q2
0,(PPN1)
γ−1≃ − 4Q2
0
1+2Q2
0
,(PPN2)
wi h Sola –Sys em limi s Q2
0≪10−5unless ςis hea y [20–23]. Nume ical cue: adop ing |γ−1|≲2×10−5implies
he explici bound Q2
0≲5×10−6 o he ligh - ield case.
X. CONSTRAINTS & VIABILITY
GW170817: (T2) en o ces cT=1; si ens cons ain ˙
F/F [13,17].
Cosmology: CMB+BAO+SNe+ σ8 es (QS1)–(G1) [1,24,25].
Labo a o y/ i h– o ce: E¨o –Wash, MICROSCOPE equi e sc eening o small Q0[21–23].
Pa ame e space: a p ac ical benchma k is F= 1 + ας,Kς=κς, masses (m, Mς), po al λc(see igu es o
sugges ed pos e io s).
Cu o and ope a o pos u e. We assume a cu o ΛQOS high enough ha highe -de i a i e ope a o s a e negligible
on cosmological scales o in e es (e.g. k≲0.2–0.3hMpc−1), ensu ing ha (A1)–(A2) domina e la e- ime dynamics.
Labo a o y applicabili y may equi e ei he (i) sc eening in dense en i onmen s o (ii) su icien ly small Q0and/o
hea y Mςso ha i h- o ce e ec s emain below cu en bounds; his pos u e is consis en wi h he PPN discussion
abo e.
0.0 0.5 1.0 1.5 2.0
Redshi
z
80
100
120
140
160
180
200
H
(
z
) [kms 1Mpc 1]
Figu e 4: Expansion His o y
CDM
QOS (illus a i e)
FIG. 4. Illus a i e empla e. Expansion his o y compa ison. ΛCDM uses (Ωm0,ΩΛ0) = (0.3,0.7). The QOS cu e is a
small illus a i e de ia ion ied o F(a) (see ex ) o isualize po en ial backg ound e ec s; ull backg ound i s ollow om
(B1)–(B4).
Figu e 4(Expansion his o y). The ΛCDM baseline adop s (Ωm0,ΩΛ0) = (0.3,0.7). The QOS cu e is shown as an
illus a i e backg ound de ia ion ied di ec ly o he nonminimal coupling h ough F(a), using he minimal mapping
8
3M2
PlF(a)H2≈ρm0a−3+ρΛand hence HQOS(a)≈HΛCDM(a)/pF(a). This cons uc ion isola es he quali a i e
imp in o an e ol ing e ec i e Planck mass on H(z) while a oiding model–dependen assump ions abou addi ional
sou ces o sc eening in he backg ound sec o ; ull i s ollow om he comple e se o backg ound equa ions (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
Syn he ic Pos e io : ( ,
c
)
1
2
2
3
3
FIG. 5. Illus a i e empla e. Syn he ic 2D pos e io densi y (con ou s) and samples (poin s) o (α, λc) cen e ed on he
benchma k (0.05,10−4). In ended as a isual empla e o a eal MCMC; eplace wi h da a-d i en con ou s in u u e wo k.
Figu e 5(Syn he ic pos e io ). The wo–dimensional pos e io illus a es he expec ed degene acy s uc u e
be ween he nonminimal–coupling ampli ude αand he po al pa ame e λc, cen e ed on he benchma k (0.05,10−4).
Ellip ical 1σ, 2σ, and 3σcon ou s e lec co ela ed cons ain s ha ypically a ise when backg ound and pe u ba ion
obse ables espond o bo h pa ame e s in andem. The o e laid samples a e d awn om a Gaussian app oxima ion
o he likelihood and a e included only as a isual empla e o a u u e da a–d i en MCMC; he loca ion and wid hs
o he con ou s in his igu e a e he e o e illus a i e, no de i ed om eal da ase s.
Figu e 6(Hyd ogen–le el shi s). In he small–ς egime, he ac ional ene gy shi ollows he quad a ic scaling
∆En/En=C ς2wi h a dimensionless coe icien C=λc(1 + α/2)/p1+(Mς/m)2. Fo he benchma k (α, κς, λc) =
(0.05,1.0,10−4) and Mς≪m, one inds C≃1.025 ×10−4, yielding a gen ly ising cu e ha quan i ies he leading
QOS imp in on a omic le els. This p o ides a clean, model–ancho ed scaling law o guide sensi i i y es ima es in
p ecision–spec oscopy es s.
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
Illus a i e Hyd ogen-Le el Shi s s.
FIG. 6. Hyd ogen-le el ac ional shi ∆En/Enin he small-ς egime o (α, κς, λc) = (0.05,1.0,10−4). We illus a e he
scaling ∆En/En=C ς2wi h C=λc(1 + α/2)/p1 + (Mς/m)2(dimensionless; he e Mς≪mso C≃1.025 ×10−4).
XI. DISTINCT PREDICTIONS & TEST EQUATIONS
(a) G ow h σ8:in eg a e (G1) o D(a) and (a) = dln D/d ln a(Fig. 1).
(b) Lensing slip: use (QS2) o o ecas η(k, z) (Fig. 2).
(c) GW ampli ude/damping: om (T1), compa e dGW
L s. dEM
L(Fig. 3).
(d) Hyd ogen spec al shi s: small–ςes ima e ∆En/En∼C ς2+O(ς4) wi h model–dependen C(Appendix B;
c . [28]).
(e) Spin– ela ed had on obse ables: p oposed in p io QOS wo k ( o be de eloped in a dedica ed pape ).
XII. DISCUSSION
Posi ioning and no el y. QOS, cas as an EFT, si s alongside GR+ΛCDM and scala – enso pee s (B ans–
Dicke, Ho ndeski, DHOST). Unlike hose amewo ks, he in oduc ion o wo scala s is ene ge ically mo i a ed by
he implosi e–explosi e decomposi ion and a quan ized g a i a ional coupling ς ha modula es he e ec i e Planck
mass while p ese ing cT= 1.
Wha is es able now. The closed o ms (QS1) and (QS2) enable immedia e con on a ion wi h edshi –space
dis o ions (g ow h), galaxy–galaxy lensing (slip), and si en Hubble diag ams (GW damping). The backg ound sec o
(B1)–(B4) pe mi s i s o H(z) and dA(z) wi h Hubble– ension–sensi i e o ecas s (Fig. 4).