Time-Va ying Scala Mass in uDRD:
Alle ia ing JWST High-Redshi Galaxy
Anomalies
Wi h Subs an ial Na owing o he H0Tension and Tes able S8P edic ions
E. W. Maina
No embe 5, 2025
Final Submission Ve sion
Abs ac
We ex end he uni ied Dimensional Resonance Dynamics (uDRD) amewo k by
p omo ing he scala ield mass mϕ om a cons an o a ime-dependen pa ame e :
m2
ϕ(a) = m2
0·a−γ, whe e γis a dimensionless exponen con olling he e olu ion a e.
This single modi ica ion p ese es all es ablished successes o uDRD (Sola Sys em
sc eening, galaxy o a ion cu es, clus e phenomenology, cosmological EFT compli-
ance) while add essing c i ical obse a ional ensions in he ea ly uni e se. When
γ= 0, he model educes o s anda d uDRD; o γ > 0, he ϕ- ield’s ene gy densi y
scales as ρϕ∝a−(3+γ), p o iding enhanced g a i a ional suppo a high edshi . We
de i e his scaling igo ously om oscilla ing scala ield dynamics in cu ed space ime.
Fo a benchma k alue γ= 0.05—selec ed o balance obse a ional imp o emen s
agains Big Bang Nucleosyn hesis cons ain s—we p edic : (1) app oxima ely 14%
mo e e ec i e da k ma e a z= 12, enabling 20% mo e massi e halos ha pa ially
alle ia e ( hough do no ully esol e) he JWST “ oo-ea ly” galaxy anomaly; (2) a ∼4–
5% educ ion in he sound ho izon s, inc easing he CMB-in e ed Hubble cons an
om 67.4 o app oxima ely 70–71 km s−1Mpc−1, he eby subs an ially na owing he
H0 ension om ∼5.6σ o ∼2–3σ; (3) a ∼6% inc ease in σ8due o enhanced s uc u e
g ow h, po en ially wo sening he S8 ension by ∼1σ. The enhanced ea ly-uni e se
ene gy densi y has negligible impac on Big Bang Nucleosyn hesis (∆Ne ≪0.01),
lea ing his mechanism uncons ained by p imo dial abundance measu emen s. All
p edic ions a e immedia ely alsi iable wi h cu en da a om JWST, Planck, DESI,
and eROSITA. We discuss degene acies wi h ea ly da k ene gy models and p o ide c i-
e ia o dis inguish scena ios based on pe sis en la e- ime e ec s in s uc u e o ma ion
and oid lensing.
1
1 In oduc ion
1.1 Mo i a ion: New ensions in he ea ly uni e se
The uni ied Dimensional Resonance Dynamics (uDRD) amewo k [1] was de eloped o p o-
ide a c oss-scale desc ip ion o g a i a ional phenomena om quan um scales ( m) o cos-
mological dis ances (Gpc), using a wo- ield geome ic ex ension o Gene al Rela i i y. The
heo y success ully add esses mul iple obse a ional challenges: i ep oduces galaxy o a-
ion cu es and he adial accele a ion ela ion (RAR) wi h a single pa ame e η, explains
colliding clus e phenomenology (Bulle Clus e , MACS J0025, Abell 520) h ough a sha ed
ampli ude A(a) wi hou pe -sys em e uning, main ains Sola Sys em compliance wi h ma -
gins o de s o magni ude below Cassini/LLR bounds, and in eg a es in o he E ec i e Field
Theo y o Da k Ene gy (EFT-o -DE) wi h luminal enso p opaga ion (αT= 0).
Howe e , wo c i ical obse a ional ensions ha e in ensi ied in ecen yea s:
JWST high- edshi galaxy anomalies. The James Webb Space Telescope (JWST) has
e ealed an unexpec edly high abundance o massi e, luminous galaxies a edshi s z≳10
o 15 [2, 3, 4]. Obse a ions om he JADES, CEERS, and GLASS su eys show galaxies
wi h s ella masses M∗∼1010 o 1011 M⊙a cosmic ages ≲500 My , appea ing “ oo
massi e, oo ea ly” ela i e o ΛCDM p edic ions. The cumula i e numbe densi y o hese
objec s exceeds ΛCDM expec a ions by ac o s o 3 o 10, depending on mass h eshold
and edshi bin [4]. While sys ema ic unce ain ies in s ella popula ion syn hesis and
pho ome ic edshi s emain unde in es iga ion, he ension appea s obus ac oss mul iple
su eys and selec ion me hods.
The H0 ension. The Hubble cons an measu ed om he cosmic mic owa e backg ound
(CMB) and ba yon acous ic oscilla ions (BAO) yields HCMB
0= 67.4±0.5 km s−1Mpc−1[5],
while local dis ance ladde measu emen s gi e Hlocal
0= 73.0±1.0 km s−1Mpc−1[6]. This
∼5.6σdisc epancy pe sis s despi e ex ensi e sc u iny o sys ema ic unce ain ies in bo h
app oaches.
1.2 The uDRD-e ol ed ex ension
We ex end uDRD by in oducing a single new pa ame e γ ha con ols he ime e olu ion
o he ϕ- ield’s mass:
m2
ϕ(a) = m2
0·a−γ,(1)
whe e m0is he p esen -day (a= 1) mass scale and γis a dimensionless exponen .
Enhanced ea ly-uni e se densi y. Fo γ > 0, he ϕ- ield was dense in he pas . A a
gi en edshi z, he ene gy densi y a io ela i e o s anda d CDM is
R(z)≡ρϕ,e ol ed(z)
ρϕ,s anda d(z)= (1 + z)γ.(2)
2
A z= 12 (a key JWST edshi ) wi h γ= 0.05, we ob ain R= (13)0.05 ≈1.14: he
ϕ- ield p o ides app oxima ely 14% mo e g a i a ional suppo han in s anda d uDRD o
ΛCDM. We adop γ= 0.05 as ou benchma k alue, chosen o balance JWST imp o emen s
agains po en ial cons ain s om p imo dial nucleosyn hesis ( hough as shown in Sec. 3.5,
he model is ac ually uncons ained by BBN).
Theo e ical jus i ica ion. The ansa z (1) ep esen s he phenomenological explo a ion
o a well-es ablished heo e ical mechanism. In quan um ield heo y on cu ed space ime,
scala ield masses gene ically acqui e cu a u e-dependen co ec ions h ough non-minimal
coupling o he Ricci scala :
m2
e =m2
0+ξ R, (3)
whe e ξis a dimensionless coupling cons an and Ris he Ricci scala . On a F iedmann-
Lemaˆı e-Robe son-Walke (FRW) backg ound, R= 6(2H2+˙
H). Fo a ma e -domina ed
uni e se, H∝a−3/2, gi ing R∝a−3, which na u ally induces powe -law unning o he
e ec i e mass. The pa ame e γis he e o e he measu ed s eng h o his undamen al,
expec ed e ec .
2 Theo y: De i a ion om Fi s P inciples
2.1 The oscilla ing egime and ma e -like beha io
When he ield oscilla es (H < mϕ(a)), he ime-a e aged ield ampli ude ⟨¯
ϕ2⟩dilu es as
a−3 o ensu e he o al ene gy densi y beha es as p essu eless dus . Howe e , he po en ial
ene gy densi y now includes he ime- a ying mass:
ρϕ(a)≈m2
ϕ(a)· ⟨¯
ϕ2(a)⟩ ∝ a−γ·a−3=a−(3+γ).(4)
This is he cen al esul : he ϕ- ield’s ene gy densi y scales as a−(3+γ), no a−3.
2.2 Modi ied F iedmann equa ion
The modi ied Hubble pa ame e is:
H2(a) = H2
0Ω ,0a−4+ Ωb,0a−3+ Ωϕ,0a−(3+γ)+ ΩDE(a).(5)
The e m Ωϕ,0a−(3+γ) eplaces he s anda d CDM e m and is he sou ce o all phe-
nomenological di e ences.
3 Quan i a i e Obse able P edic ions
3.1 CMB acous ic scale and subs an ial na owing o he H0 en-
sion
Physical mechanism. The sound ho izon a he d ag epoch (z∗≈1090) is
s=Za∗
0
cs(a)da
a2H(a),(6)
3
whe e cs=c/p3(1 + 3ρb/(4ργ)) is he sound speed in he pho on-ba yon luid. Fo γ > 0,
he ac o a−(3+γ)makes H(a)la ge a ea ly imes compa ed o s anda d CDM scaling a−3.
A la ge Hin he in eg and yields a smalle s.
CMB angula scale cons ain . The angula acous ic scale measu ed by Planck is
θ∗= s
DA(z∗),(7)
whe e DA(z∗) is he angula diame e dis ance o ecombina ion. Since θ∗is igh ly con-
s ained (∆θ∗/θ∗∼10−4), a smalle smus be compensa ed by a smalle DA, implying a
la ge in e ed H0when i ing he CMB da a.
Quan i a i e calcula ion. Nume ical in eg a ion o (6) using Planck 2018 cosmological
pa ame e s yields:
LCDM
s≈144.4 Mpc,(8)
e ol ed
s≈138.2 Mpc (γ= 0.05),(9)
ep esen ing a 4.3% educ ion. To ma ch he ixed CMB angula scale θ∗, his implies an
in e ed Hubble cons an o
HCMB,in e ed
0= 67.4×144.4
138.2≈70.4 km s−1Mpc−1.(10)
Subs an ial na owing o he H0 ension. The CMB-in e ed alue (10) ep esen s
a signi ican imp o emen o e he ΛCDM p edic ion. The ension is educed om ap-
p oxima ely 5.6σ(di e ence o 5.6 km s−1Mpc−1) in s anda d ΛCDM o app oxima ely 2.6σ
(di e ence o 2.6 km s−1Mpc−1) in uDRD-e ol ed wi h γ= 0.05. This ep esen s a ∼50%
educ ion in he disc epancy—a subs an ial imp o emen ha b ings he ea ly-uni e se and
la e- ime measu emen s in o much be e ag eemen , hough no comple e esolu ion.
Impo an ly, his imp o emen a ises na u ally om he heo e ically mo i a ed ime-
a ying mass mechanism, wi hou ine- uning o adding new phenomenological pa ame e s
beyond he single exponen γ.
La e- ime measu emen s emain una ec ed. La e- ime p obes (SNe Ia, Cepheids,
TRGB) measu e H0a z∼0–2, whe e he co ec ion (1 + z)γis modes . Fo γ= 0.05
and z= 1, he enhancemen is only 20.05 ≈1.035, ansla ing o ∼1.7% e ec on Hand
negligible shi in H0compa ed o obse a ional unce ain ies.
3.2 JWST galaxy abundance a z≳10: Pa ial alle ia ion
Enhanced ma e densi y. In uDRD-e ol ed, he mean ma e densi y a high zis
¯ρϕ(z) = ¯ρϕ,0(1 + z)3+γ.(11)
Fo γ= 0.05 and z= 12, he densi y enhancemen is R(12) = 130.05 ≈1.14.
4
Halo mass unc ion scaling. The cumula i e numbe densi y o halos scales app oxi-
ma ely as
N(> M h, z)∝¯ρ3/2
ϕ(z)∝(1 + z)(9+3γ)/2.(12)
A z= 12 wi h γ= 0.05: Ne ol ed
NΛCDM
= (13)0.075 ≈1.21.(13)
Pa ial alle ia ion o JWST anomalies. Fo mass h eshold M h = 1010 M⊙, uDRD-
e ol ed wi h γ= 0.05 p edic s app oxima ely 20% mo e massi e halos a z= 10–15 han
ΛCDM. This pa ially alle ia es he JWST obse a ions, which show ac o o 3–10 excesses
depending on mass and edshi bin. The model accoun s o a modes ac ion o he disc ep-
ancy, po en ially mo e i sys ema ic unce ain ies in s ella mass es ima es o pho ome ic
edshi s educe he epo ed excess. Al e na i ely, a la ge alue γ∼0.1–0.15 would mo e
ully add ess he JWST anomaly bu a he cos o inc eased ension wi h S8measu emen s
(see Sec. 3.5).
3.3 S uc u e g ow h a e (z)
The s uc u e g ow h a e is
(z)≡dln D
dln a,(14)
whe e D(z) is he linea g ow h ac o .
Fo γ= 0.05, we p edic modes enhancemen s:
Redshi z ΛCDM(z) e ol ed(z) Ra io
0.5 0.75 0.756 1.008
1.0 0.82 0.830 1.012
2.0 0.88 0.895 1.017
The 1–2% enhancemen is po en ially measu able wi h upcoming DESI BAO+RSD mea-
su emen s.
3.4 Clus e abundance e olu ion
Fo γ= 0.05 and z= 1.5, he densi y enhancemen is R(1.5) = (2.5)0.05 ≈1.047. The
cumula i e numbe densi y o clus e s scales as ¯ρ3/2
m, gi ing
Ne ol ed(> M, z = 1.5)
NΛCDM(> M, z = 1.5) ≈(1.047)3/2≈1.07.(15)
This ∼7% enhancemen a z= 1.5 is measu able wi h upcoming eROSITA and SPT-3G
su eys.
5
3.5 BBN cons ain s and he S8 ension
BBN: No signi ican cons ain . A common conce n wi h enhanced ea ly-uni e se en-
e gy densi y is he impac on Big Bang Nucleosyn hesis h ough he e ec i e numbe o
ela i is ic species ∆Ne . Howe e , he ϕ- ield in uDRD-e ol ed beha es as ma e (w= 0),
no adia ion (w= 1/3), h oughou he BBN epoch.
A he BBN edshi zBBN ∼108–1010 (co esponding o empe a u es T∼0.01–10 MeV),
he enhancemen ac o is R= (1 + zBBN)γ. Fo γ= 0.05 and zBBN ∼109:
R(109) = (109)0.05 ≈2.5.(16)
Howe e , his enhanced ma e densi y con ibu es o he Hubble a e as
H2∝ρ +ρm⇒∆H
H≈1
2
∆ρm
ρ +ρm
.(17)
A BBN, adia ion domina es: ρ ≫ρm. The ac ional change in His
∆H
H∼1
2
Ωm
Ω
aBBN (R−1) ∼1
2×6×10−10 ×1.5∼5×10−10,(18)
which is u e ly negligible. The co esponding ∆Ne (which measu es he de ia ion in adi-
a ion con en ) is
∆Ne ∼∆H
H2
≪0.01,(19)
well below he obse a ional bound ∆Ne <0.3 om p imo dial deu e ium and helium
abundances [5].
Conclusion: The uDRD-e ol ed ex ension wi h γ= 0.05 is comple ely uncons ained
by BBN measu emen s. This is a signi ican s eng h o he model, as i a oids he igh
cons ain s ha plague many ea ly-uni e se modi ica ions.
S8 ension: A es able ade-o . Enhanced ea ly-uni e se s uc u e g ow h inc eases
he ampli ude o ma e luc ua ions σ8a la e imes. The g ow h ac o D(z) sa is ies a
modi ied equa ion wi h enhanced sou ce e m p opo ional o Ωm(a)∝a−(3+γ). In eg a ing
om high edshi o oday, he cumula i e e ec is app oxima ely
σ8,e ol ed
σ8,LCDM
≈Ωm,e ol ed(z∼10)
Ωm,LCDM(z∼10) 1/2
≈(1 + z)γ/2z∼10
≈1.06.(20)
Fo γ= 0.05, his ep esen s a ∼6% inc ease in σ8. Cu en measu emen s show a mild
S8 ension: Planck CMB gi es S8=σ8pΩm/0.3 = 0.834±0.016, while weak lensing su eys
(DES, KiDS) yield S8≈0.77±0.02—a ∼2.5σdisc epancy. Boos ing σ8by 6% would wo sen
his ension o app oxima ely 3.5σ.
6
The ade-o assessmen . The uDRD-e ol ed ex ension p esen s a clea ade-o :
Successes: Subs an ially na ows he H0 ension ( om 5.6σ o 2.6σ, a ∼50% educ-
ion) and pa ially alle ia es JWST high- edshi galaxy anomalies.
Cos : Po en ially wo sens he S8 ension by ∼1σ.
BBN: No cons ain — he model is sa e o all γ≲0.2.
This is a es able p edic ion, no a a al law. I u u e DESI Yea -5, Euclid, o LSST
measu emen s show S8 alues highe han cu en weak lensing es ima es (close o he
Planck alue), he model is indica ed. I S8 emains pe sis en ly low, γ < 0.03 is equi ed,
educing (bu no elimina ing) he model’s explana o y powe o JWST and H0.
3.6 Summa y o p edic ions
Obse able ΛCDM uDRD-e ol ed (γ= 0.05) Ra io Su ey
HCMB
0[km/s/Mpc] 67.4 70.4 1.045 Planck/ACT
H0 ension 5.6σ2.6σ0.46 —
N(M > 1010M⊙, z = 12) n01.21 n01.21 JWST JADES
(z= 1) 0.82 0.830 1.012 DESI/Euclid
σ8( oday) 0.811 0.860 1.060 Planck+LSS
Nclus e (z= 1.5) ncl 1.07 ncl 1.07 eROSITA/SPT
Table 1: Summa y o quan i a i e p edic ions o uDRD-e ol ed wi h γ= 0.05 compa ed o
ΛCDM. The model subs an ially na ows he H0 ension by ∼50% and pa ially alle ia es
JWST high- edshi galaxy anomalies, a he cos o a modes 6% inc ease in σ8 ha may
wo sen he S8 ension. C ucially, he model is uncons ained by BBN. All p edic ions a e
alsi iable wi h cu en o nea - e m da a.
4 Discussion
4.1 Degene acies wi h ea ly da k ene gy
uDRD-e ol ed mimics ea ly da k ene gy (EDE) in boos ing ea ly H(z), bu di e s unda-
men ally in i s equa ion o s a e and pe sis ence. EDE models ypically in oke a luid o
scala ield wi h w≈1/3–1 ha ac i a es be o e ecombina ion and dilu es apidly as a−4o
as e pos - ecombina ion. In con as , he uDRD ϕ- ield is p essu eless (w= 0) oscilla ing
da k ma e wi h pe sis en a−(3+γ)scaling ha a ec s la e- ime obse ables.
Dis inguishing signa u es:
S uc u e g ow h: EDE esol es H0wi hou signi ican ly boos ing la e- ime σ8;
uDRD-e ol ed boos s bo h, wo sening S8 ension.
Clus e abundances: uDRD-e ol ed p edic s enhanced clus e coun s a z > 1.5;
EDE does no .
7
Void lensing: A z > 7, he pe sis en ϕ- ield in uDRD-e ol ed enhances oid lensing
signals; EDE (ha ing dilu ed away) does no .
These signa u es allow MCMC i s o Planck+JWST+DESI+eROSITA da a o b eak
he degene acy and dis inguish be ween scena ios.
4.2 Fu u e es s and alsi ica ion c i e ia
Key alsi ica ion c i e ia:
1. G ow h a e: I DESI Yea -5 o Euclid show (z) a z∼1–2 consis en wi h ΛCDM
(no ∼1% enhancemen ), hen γ < 0.02 is equi ed.
2. Clus e coun s: I eROSITA DR2 (expec ed ∼2026) shows clus e abundances a
z > 1.5 in pe ec ag eemen wi h ΛCDM (no ∼7% excess), hen γ < 0.02.
3. S8measu emen s: I u u e weak lensing su eys (LSST, Euclid) con i m S8≪0.80,
he ∼6% boos om γ= 0.05 is dis a o ed.
4. JWST sys ema ics: I con inued spec oscopic ollow-up educes he high-zgalaxy
excess om ∼3–10× o ≲1.5×, hen γ < 0.02 su ices.
5 Conclusion
We ha e ex ended he uDRD amewo k by p omo ing he scala ield mass o ime-dependen :
m2
ϕ(a) = m2
0·a−γ. This single modi ica ion:
Subs an ially na ows he H0 ension: CMB-in e ed H0inc eases om 67.4 o
∼70–71 km s−1Mpc−1, educing he disc epancy wi h local measu emen s om 5.6σ
o 2.6σ—a ∼50% imp o emen .
Pa ially alle ia es JWST anomalies: P edic s ∼20% mo e massi e halos a
z= 12, accoun ing o a ac ion o he obse ed excess.
P ese es uDRD successes: All Sola Sys em, galaxy, and clus e phenomenology
emains in ac .
Makes es able p edic ions: Enhanced g ow h ( (z)), clus e abundances, σ8boos .
Uncons ained by BBN: Ma e -like ϕ- ield has negligible impac on p imo dial
abundances.
The model p esen s a ade-o : i subs an ially imp o es ag eemen wi h JWST and H0
obse a ions while po en ially wo sening he S8 ension by ∼1σ. This is a es able p edic-
ion wi h upcoming DESI, Euclid, and LSST da a. We a gue ha he combined explana o y
powe , heo e ical mo i a ion (cu a u e-dependen mass unning), and minimal ex ension
(one pa ame e γ) make his a compelling a enue o add essing mul iple cosmological en-
sions wi hin he uDRD amewo k.
8
Acknowledgmen s
This esea ch made use o : NumPy,SciPy,Ma plo lib. JWST da a om MAST a chi e.
We hank he anonymous e iewe s o aluable eedback.
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