A screened time-drag scalar field: percent-level late-time growth and the cosmic radio dipole excess

Zenodo DOI: 10.5281/zenodo.17693657
A sc eened ime-d ag scala ield: pe cen -le el la e- ime g ow h
and he cosmic adio dipole excess
Paul Cooney1
1Independen esea che , Innis il, On a io, Canada∗
(Da ed: No embe 23, 2025)
We p esen a minimal, ghos - ee, g adien -s able scala – enso heo y in which a single scala
ield τwi h a densi y-dependen kine ic coe icien Z(ρm) p oduces ∼1% modi ica ions o he
g ow h a e a z≲2 while p ese ing he exac ΛCDM backg ound expansion. Kine ic sc eening
supp esses i h o ces by mo e han 14 o de s o magni ude locally and by >1024 a ecombina ion.
Linea pe u ba ions yield a ime-dependen e ec i e g a i a ional s eng h Ge (a) = G[1+αe (a)]
wi h αe (a)≃(α/2) Ωm(a)/[Ωm(a)+ΩΛ] o a single dimensionless coupling α∼0.02. La ge-
scale g adien s in he backg ound alue o ˙τinduce a non-kinema ic con ibu ion o numbe -coun
dipoles o o de Dτ∼0.01–0.02 ha is au oma ically aligned wi h he CMB dipole, peaks a z∼1,
and anishes a bo h low and high edshi . The model is consis en wi h cu en cons ain s om
BBN, CMB, Sola Sys em es s, and g a i a ional-wa e obse a ions, and makes sha p, pe cen -le el
p edic ions o upcoming DESI, Euclid, LSST, and SKA measu emen s.
I. INTRODUCTION
Al hough ΛCDM emains ema kably success ul, wo
mild la e- ime anomalies pe sis :
(i) a ∼2–3σp e e ence o enhanced clus e ing ampli-
ude in low- edshi p obes [1,2];
(ii) a ac o ∼2–4 excess in he local adio and mid-
in a ed sou ce-coun dipole ampli ude ela i e o
he kinema ic expec a ion [3,4].
We in oduce a single-pa ame e , s ongly sc eened
scala – enso ex ension ha simul aneously accoun s o
bo h classes o anomalies. The model modi ies he linea
g ow h a e a he pe cen le el and gene a es a non-
kinema ic con ibu ion o he cosmic adio/mid-in a ed
dipole, while lea ing he backg ound expansion exac ly
equal o ΛCDM. The homogeneous ime-d ag scaling un-
de lying hese e ec s is de i ed in ull in he s andalone
Appendix (Secs. A–C).
II. ACTION AND SCREENING
We conside a scala – enso heo y de ined by he ac-
ion
S=Zd4x√−gM2
Pl
2R+1
2Z(ρm)gµν ∂µτ∂ντ−ρΛ+Lm,
(1)
whe e τis a dimensionless scala ield, ρΛis he cosmo-
logical cons an densi y, and ma e couples minimally
o he Jo dan- ame me ic gµν . The densi y-dependen
∗paul.co[email p o ec ed] o.ca
kine ic coe icien is chosen as
Z(ρm)=αρm
1+(ρm/ρ∗)4, ρ∗≃5×10−27 h2g cm−3,
(2)
wi h αa small dimensionless coupling and ρ∗o o de he
p esen -day ma e densi y, so ha he ield is sc eened
a ea ly imes and in high-densi y en i onmen s, and be-
comes ac i e only when ρm∼ρΛ.
Fo ρm≫ρ∗ he e ec i e kine ic coe icien scales as
Z∝ρ−3
m, supp essing scala -media ed o ces by pow-
e s o ρm/ρ∗and easily sa is ying Sola Sys em and
ecombina ion-e a cons ain s. Fo ρm≪ρ∗one has
Z≃αρm, and he ield beha es as an unsc eened k-
essence scala wi h a ime-dependen no malisa ion ixed
by α.
III. BACKGROUND SCALING SOLUTION
On spa ially la FLRW backg ounds wi h p essu eless
ma e , ρm(a) = ρm,0a−3, a ia ion o he ac ion (1) wi h
espec o τyields he exac homogeneous equa ion
d
d a3Z(ρm) ˙τ= 0,(3)
which in eg a es o a3Z(ρm) ˙τ=Cwi h Ca single in-
eg a ion cons an . In he la e- ime unsc eened egime
(ρm≪ρ∗), whe e Z(ρm)≃αρm, he gene al homoge-
neous solu ion has cons an eloci y,
˙τ= ∗=C
αρm,0
= cons an .(4)
The co esponding kine ic ene gy densi y is
ρkin =1
2Z(ρm) ˙τ2≃α
2ρm 2
∗.(5)
2
A physically mo i a ed choice o Cis o equi e ha
he kine ic ene gy acks he squa e o he ma e ac-
ion,
ρkin
ρm+ρΛ
=α
2ρm
ρm+ρΛ2
,(6)
which ensu es ha he scala emains subdominan a all
epochs and ha i s e ec on he g ow h a e peaks nea
ma e –Λ equali y. This condi ion uniquely ixes
˙τ2=ρm(a)
ρm(a)+ρΛ
=Ωm(a)
Ωm(a)+ΩΛ
,(7)
so ha
ρkin =α
2
ρ2
m
ρm+ρΛ
,ρkin
ρm+ρΛ
≲α
8∼0.0025 (α≃0.02).
(8)
The backg ound expansion he e o e emains indis in-
guishable om ΛCDM, while he ime-d ag ield modi ies
he g ow h o s uc u e a he pe cen le el. A de ailed
de i a ion o Eq. (7) and i s k-essence comple ion is p o-
ided in Appendix Aand Appendix C.
IV. LINEAR PERTURBATIONS AND Ge (a)
In he quasi-s a ic, sub-ho izon egime he scala ield
modi ies he Poisson equa ion o
k2Φ=−4πGe (a)a2ρmδm,(9)
whe e he e ec i e g a i a ional s eng h is
Ge (a) = G1 + α
2
Ωm(a)
Ωm(a)+ΩΛ.(10)
This co esponds o a ac ional enhancemen
αe (a)≡Ge (a)−G
G=α
2
Ωm(a)
Ωm(a)+ΩΛ
,(11)
which anishes in bo h he deep ma e e a and he
asymp o ic de Si e u u e, and peaks a ound z∼1.
Figu e 1shows he esul ing pe cen -le el enhancemen
o σ8(z) ela i e o Planck ΛCDM o α= 0.02, oge he
wi h low- edshi measu emen s om DESI [1] and o he
su eys.
The scala sec o can be ecas as a k-essence he-
o y wi h PX>0, PXX = 0, and sound speed c2
s= 1,
gua an eeing absence o ghos s and g adien ins abili-
ies and ensu ing luminal p opaga ion consis en wi h
GW170817 [5]. A de ailed discussion appea s in Ap-
pendix A.
V. NUMBER-COUNT DIPOLE
CONTRIBUTION
Spa ial g adien s in he backg ound alue o ˙τin-
duced by la ge-scale modes p oduce an addi ional, non-
0.0 0.5 1.0 1.5 2.0
Redshi
z
10
5
0
5
10
(
8)/(
8)Planck
(%)
= 0.02
model
BOSS DR12
FIG. 1. Pe cen age enhancemen o σ8(z) ela i e o Planck
ΛCDM o α= 0.02. Rep esen a i e low- edshi measu e-
men s om DESI and o he su eys a e o e laid o illus a-
ion.
kinema ic con ibu ion o ela i is ic numbe -coun luc-
ua ions. Using he ull ela i is ic o malism o ob-
se ed numbe coun s [6,7], and he scaling (7), one inds
a dipole con ibu ion o he o m
Dτ(z)≃0.018 α
0.02ΩΛ
Ωm(z)+ΩΛ2 + dln n
dln L,(12)
whe e n(L) is he luminosi y unc ion o he sou ce pop-
ula ion and he angle b acke s deno e a sui able a e age
o e he su ey selec ion.
Fo ypical adio and mid-in a ed samples wi h ⟨2 +
dln n/d ln L⟩≃3–5, he o al p edic ed dipole (kinema ic
plus τ-induced) lies in he ange D≃0.016–0.020 a
z∼1, in good ag eemen wi h ecen measu emen s om
NVSS, Ca WISE, and ela ed su eys [3,4]. The shape
and edshi dependence o Dτ(z) a e sha p p edic ions
o upcoming SKA and LSST c oss-co ela ions.
VI. THEORETICAL CONSISTENCY AND
INTERPRETATION
The model sa is ies s anda d heo e ical consis ency
condi ions:
•The k-essence ep esen a ion ensu es PX>0 and
c2
s= 1, so he e a e no ghos s o g adien ins abili-
ies (Appendix A).
•The g a i a ional slip pa ame e sa is ies η(a, k)≃
1 up o O(10−3) co ec ions on all ele an scales,
main aining consis ency wi h weak lensing and
RSD cons ain s (Appendix B).
3
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Median edshi
z
0.0
0.5
1.0
1.5
2.0
2.5
Dipole ampli ude (%)
Kinema ic only
Kinema ic + (
= 0.02
)
NVSS
Ca WISE
RACS/EMU
FIG. 2. Schema ic p edic ion o he o al dipole ampli ude as
a unc ion o median edshi o α= 0.02, including bo h he
kinema ic and τ-induced con ibu ions. Rep esen a i e adio
and mid-in a ed measu emen s a e shown o compa ison.
•Kine ic sc eening yields s ong supp ession o i h
o ces in he Sola Sys em and a ecombina ion,
easily sa is ying local and ea ly-Uni e se bounds.
A he modynamic ein e p e a ion o he ime-d ag
ield, in e ms o an e ec i e ield-clock and associa ed
empe a u e scale, is p o ided in Appendix D. This pic-
u e is pu ely in e p e a i e and does no a ec any ob-
se able p edic ions.
VII. CONCLUSIONS
We ha e p esen ed a sc eened scala – enso model in
which a single dimensionless coupling α≃0.02 p oduces:
•a pe cen -le el enhancemen o he la e- ime
g ow h a e, consis en wi h cu en low- edshi
measu emen s; and
•a non-kinema ic con ibu ion o he cosmic
adio/mid-in a ed dipole o ampli ude Dτ≃
0.016–0.020 a z∼1, au oma ically aligned wi h
he CMB dipole.
The backg ound expansion emains exac ly ΛCDM,
and he model sa is ies all cu en heo e ical and obse -
a ional consis ency es s. Fo hcoming da a om DESI,
Euclid, LSST, and SKA will be able o con i m o alsi y
his speci ic ime-d ag scena io a he pe cen le el.
Appendix A: k-essence comple ion and heo e ical
consis ency
The scala sec o may be ew i en exac ly as a mini-
mally coupled k-essence ield wi h
P(X, ρm)=αρm+ρΛ
ρm
X−ρΛ, X ≡ −1
2∂µτ∂µτ.
(A1)
The s abili y condi ions ollow immedia ely:
P,X =αρm+ρΛ
ρm
>0, P,XX = 0, c2
s= 1.(A2)
Thus he heo y is ghos - ee and g adien -s able, wi h
luminal scala p opaga ion in acco dance wi h he
GW170817 cons ain [5]. The backg ound expansion e-
mains exac ly ΛCDM because he scala con ibu es
ρkin =α
2
ρ2
m
ρm+ρΛ≪ρm, ρΛ(α≲0.03),(A3)
ensu ing negligible back eac ion a he sub-pe cen le el.
Appendix B: G a i a ional slip and me ic
consis ency
In he quasi-s a ic, sub-ho izon limi , he pe u bed
scala and me ic equa ions imply
Ψ = Φ + OH2
k2,(B1)
which yields a g a i a ional slip pa ame e
η(a, k)≡Φ
Ψ=1+O(10−3) (B2)
on all obse a ionally ele an scales. This lies sa ely
wi hin cu en and o ecas Euclid/LSST sensi i i ies
and ensu es consis ency wi h weak lensing and RSD anal-
yses wi hou equi ing addi ional uning.
Appendix C: Backg ound e olu ion and he o igin o
he ime-d ag scaling
We de i e he exac homogeneous equa ion o mo ion
and show how he la e- ime scaling
˙τ2=ρm
ρm+ρΛ
(C1)
a ises om ixing he single in eg a ion cons an o he
heo y.
S a ing om he ac ion and kine ic coe icien de ined
in Eqs. (1)–(2), a ia ion yields
d
d a3Z(ρm) ˙τ= 0 =⇒a3Z(ρm) ˙τ=C, (C2)
4
whe e Cis he unique in eg a ion cons an . In he la e-
ime unsc eened egime (ρm≪ρ∗),
Z(ρm)≃αρm=αρm,0a−3,(C3)
so he gene al homogeneous solu ion is
˙τ= ∗=C
αρm,0
= cons an .(C4)
The kine ic ene gy densi y is
ρkin =1
2Z˙τ2≃α
2ρm 2
∗.(C5)
We ix Cby imposing he physically mo i a ed condi ion
ρkin
ρm+ρΛ
=α
2ρm
ρm+ρΛ2
,(C6)
ensu ing (i) subdominan kine ic ene gy and (ii) a ime-
dependen Ge (a) peaking nea ma e –Λ equali y. This
uniquely o ces Eq. (C1), eco e ing he main- ex scaling
wi hou in oking any dynamical a ac o claims.
Appendix D: The modynamic ein e p e a ion
The ield de ines a local “clock” wi h a e
dτ
d =sΩm(a)
Ωm(a)+ΩΛ
,(D1)
which slows as Λ domina es. The o al ield ime is ini e,
τ inal =Z∞
0
d dτ
d <∞,(D2)
e en hough FRW ime ex ends inde ini ely. This be-
ha iou is non-pa hological: τsimply becomes asymp o -
ically ozen in a de Si e u u e. A use ul in e p e i e
(non-dynamical) quan i y is he e ec i e empe a u e
Te (a)∝H(a)dτ
d ,(D3)
mo i a ed by Un uh–de Si e scaling. Because bo h
H(a) and dτ/d dec ease,
Te cools as e han in pu e ΛCDM.(D4)
Ma e - ich egions ha e a sligh ly la ge backg ound
alue o dτ/d , p o iding an in ui i e in e p e a ion o
why g a i a ional collapse p oceeds mo e e icien ly he e
— ma ching he pe cen -le el enhancemen p edic ed in
he pe u ba i e analysis. This ein e p e a ion modi-
ies no obse ables and is included only o concep ual
cla i y. does his e sion include appendix d?
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