Cosmology in Warped Extra Dimensions
description
Transcript of Cosmology in Warped Extra Dimensions
Cosmology in Warped Extra Dimensions
I) Dark Matter
( K.K., ‘Sterile Neutrino Dark Matter in Warped Extra Dimensions’ arXiv:0711.1570[hep-ph] )
1) Motivation
2) Setup: Bulk fields in warped 5D
3) Sterile Neutrino properties a) Coupling to the radion (AdS/CFT interpretation) b) Sterile Neutrino Mass c) Abundance
4) Examples
II) Baryon Asymmetry of the Universe( T. Gherghetta, K.K., M. Yamaguchi ‘Warped Leptogenesis with Dirac Neutrino Masses’ arXiv:0705.1749[hep-ph])
III) Conclusion/Discussion
Kenji Kadota, Theoretical Physics Institute, Univ. of Minnesota
Motivation• No absolutely stable collisionless particles in a simple Randall-Sundrum model( c.f. Flat Extra-Dimension: KK parity KK Dark Matter Dines et al ‘99, Appelquist et al ‘00,Cheng et al ‘02, Servant et al ‘02, Agashe & Servant ‘04, ‘05)
• Particles with the life-time longer than the age of the Universe Sterile (chargeless, right-handed) Neutrino
Advantages of 5D compared with 4D for sterile neutrino dark matter scenario1. Fine-tuning ameliorated (thanks to warp factor and small wave function overlaps)2. Production mechanism (radion decay)
Can be either Cold or Warm Dark Matter
Warm DM: Free-streams erasing the inhomogeneities
Warm dark matter: bigger free-streaming than that of cold dark matter•Missing satellite problem (satellite: small galaxies, the mass 10-3 of Milky Way galaxy)•Cusp/core problem
Simple warm dark matter model accounting for all the dark matter in the universe is excluded.‘Simple’ warm dark model:Sterile neutrino produced from the active-sterile neutrino mixing (Dodelson-Widrow ‘94)
Lyman-alpha forrest: lower limit 10 keVX-ray: upper bound 8 keV
Our scenario: Radion decay produces sterile neutrinosWe assume negligible mixing production, negligible Yukawa coupling
(c.f.• Large lepton asymmetry : Shi&Fuller ‘99• Additional singlet scalar : Kusenko ‘06• Inflaton : Shaposhnikov and Tkachev ‘06 • Subdominant warm dark matter: Palazzo, Cumberbatch, Solsar, Silk ‘07)
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Cosmology in Warped Extra Dimensions
I) Dark Matter
( K.K., ‘Sterile Neutrino Dark Matter in Warped Extra Dimensions’ arXiv:0711.1570[hep-ph] )
1) Motivation
2) Setup: Bulk fields in warped 5D
3) Sterile Neutrino properties a) Coupling to the radion (AdS/CFT interpretation) b) Sterile Neutrino Mass c) Abundance
4) Examples
II) Baryon Asymmetry of the Universe( T. Gherghetta, K.K., M. Yamaguchi ‘Warped Leptogenesis with Dirac Neutrino Masses’ arXiv:0705.1749[hep-ph])
III) Conclusion/Discussion
€
ds2 = e−2 y / Rη μν dx μ dxν − dy 2 =R
z
⎛
⎝ ⎜
⎞
⎠ ⎟2
(η μν dx μ dxν − dz2)
€
z ∈ [R,R'],1/R ~ M p,1/R' ~ TeV
Setup: 5D Warped space-time
€
(z = R ey / R , η μν = (1,−1,−1,−1,−1))
All fields in the bulk€
Planck brane : z = R
€
TeV brane : z = R'
SM fields+ Three right-handed Neutrinos (one of which is sterile dark matter N)
Brane stabilized by Goldberg-Wise ‘99
€
z → λz, x → λx
€
χ(x,y) ~ χ (n )(x) fL(n )(z),
n
∑
ψ (x,y) ~ ψ (n )(x) fR(n )(z)
n
∑€
Ψ=χψ ⎛
⎝ ⎜
⎞
⎠ ⎟
€
ψ(x)
€
χ(x)
€
ψ (1)
€
ψ (2)
€
~ TeV
€
χ (1)
€
χ (2)
Bulk fields
€
fL(0)(z) ~
z
R
⎛
⎝ ⎜
⎞
⎠ ⎟(1/2-c)
(c < 1/2 IR; c > 1/2 UV)
fR(0)(z) = 0 (Dirichlet b.c.)
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χ (0)
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mD = c /R
€
S5D ∋mD (χψ +ψ χ ) +K
€
χ (0) could be dark matter
Cosmology in Warped Extra Dimensions
I) Dark Matter
( K.K., ‘Sterile Neutrino Dark Matter in Warped Extra Dimensions’ arXiv:0711.1570[hep-ph] )
1) Motivation
2) Setup: Bulk fields in warped 5D
3) Sterile Neutrino properties a) Coupling to the radion (AdS/CFT interpretation) b) Sterile Neutrino Mass c) Abundance
4) Examples
II) Baryon Asymmetry of the Universe( T. Gherghetta, K.K., M. Yamaguchi ‘Warped Leptogenesis with Dirac Neutrino Masses’ arXiv:0705.1749[hep-ph])
III) Conclusion/Discussion
Holographic Interpretation (Maldacena ‘97, Gubser et al ‘98, Witten ‘98, Arkani-hamed et al ‘00, Rattazzi et al ‘01)
5D Randall-Sundrum
1. Coordinate z along AdS2. Planck brane at z=R3. TeV brane at z=R’
4. Radion
5. Planck brane localized field6. TeV brane localized field7. At finite temperature, two stationary so
lutions: RS geometry & AdS-Schwarzschild space
4D Strongly coupled CFT with gravity
1. Energy Scale in CFT2. Cutoff of CFT =1/R3. CFT spontaneously breaks confor
mal invariance4. Pseudo-Goldstone boson of broken
conformal invariance5. Elementary fields coupled to CFT6. Composites of CFT 7. Confinement & Deconfinement phases
€
ds2 =R
z
⎛
⎝ ⎜
⎞
⎠ ⎟2
(η μν dx μ dxν − dz2)
€
z → λz,x → λx
Radion Couplings
€
radion coupling ~mN
Λr
r(x)N(x)N(x),1
Λr
r(x)F μν (x)Fμν (x)
€
Goldstone coupling : r
f∂μ J μ
J: Global current whose breaking leads to Goldstone bosonf: symmetry breaking scale
€
Conformal (Dilatation) symmetry : Jμ = Tμν xν ⇒r
fTμ
μ
massive fermion⇒ Tμμ ~ mNN
massless gauge fields (anaomalous contributions)⇒ Tμμ ~ −
g2
32π 2Fμν F μν
€
c.f. Axion coupling to gluons : a
fPQ
gs2
32π 2G ˜ G
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
€
d4 x∫ AmN
Λr
r(x)N(x)N(x), A = dz wave function overlap( )∫
Cosmology in Warped Extra Dimensions
I) Dark Matter
( K.K., ‘Sterile Neutrino Dark Matter in Warped Extra Dimensions’ arXiv:0711.1570[hep-ph] )
1) Motivation
2) Setup: Bulk fields in warped 5D
3) Sterile Neutrino properties a) Coupling to the radion (AdS/CFT interpretation) b) Sterile Neutrino Mass c) Abundance
4) Examples
II) Baryon Asymmetry of the Universe( T. Gherghetta, K.K., M. Yamaguchi ‘Warped Leptogenesis with Dirac Neutrino Masses’ arXiv:0705.1749[hep-ph])
III) Conclusion/Discussion
Sterile Neutrino Mass
€
Planck brane : z = R
€
TeV brane : z = R'€
N (0)
€
mM = dMδ(y)
€
mN ~1
RdM
R
R'
⎛
⎝ ⎜
⎞
⎠ ⎟
1−2c
(1− 2c) for c <1/2,R
R'~
TeV
M p
€
For TeV brane Majorana mass, mN ~1
R'dM
R
R'
⎛
⎝ ⎜
⎞
⎠ ⎟2c−1
(2c −1) for c >1/2 ⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
SterileWe assume negligible Yukawa (i.e. no mixing)Negligible Dirac mass
Cosmology in Warped Extra Dimensions
I) Dark Matter
( K.K., ‘Sterile Neutrino Dark Matter in Warped Extra Dimensions’ arXiv:0711.1570[hep-ph] )
1) Motivation
2) Setup: Bulk fields in warped 5D
3) Sterile Neutrino properties a) Coupling to the radion (AdS/CFT interpretation) b) Sterile Neutrino Mass c) Abundance
4) Examples
II) Baryon Asymmetry of the Universe( T. Gherghetta, K.K., M. Yamaguchi ‘Warped Leptogenesis with Dirac Neutrino Masses’ arXiv:0705.1749[hep-ph])
III) Conclusion/Discussion
Sterile neutrino abundance
• Boltzmann equation
€
dY
dT~ Ccol ,Y ≡
nN
s,Ccol ~ Γrnr
Γr,partial~ mrλ
2,L4 D ~ λr(x)N(x)N(x)€
nN
€
(Thermal abundance for nr
Temperature integration from T ~ μTeV down to T << mr )
€
λ2 ~ 10−20 1MeV
mN
⎛
⎝ ⎜
⎞
⎠ ⎟
mr
100GeV
⎛
⎝ ⎜
⎞
⎠ ⎟
To account for all the current dark matter, €
1
Λr
r(x)F μν (x)Fμν (x)
Γ(rA ↔ ff ) ~ TeV
H ~ (TeV / M p ) × TeV
Cosmology in Warped Extra Dimensions
I) Dark Matter
( K.K., ‘Sterile Neutrino Dark Matter in Warped Extra Dimensions’ arXiv:0711.1570[hep-ph] )
1) Motivation
2) Setup: Bulk fields in warped 5D
3) Sterile Neutrino properties a) Coupling to the radion (AdS/CFT interpretation) b) Sterile Neutrino Mass c) Abundance
4) Examples
II) Baryon Asymmetry of the Universe( T. Gherghetta, K.K., M. Yamaguchi ‘Warped Leptogenesis with Dirac Neutrino Masses’ arXiv:0705.1749[hep-ph])
III) Conclusion/Discussion
Examples
€
(cN ,1/R') ~ (−0.28,4TeV )⇒ (mN ,λ ) ~ (17keV ,7 ×10−10)
€
(cN ,1/R') ~ (0.63,0.4TeV )⇒ (mN ,λ ) ~ (5MeV ,4 ×10−11)
Lyman-alpha: lower limit 10 keV
€
1/R = M p,dM =1,mr = 300GeV
Sterile Neutrino dark matter model in 4D typically suffers from fine-tunings, which is relaxed in 5D.
Cosmology in Warped Extra Dimensions
I) Dark Matter
( K.K., ‘Sterile Neutrino Dark Matter in Warped Extra Dimensions’ arXiv:0711.1570[hep-ph] )
1) Motivation
2) Setup: Bulk fields in warped 5D
3) Sterile Neutrino properties a) Coupling to the radion (AdS/CFT interpretation) b) Sterile Neutrino Mass c) Abundance
4) Examples
II) Baryon Asymmetry of the Universe( T. Gherghetta, K.K., M. Yamaguchi ‘Warped Leptogenesis with Dirac Neutrino Masses’ arXiv:0705.1749[hep-ph])
III) Conclusion/Discussion
Kenji Kadota, Theoretical Physics Institute, Univ. of Minnesota
Mass splitting due to the Majorana mass confined on Planck brane
€
NR
€
NL
<<TeV(e.g, 10-9TeV)
€
NR
€
NL
Lepton number violation leads to the small mass splittings
TeV Scale Warped Leptogenesis (T. Gherghetta, K.K. & M. Yamahuchi, arXiv:0705.1749[hep-ph])
€
ε =Γ(N+(1) → LH*) − Γ(N+
(1) → LcH)
Γ(N+(1) → LH*) + Γ(N+
(1) → LcH)~
Im[ λ +* λ−( )
2]
λ +
2λ−
2
λ−
2
mN+
(1) − mN−
(1)
mN−
(1)
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
€
YB ~ O(10−10) ~ −1
3YL ~
ε
g*
,g* ~ O(100)
€
Sphaleron : Decay temp bigger than Tc ⇒ λ− ≥10−8
Out of equilibrium decay⇒ λ− ≤10−7
~TeV
Enough baryon asymmetry even at TeV scale!(c.f. T~1010GeV for standard leptogenesis.)
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Discussion/Conclusion
TeV Scale Warped Leptogenesis
• Global symmetry breaking term (Majorana mass) confined on Planck brane while RH Neutrino localized around TeV brane
Small mass splitting for big CP asymmetry at TeV scale
(Warm, Cold) Dark Matter in Warped Extra Dimensions
• No absolutely stable collisionless/chargeless particles• Long-lived Sterile neutrino Produced by radion decay Fine-tunings ameliorated
Future work in progress: Phase transitions (e.g. entropy dilution etc), Thermal corrections etc
€
ds2 =R
z
⎛
⎝ ⎜
⎞
⎠ ⎟2
(η μν dx μ dxν − dz2)
€
ds2 =R
z
⎛
⎝ ⎜
⎞
⎠ ⎟2
e−2F(x,z )η μν dx μ dxν − (1+ G(x,z))2 dz2( ),G = 2F
€
φ(x,z) = φ0 + ϕ (Goldberger - Wise '99)
€
F(x,z) =z
R'
⎛
⎝ ⎜
⎞
⎠ ⎟2
r(x)
Λr
,Λr ≡6
R'
€
g =R
z
⎛
⎝ ⎜
⎞
⎠ ⎟5
e−4F (1+ 2F),eaM = diag
z
R(eF ,eF ,eF ,eF ,1/(1+ 2F))
€
d5x∫ R
z
⎛
⎝ ⎜
⎞
⎠ ⎟5
z
R
⎛
⎝ ⎜
⎞
⎠ ⎟ −iχ σ μ∂μ χ − iψσ μ∂μψ +
1
2ψ
t ∂ 5χ − χ
t ∂ 5ψ ( )
⎛
⎝ ⎜
⎞
⎠ ⎟+ mD (ψχ − χ ψ )
⎡
⎣ ⎢
⎤
⎦ ⎥,mD ≡
c
R
€
g =R
z
⎛
⎝ ⎜
⎞
⎠ ⎟5
,eaM = diag
z
R(1,1,1,1,1)
Radion coupling to Fermion
€
d4 x∫ AmN
Λr
r(x)N(x)N(x), A = dz wave function overlap( )∫
TeV Scale Warped Leptogenesis
€
ε =Γ(N+(1) → LH*) − Γ(N+
(1) → LcH)
Γ(N+(1) → LH*) + Γ(N+
(1) → LcH)~
Im[ λ +* λ−( )
2]
λ +
2λ−
2
λ−
2
mN+
(1) − mN−
(1)
mN−
(1)
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
, m
N+(1) − m
N−(1)
mN−
(1)
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟~ 10−9
€
YB ~ O(10−10) ~ −1
3YL ~
ε
g*
,g* ~ O(100)
€
Sphaleron : Temp at decay TD ~ Γ1 ~ l− mN1 bigger than Tc ⇒ λ− ≥10−8
Out of equilibrium decay : Γ1 < H(T = mN1),TD < mN1
⇒ λ− ≤10−7
~TeV
Enough baryon asymmetry even at TeV scale
CDM/WDM
(Abazajian et al ‘01,’06)
€
λFS ~ 40Mpc30eV
mN
⎛
⎝ ⎜
⎞
⎠ ⎟
p /T
3.15
⎛
⎝ ⎜
⎞
⎠ ⎟,MFS ~ 2.6 ×1011 Msun (Ωmh2)
1keV
mN
⎛
⎝ ⎜
⎞
⎠ ⎟
3p /T
3.15
⎛
⎝ ⎜
⎞
⎠ ⎟
3