Cosmology and String Theory F. Quevedo Cambridge CORFU 2005.
Cosmology in LARGE volume string models
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Transcript of Cosmology in LARGE volume string models
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Cosmology in LARGE volume string models
Tetsutaro Higaki
arXiv: 1208.3563 published in JHEP 1211 (2012) 125 with Fuminobu Takahashi at Tohoku U.
See also arXiv: 1208.3562 by Cicoli, Conlon and Quevedo
01/29/2013@Osaka U.
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Production of a hot dark mattervia LARGE extra dimensions.
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1. Motivation: Exploring the origin of the Universe.
1. Introduction
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The present universe consists of
Dark matter and dark energy clearly requirenew physics beyond the Standard Model (SM).
What is the Universe made of?
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Past and now of the Universe
In the early Universe• Baryons• Dark matter (Cold DM)• Photons• Neutrinosdominated.
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Past and now of the Universe
In the early Universe• Baryons• Dark matter (Cold DM)• Photons• Neutrinos + Dark radiationdominated.
Sterile 4th neutrino-like(A part of hot dark matter)
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My motivation
Dark radiationNeff ~ 4
||A probe of high energy physics!?
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The Standard
Model
Moduli& Hidden
sectors
E.g. Gravity
Anomaly cancellation condition
Overview of string-theory-models
Hidden sectors appear naturallythrough stringy compactifications!
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Supergravity models on aLARGE Swiss-cheese Calabi-Yau (CY)
SM
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Main characters in 4D SUGRA
1. Size of CY3 2.Higgs 3. Axion (Ex-dim.) (DR)
4. Wino (CDM)
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Contents
1. Introduction: Motivations and short summary
2. Observations and dark Radiation
3. LARGE volume scenario (LVS)
4. Dark radiation and dark matter from the modulus decay
5. Conclusion and open questions
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2. Observations of dark radiation (a hot DM)
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Dark radiation (DR)
• 4th neutrino-like component in cosmic ν background
Ultralight mass: MDR m≦ ν 0.1 eV≦Almost no interaction: Gravity or…
How can we detect the presence indirectly?
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In radiation-dominated era with T 1MeV ≦
DR
DR and expansion of the universe
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The expansion rate gets increased by ΔNeff.
H: Expansion rate (Hubble parameter)
The Friedman equation in rad. era
DR and expansion of the universe
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4He abundaceis sensitive to the expansion rate H at BBN era ~ 1 sec.
Cosmic Microwave Background (CMB)is sensitive to H at~ 380,000 year.
Mild DR evidence
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Cyburt, Fields, Olive (2008)
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Cyburt, Fields, Olive (2008)
HII region(H+, He*,O*,…)
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CMB
ΔT/T0 map on the sky sphere, where T0 = 2.73K.
WMAP 9-year
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CMB
Fourier form of ΔT/T0 map on the sky sphere, where T0 = 2.73K.
WMAP 9-year, 1212.5226
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South Pole Telescope (SPT)
Wilkinson Microwave Anisotropy Probe(WMAP)
Atacama Cosmology Telescope (ACT) in Chili
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Recent other CMB data
• WMAP 9-year, 1212.5226:
• Atacama Cosmology Telescope (ACT), 1301.0824:
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Recent other CMB data
• WMAP 9-year, 1212.5226:
• Atacama Cosmology Telescope (ACT), 1301.0824:
– Fewer # of data– Different frequency in CMB
Note: Tension between BAO and H0.
Wrong!!;will be
modified.
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Adoption of SPT result
So, both 4He abundance and CMB mildly prefer the presence of extra radiation:
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in 4D N=1 supergravity (SUGRA) framework.
For confirmation of dark radiation
WMAP 9-year, 1212.5226Needs data from the Planck.
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3. LARGE volume scenario (LVS):IIB orientifold supergravities in flux vacua
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Motivation for string theory
Unified theory including quantum gravity!
Closed string= Gravity
Open string= Gauge
D-brane
Open stringbetween branes
= Matter
nucleons
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Extra dimensions and SUSY
• The quantum gravity theory requiresextra 6 dimensions and supersymmetry (SUSY).
M4 ×
4 + 6 = 10
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The Standard
Model
Moduli& Hidden
sectors
E.g. Gravity
Anomaly cancellation condition
Phenomenological motivation
Hidden sectors appear naturallythrough stringy compactifications!
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Moduli in a Calabi-Yau space
SUSY-preservedcompactification
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4-cycle size: T (Kähler moduli)
3-cycle size: U (Complex structure moduli)
+ String Dilaton: S
Moduli in a Calabi-Yau space
SUSY-preservedcompactification
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Why moduli and axions?
1. Ubiquitous in string vacua.
2. VEVs = physical constants:• Size of extra dimension;
• Gauge/Yukawa couplings,
• SUSY-breaking parameters.
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Moduli ~ gauge couplings
(Ex) (4+n) dim. gauge theory on a brane (M4×Σn):
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Moduli ~ gauge couplings
(Ex) (4+n) dim. gauge theory on a brane (M4×Σn):
Moduli field φ : Volume of a cycle
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Moduli ~ gauge couplings
(Ex) (4+n) dim. gauge theory on a brane (M4×Σn):
Moduli field φ : Volume of a cycle
An extra 6 dimension spacecan have many Σn .
↓ Many moduli
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Axions ~ θ-term
(Ex) (4+n) dim. gauge theory on a brane (M4×Σn):
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Axions ~ θ-term
(Ex) (4+n) dim. gauge theory on a brane (M4×Σn):
Axion field a: Integrand of tensor field Cn (NSNS, RR)
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Axions ~ θ-term
(Ex) (4+n) dim. gauge theory on a brane (M4×Σn):
An extra 6 dimension spacecan have many Σn .
↓ Many axions
Axion field a: Integrand of tensor field Cn (NSNS, RR)
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What are their masses?
What are their VEVs?(= couplings etc.)
Moduli/axion stabilization
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Flux compactifications with O-planes and D-branes
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Moduli/axion stabilization
• Finding a vacuum of moduli in a string model
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Example of potential for moduli
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Ultralight axion(s)
• In a LARGE volume limit of compact space,axion will get ultralight thanks to a residual gauge symmetries on Cn in 10D:
• The axions originate from gravity Cn (NSNS or RR-field).
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Model:LARGE volume scenario
(LVS)
V. Balasubramanian, P. Berglund, J. P. Conlon and F. Quevedo.(2005);
R. Blumenhagen , J. P. Conlon , S. Krippendorf, S. Moster and F. Quevedo.(2009)
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Cartoon of LVS models:Swiss cheese Calabi-Yaus
Note: 418 such explicit CY models; a single hole model J. Gray, Y.H. He, V. Jejjala, B. Jurke, B. Nelsond and J. Simon (2012)
Intersection # among 2cycles is important.
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Note: 418 such explicit CY models; a single hole model J. Gray, Y.H. He, V. Jejjala, B. Jurke, B. Nelsond and J. Simon (2012)
Instantons3-form
FluxModuli stabilization
forvolume, holes, shapes.
Cartoon of LVS models:Swiss cheese Calabi-Yaus
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Note: 418 such explicit CY models; a single hole model J. Gray, Y.H. He, V. Jejjala, B. Jurke, B. Nelsond and J. Simon (2012)
Local model:MSSM + U(1)Aon D3-branes.
It is on a singularity,which is stabilized by FI=0.
QL
QR
LL
eR
U(2)
U(3)
U(1)
U(1)
Cartoon of LVS models:Swiss cheese Calabi-Yaus
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Matter content of the MSSM(Minimal Supersymmetric Standard Model)
R-parity(Superpartner)= -1 R-parity(SM-particles)= +1
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Model details
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Notation for 4D N=1 SUGRA
Lagrangian:
K : Kähler potential, W: Superpotential
f : gauge coupling function
,
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Volume moduli stabilization in LVS
Tb: Overall volume + DRTs: Hole volume + heavy axion
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Scalar potential
Other moduli can be irrelevant in this analysis.
as=2πτs = Re(Ts)
Vpot
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Exponentially LARGE volume CY
LARGE moduli VEV:
ξ =O(1) χ(CY) : A choice of Swiss cheese CY.∝gs =O(0.1) : A choice of quantized flux.
Note: SUSY-breaking AdS; needs ΔVpot ~ Vol(CY)-3 for dS/Mink.
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• Masses: Gravitino and the lightest modulus
• SUSY-breaking parameters on D3-branes (local):
CY volume controls everything
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Mass scales
•Overall volume: ~ 106 GeV
•Holes (volume): ~ 1012 GeV
•Shape: ~ 1011 GeV ~ gravitino mass
•Singularity: ~ 1015 GeV ~ string scale
for Volume (CY) = O(107) in string unit;1/R= O(1013) GeV
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Mass scales
•Overall volume: ~ 106 GeV
•Holes (volume): ~ 1012 GeV
•Shape: ~ 1011 GeV ~ gravitino mass
•Singularity: ~ 1015 GeV ~ string scale
for Volume (CY) = O(107) in string unit;1/R= O(1013) GeV
Instantons(ED3-branes)3-form
Flux
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A dark radiation candidate in LVS
TH, Takahashi;Cicoli, Conlon, Quevedo(2012)
ab:= Im(Tb): Axion as dark radiation
• stays ultralight even if we have
where Re(Tb)= Vol(CY)2/3 = 105 >>1.
• is only gravitationally interacting.
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5. Dark radiation and dark matter from the modulus decay
TH, Takahashi
See alsoCicoli, Conlon, Quevedo
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Why modulus decay?
• Answer: It reheats the universe, producing DM and DR.
: Canonically-normalized fluctuation of Tb
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Moduli problem in LVS
• Before inflation, modulus will be in the vacuum
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• Inflation produces additional potential for φ
Moduli problem in LVS
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• During inflation, modulus is sitting false vacuum
Moduli problem in LVS
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• During inflation, modulus is sitting false vacuum
Moduli problem in LVS
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• For Hinf > mφ1 decompactification occurs.
Moduli problem in LVS
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• For Hinf > mφ1 decompactification occurs.
is required.
Moduli problem in LVS
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• At the end of inflation, inflaton contribution will vanish.
Moduli problem for Hinf m≦ φ1 TH, Kamada, Takahashi
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• At the end of inflation, modulus starts to oscillate
for mInflaton > mφ1.
Amplitude:
Moduli problem for Hinf m≦ φ1 TH, Kamada, Takahashi
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• At the end of inflation, modulus starts to oscillate
for mInflaton > mφ1.
Energy (matter-like):
Moduli problem for Hinf m≦ φ1 TH, Kamada, Takahashi
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from inflaton decay
Moduli decay: New radiation
at H = Γφ1 At the end of inflation,Modulus starts to oscillate
Hinf m≦ φ1 < minflaton
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Modulus decay in LVS and No-scale
• z: Coefficient for higgsino mass (μ-term)
• V= Re(Tb)3/2 : Swiss-cheese CY volume
• Wmatter: Yukawa-terms for matter Qi
b b
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Modulus decay into Higgs and axions
• Decay width of modulus φ1
• Reheating temperature and branching to DR
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nH : The total number of Higgs multipletsz2 n⇔ H
• Decay width of modulus φ1 with z=1
• Partial decay width to DR with z=1
If there are additional Higgses,…
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Dark radiation vs z (nH=1)
mφ ~ V-3/2
ΔNeff obs ~ 1
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Gauge-Higgs Unification in SUSY?
We have z ~ 1 (tanβ ~ 1),
if K ~ |Hu + Hd†|2 with a shift symmetry
Hu → Hu + ic, Hd → Hd + ic.
Hebecker et al.
Non-chiral Higgs pair
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Dark matter: Wino(With assumed R-parity)
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DM: Motivation for SUSY
R-parity(Superpartner)= -1 R-parity(SM-particles)= +1
DM = Wino is assumed
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Modulus decay into Wino DM
φ1
Hu
Hd
Br = O(1)
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Modulus decay into Wino DM
Hu
Hd
Br = O(0.01)~ 1/Nchannel
for m0 = 1/V2 = O(10) TeV,
μ ~ M1/2 = 1/log(V)V2 = O(1) TeV.
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Wino DM pair annihilation
These process hardly depends on the branching fraction.
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Wino abundance Ωwinoh2 vs z
(ΩCDMh2)obs ~ 0.1
For z ~ 1.5, ΔNeff ~ 1
mWino ~ 500GeV
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Moroi, Nakayama (2011)
Constraint on Wino-like DM massmWino 500 GeV!≧
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DR and DM from modulus decay
Higgs from φ1 DR (no-scale), DM (the decay)
• For z ~ 1.5 or 2-3 ×(Hu, Hd) with each z = 1, DR can be explained.
• For mWino ~ 500 GeV, DR and DM are explained.
• If higgsino is DM, they are too many produced.
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6.Conclusion and open questions
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Production of a hot dark mattervia LARGE extra dimensions.
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LARGE Swiss-cheese CY in the cosmos
LARGE Volume modulus : φ
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The φ decay: φ→ Higgs + axions + Wino
in 4D N=1 supergravity (SUGRA) framework.
Summary of cosmology
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The φ decay: φ→ Higgs + axions + Wino
• reheats the universe at Tdec ~ 1GeV.
in 4D N=1 supergravity (SUGRA) framework.
Summary of cosmology
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The φ decay: φ→ Higgs + axions + Wino
• reheats the universe at Tdec ~ 1GeV.
• also produces DR of string-theoretic axions. LARGE volume CY: Ultralight axion and No-scale
in 4D N=1 supergravity (SUGRA) framework.
Summary of cosmology
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The φ decay: φ→ Higgs + axions + Wino
• reheats the universe at Tdec ~ 1GeV.
• also produces DR of string-theoretic axions. LARGE volume CY: Ultralight axion and No-scale
• also produces DM of Winos (with assumed R-parity).
in 4D N=1 supergravity (SUGRA) framework.
Summary of cosmology
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in 4D N=1 supergravity (SUGRA) framework.
For confirmation of dark radiation
WMAP 9-year, 1212.5226Needs data from the Planck.
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Many open questions
Concrete stringy realization?
Vacuum selection rule?
Reconsideration of “naturalness”?:Mnew phys >> TeV ?
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Swiss-cheese can be useful not only for “food life”
but also for “our lives” in the cosmos.
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Thank you!
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Backup
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100points of HII regions(Ionized hydrogen: T ~ 104K)
Yp vs Oxygen
Spectraanalysis
Steigman (2012)
(Time?: O needs time for production)
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Tension in H0 observations
WMAP 9-year, 1212.5226