Cosmology in LARGE volume string models

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.

Production of a hot dark mattervia LARGE extra dimensions.

1. Motivation: Exploring the origin of the Universe.

1. Introduction

The present universe consists of

Dark matter and dark energy clearly requirenew physics beyond the Standard Model (SM).

What is the Universe made of?

Past and now of the Universe

In the early Universe• Baryons• Dark matter (Cold DM)• Photons• Neutrinosdominated.

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)

My motivation

Dark radiationNeff ～ 4

||A probe of high energy physics!?

The Standard

Model

Moduli& Hidden

sectors

E.g. Gravity

Anomaly cancellation condition

Overview of string-theory-models

Hidden sectors appear naturallythrough stringy compactifications!

Supergravity models on aLARGE Swiss-cheese Calabi-Yau (CY)

SM

Main characters in 4D SUGRA

1. Size of CY3 　 2.Higgs 3. Axion 　　　 (Ex-dim.) 　　　　　　　　　　　　　　　 (DR) 　

4. Wino (CDM)

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

2. Observations of dark radiation (a hot DM)

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?

In radiation-dominated era with T 1MeV ≦

DR

DR and expansion of the universe

The expansion rate gets increased by ΔNeff.

H: Expansion rate (Hubble parameter)

The Friedman equation in rad. era

DR and expansion of the universe

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

Cyburt, Fields, Olive (2008)

Cyburt, Fields, Olive (2008)

HII region(H+, He*,O*,…)

CMB

ΔT/T0 map on the sky sphere, where T0 = 2.73K.

WMAP 9-year

CMB

Fourier form of ΔT/T0 map on the sky sphere, where T0 = 2.73K.

WMAP 9-year, 1212.5226

South Pole Telescope (SPT)

Wilkinson Microwave Anisotropy Probe(WMAP)

Atacama Cosmology Telescope (ACT) in Chili

Recent other CMB data

• WMAP 9-year, 1212.5226:

• Atacama Cosmology Telescope (ACT), 1301.0824:

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.

Adoption of SPT result

So, both 4He abundance and CMB mildly prefer the presence of extra radiation:

in 4D N=1 supergravity (SUGRA) framework.

For confirmation of dark radiation

WMAP 9-year, 1212.5226Needs data from the Planck.

3. LARGE volume scenario (LVS):IIB orientifold supergravities in flux vacua

Motivation for string theory

Unified theory including quantum gravity!

Closed string= Gravity

Open string= Gauge

D-brane

Open stringbetween branes

= Matter

nucleons

Extra dimensions and SUSY

• The quantum gravity theory requiresextra 6 dimensions and supersymmetry (SUSY).

M4 ×

4 + 6 = 10

The Standard

Model

Moduli& Hidden

sectors

E.g. Gravity

Anomaly cancellation condition

Phenomenological motivation

Hidden sectors appear naturallythrough stringy compactifications!

Moduli in a Calabi-Yau space

SUSY-preservedcompactification

4-cycle size: T (Kähler moduli)

3-cycle size: U (Complex structure moduli)

+ String Dilaton: S

Moduli in a Calabi-Yau space

SUSY-preservedcompactification

Why moduli and axions?

1. Ubiquitous in string vacua.

2. VEVs = physical constants:• Size of extra dimension;

• Gauge/Yukawa couplings,

• SUSY-breaking parameters.

Moduli ～ gauge couplings

(Ex) (4+n) dim. gauge theory on a brane (M4×Σn):



Moduli field φ : Volume of a cycle



Moduli field φ : Volume of a cycle

An extra 6 dimension spacecan have many Σn .

↓ Many moduli

Axions ～ θ-term


Axions ～ θ-term


Axion field a: Integrand of tensor field Cn (NSNS, RR)

Axions ～ θ-term


An extra 6 dimension spacecan have many Σn .

↓ Many axions

Axion field a: Integrand of tensor field Cn (NSNS, RR)

What are their masses?

What are their VEVs?(= couplings etc.)

Moduli/axion stabilization

Flux compactifications with O-planes and D-branes

Moduli/axion stabilization

• Finding a vacuum of moduli in a string model

Example of potential for moduli

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).

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)

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.


Instantons3-form

FluxModuli stabilization

forvolume, holes, shapes.



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)


Matter content of the MSSM(Minimal Supersymmetric Standard Model)

R-parity(Superpartner)= -1 R-parity(SM-particles)= +1

Model details

Notation for 4D N=1 SUGRA

Lagrangian:

K : Kähler potential, W: Superpotential

f : gauge coupling function

,

Volume moduli stabilization in LVS

Tb: Overall volume + DRTs: Hole volume + heavy axion

Scalar potential

Other moduli can be irrelevant in this analysis.

as=2πτs = Re(Ts)

Vpot

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.

• Masses: Gravitino and the lightest modulus

• SUSY-breaking parameters on D3-branes (local):

CY volume controls everything

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

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

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.

5. Dark radiation and dark matter from the modulus decay

TH, Takahashi

See alsoCicoli, Conlon, Quevedo

Why modulus decay?

• Answer: It reheats the universe, producing DM and DR.

: Canonically-normalized fluctuation of Tb

Moduli problem in LVS

• Before inflation, modulus will be in the vacuum

• Inflation produces additional potential for φ


• During inflation, modulus is sitting false vacuum


• For Hinf > mφ1 decompactification occurs.


• For Hinf > mφ1 decompactification occurs.

is required.


• At the end of inflation, inflaton contribution will vanish.

Moduli problem for Hinf m≦ φ1 TH, Kamada, Takahashi

• At the end of inflation, modulus starts to oscillate

for mInflaton > mφ1.

Amplitude:


• At the end of inflation, modulus starts to oscillate

for mInflaton > mφ1.

Energy (matter-like):


from inflaton decay

Moduli decay: New radiation

at H = Γφ1 At the end of inflation,Modulus starts to oscillate

Hinf m≦ φ1 ＜ minflaton

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

Modulus decay into Higgs and axions

• Decay width of modulus φ1

• Reheating temperature and branching to DR

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,…

Dark radiation vs z (nH=1)

mφ ～ V-3/2

ΔNeff obs ～ 1

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

Dark matter: Wino(With assumed R-parity)

DM: Motivation for SUSY

R-parity(Superpartner)= -1 R-parity(SM-particles)= +1

DM = Wino is assumed

Modulus decay into Wino DM

φ1

Hu

Hd

Br = O(1)

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.

Wino DM pair annihilation

These process hardly depends on the branching fraction.

Wino abundance Ωwinoh2 vs z

(ΩCDMh2)obs ～ 0.1

For z ～ 1.5, ΔNeff ～ 1

mWino ～ 500GeV

Moroi, Nakayama (2011)

Constraint on Wino-like DM massmWino 500 GeV!≧

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.

6.Conclusion and open questions

Production of a hot dark mattervia LARGE extra dimensions.

LARGE Swiss-cheese CY 　in the cosmos

LARGE Volume modulus : φ

The φ decay: φ→ Higgs + axions + Wino


Summary of cosmology


• reheats the universe at Tdec ～ 1GeV.





• also produces DR of string-theoretic axions. LARGE volume CY: Ultralight axion and No-scale





• also produces DR of string-theoretic axions. LARGE volume CY: Ultralight axion and No-scale

• also produces DM of Winos (with assumed R-parity).




For confirmation of dark radiation

WMAP 9-year, 1212.5226Needs data from the Planck.

Many open questions

Concrete stringy realization?

Vacuum selection rule?

Reconsideration of “naturalness”?:Mnew phys >> TeV ?

Swiss-cheese can be useful not only for “food life”

but also for “our lives” in the cosmos.

Thank you!

Backup

100points of HII regions(Ionized hydrogen: T ～ 104K)

Yp vs Oxygen

Spectraanalysis

Steigman (2012)

(Time?: O needs time for production)

Tension in H0 observations

WMAP 9-year, 1212.5226

Cosmology in LARGE volume string models

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