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Cosmology

Dark MatterAESHEP 2012 10 25

Kavli IPMU, University of Tokyo

UC Berkeley, Lawrence Berkeley LaboratoryHitoshi Murayama

I OD IAS

TODAI INSTIT UTES FO R ADVANCED STUD Y



How did the Universe begin?

What is its fate?What is it made of?What are its fundamental laws?

Why do we exist?

interdisciplinary institute ofastronomy , physics and mathematics

10-year program by Japanesegovernment since 2007



Oct 2007



Oct 2008



Oct 2009



Oct 2010



Oct 2011



Oct 2012

picture will be taken on Oct 19



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Oct 1 2007 Apr 1 2008 Oct 1 2008 Apr 1 2009 Oct 1 2009 Apr 1 2010 Oct 1 2010 Apr 1 2011 Oct 1 2011 Apr 1 2012 Oct 1 2012

Japanese Asian American European AustralianOthers*

Full-time Scientists paid by IPMU

*Argentina, Chile, Canada

10/01/2012

+30 students, 35 staffs ! 140 on site



brand-new building 2010



obelisk “L’Universo é scritto in

lingua matematica ”

“European town square ”


http://slidepdf.com/reader/full/murayama1-down-size-01 12/109Asahi TV



ofciallyKavli IPMU on April 1, 2012First research institute in Japan namedafter a donor, breaking new grounds



May 9, meeting with Prime Minister Noda

http://www.kantei.go.jp/jp/noda/actions/201205/09kavli.html






• Basic research is very important, because it is a

common resource shared by the wholehumanity.



Cosmology

Dark MatterAESHEP 2012 10 25

Kavli IPMU, University of TokyoUC Berkeley, Lawrence Berkeley Laboratory

Hitoshi Murayama

I OD IAS

TODAI INSTIT UTES FO R ADVANCED STUD Y



star

Big Bangdark ages

13.7Gyr

particle soup

Earth

The wholeUniverse wassmaller than

an atom



Solar System



375 km2010 4 7



Sep 30, 2008Kaguya

380,000km=1.3 light seconds



380,000km=1.3 light seconds



1.5" 108km=8.3 light minutes



Made of atoms

• everything around us is made of atoms• stars are made of atoms, too

• spectroscopy



metals



1.5" 108km=8.3 light minutes

E=mc 2

5 Mt lighter every secondturning mass to energy

burning hydrogen

proton

4He

+ 2 e + + 2 !e + 25MeV



proof nuclear fusion also produces neutrinostens of trillions of neutrinos going through our bodyevery second

1 km underground

SuperKamiokande



luck

Feb 231987

1 6 0, 0 0 0 y e a r s

distant stars aremade of atoms, too

N



Earth resolves around the Sun with 30km/sec

Solar SystemNeptune

4 light hours

I t ok

a w a

2 0 l i g h

t mi n

u t e s

16

v ∝1

√ r



High School physicsF =

M m

r 2

ma = m

v2

r

GM m

r 2 = m

v 2

r

v =GM

r ∝1

√ r

16

v ∝1

√ r



Proxima Centauri

4.2 light years



Milky Way and Galaxies



28,000light years

~10 11 stars



1 5 0 0 l y r

2 8, 0 0 0 l y r



28,000light years

few stars



Andromeda M33 = 2.5M lyr

will collide with usin 4.5 billion years



How do we measure

the rotation curve?• Special relativity

• hyperne splitting inneutral hydrogen

• 21cm line can be excitedby the cosmic

microwave background• kT 0=0.23 meV• h c/ 21cm = 0.94 " eV

f 0 = r c ∓ vc ± v

f ≈ 1 ∓cv

f

F =1

F =0

21cm



VeraRubin

1960s



100k lyrs

??



connects galaxies– 12 –

Fig. 2.— The mean surface mass density prole as a function of the distance from the centre of galaxies. The thick solid curve is the mean of all haloes above the mass threshold. The dash-dottedcurve represents the contribution from particles bound to haloes, i.e., particles that reside withinthe virial radius of all haloes. The data with error bars are the observational estimate by MSFR

as in the previous gure.Ménard et al 2009

– 14 –

Fig. 4.— Fraction of mass contained in the sphere centred on individual haloes with radius α R vir ,where R vir is the pseudovirial radius and α is the multiplier represented in the abscissa. The solidcurve is 0 . 23ln+0 .23 given in the text.

Masaki Fukugita Yoshida 2011

stacking 85k quasars near 20M galaxies



Center of Milky Way

http://www.eso.org/public/outreach/press-rel/pr-2008/phot-46-08.html






Supermassive Black Hole

• supermassive blackhole of mass~4M Msun at the center of MilkyWay

• swallows gas around it• “death cry” for about 30 min

• but can’t be dark matter, far lessthan 100billion stars







Cluster of Galaxies



Coma cluster



motion of galaxies

• galaxies are moving inthe mutual gravitational

potential• assume virialized motion

<v 2>= G N M/r

• but they are too fast, too

• rst proposal of “darkmatter”

Fred Zwicky

i i l l i



gravitational lensing



gravitational lensing

r 0r

starlens

x

y

( x,y)

d 1 d 2 -1 -0.5 0.5 1

-1

-0.5

0.5

1

deection angleθ = 2

r S

r = 4

G N M

c 2 r



Clusters of galaxies

distortion in images of BG galaxies 2D map of dark matter

0

– 8 a r e a

d e n s i t y ( g / c m

2 )

1

2

3

4

1 0 0 K l y – 8

8 0

8



“see” invisible dark matter

Subaru telescope

more than 80% of matter is not atoms!



as expected by theory

Subaru measurements.Okabe, Takada+ 11

45 clusters stacked consistent with NFW prole



collion of clusters at 4500 km/s

lucky we are not here

4 billion l r awa

Dark Matter



Dark Matter



y-through based on SDSS-III data



galaxy 13.2 billion lyr away



dark ages

13.6 billion lyr away



You can still see the Big Bang13.7 G lyr away= 13.7 Gyr ago



CMB temperature

CMB dipole

we are moving at~1% of c relative to CMB

CMB anisotropyat ~10 –5

1mm ripple on 100m sea



protons



soup of particles

p

electrons quasars

galaxies

Cosmic Microwave Background Radiation

Big Bang 380,000 yrs 10 Gyrs 13.7 Gyrs

r e c o m b i n a t i o n

time

3 8 0 k1 3 . 7 G



k y r G y r

CMB



Friedmann Universe



three possible fates• depending on the

“energy”, there arethree possible fates of

the Universe• adiabatic expansion

T ! R –1

• past universe wassmaller and hotter

• “energy” corresponds tothe curvature of space

• actually, it is at

time s i z e o

f t h e

U n

i v e r s e

E<0

E=0E>0



Current Universe• knowing the l.h.s. tells us

the current energydensity

•l.h.s. = H02 from Hubblelaw v =H0 d

• r.h.s. denes the criticaldensity %c

• dene &i =%i /%c

• ' i &i =1

R

R !2

=8 π

3G N ρ − const

H 0 =R

R = 71km/s/Mpc

ρ c =8 π

G + N − 1 H 20 = 5 . 3 × 10 − 6 GeVcm − 3



Early Universe• adiabatic expansion

T ! R –1

• T =T 0(1+ z )

• z : redshift = R0/R• $=$0(1+ z )• matter: %! R –3

• radiation (masslessparticles): %! R –4

• matter-radiationequality: z ! 3300

• recombination: z! 1300

R

R !2

=8 π

3G N ρ − const



Large-Scale Structure



CMB temperature

CMB dipole

we are moving at~1% of c relative to CMB

CMB anisotropyat ~10 –5

1mm ripple on 100m sea

2 b i l li



nearly homogeneoussmall winkles

2 0 b i l l i onl y r

l i o n l y r

2 b i l l i o n l y r



Dark Matter is



Dark Matter isour birth mother

no dark matter with dark matter



reenacting Big Ban with Cal Band



Known Factsabout Dark Matter



• By the time of matter-radiation equality anduntil now, dark matter must be non-relativistic and clump together bygravitational attraction

• must be electrically neutral

Cold and Neutral



Search for MACHOs(Massive Compact Halo Objects)

Large Magellanic Cloud

Not enough of them!

Dim Stars?

MACHO95% cl

0.2

−6 −2−8 −4 0 20.0

0.4

0.6

f =

−

7

EROS−2 + EROS−1upper limit (95% cl)

logM= 2log( /70d)tE

EROSastro-ph/0607207

Mass Limits



• Clumps to form structure

•imagine

• “Bohr radius”:

• too small m won’t “t” in a galaxy!

• m >10 ! 22 eV “uncertainty principle” bound(modied from Hu, Barkana, Gruzinov, astro-ph/0003365)

V = G N

m

rr B =

G N M m 2

Mass Limits

“Uncertaint Princi le”



• 10-31 GeV to 10 50 GeV

• we narrowed it down towithin 81 orders ofmagnitude

• a big progress in 70 years

since Zwicky

Mass Limits



• if self-coupling too big, will “smoothout” cuspy prole at the galacticcenter

• some people want it

(Spergel and Steinhardt, astro-ph/9909386)

• need core < 35 kpc/h from data( < 1.7 x 10 -25 cm2 (m/GeV)

(Yoshida, Springel, White, astro-ph/0006134)

• bullet cluster:( < 1.7x10 -24 cm2 (m/GeV)(Markevitch et al, astro-ph/0309303)

Self-Coupling

f



•At least of the order of age of the universe14Gyr

• Beyond that, it depends on decay modes,branching fractions, all model-dependent

Lifetime

l l l



Cosmological scales

101

matter

all atoms = 5 .70 +0 .39

− 0 .61



(n&)0 = (n&f = 1001(m,m~~g~‘2 JA+)N 10-S/[(m,/GeV)((~A~)/10-27 cm3 s-‘)I,

where the subscript f denotes the value at freezeout and the subscript 0 denotes theThe current entropy density is so N 4000 cmm3,and the critical density

h l l



• thermal equilibrium whenT>m !

• Once T<m ! , no more ! created

• if stable, only way to losethem is annihilation• but universe expands and

! get dilute

• at some point they can’tnd each other

• their number in comovingvolume “frozen”

pC II 10-5h2 GeVcmp3, where is the Hubble constant in units of 100 km s-l M ppresent mass d ensity in units of the critical density is given by

0,h2 = mxn,/p, N (3 x 1O-27 cm3 C1/(oAv)) .

The result is independent of the mass of the WIMP (except for logarithmic correcinversely proportional to its annihilation cross section.

Fig. 4 shows numerical solutions to the Boltzmann equation. The equilibrium (sactual (dashed lines) abundan ces per comoving volume a re plotted as a function

0 0 1

0 0 0 1

0 0 0 0 1

10 b

,h10-s

-; 10-7

caJ 10-aa

2

10-Q

p lo-‘9

lo-”

z 10-m

F o-‘3

10 100

x=m/T (time +)

Fig. 4. Comoving number density of a WIMP in the early Universe. The dashed curves are the actual the solid curve is the equilibrium abundance. From [31].

thermal relic

F



• WIMP freezes out whenthe annihilation ratedrops below the

expansion rate

• Yield Y=n/s constantunder expansion

• stronger annihilation less abundance

H ≈ g1 / 2∗

T 2

M P lΓ ann ≈ σ ann v n

H (T f ) = Γ ann

n ≈ g1

/2

∗

T 2f

M P l σ ann v

s ≈ g∗ T 3

Y = n

s ≈ g

− 1 / 2∗

1

M P l T f σ ann vΩ

χ =

m χ Y s0

ρ c

≈ g− 1 / 2∗

x f

M 3

P l σ ann v

s 0

H 2

0

Freeze-out

O d f i d



• “Known” &! =0.23determines the WIMPannihilation crosssection

• simple estimate of theannihilation crosssection

• weak-scale mass!!!

Ωχ ≈ g

− 1 / 2∗

x f

M 3P l σ ann v

s 0

H 20

σ ann v ≈ 1 .12 × 10− 10

GeV− 2

x f g

1 / 2∗

Ωχ h 2

∼ 10 − 9 GeV − 2

σ ann v ≈ πα

2

m 2χ

m χ ≈ 300 GeV

Order of magnitude

0 0 1

0 0 0 1

0 0 0 0 1

10 b

10 sh l li



• Solve the Boltzmann equation

• assume Maxwell distribution, 1=2= ! , E1=E2=m !

• Note momentum dependence may beimportant close to thresholds, resonances

• re roduce the estimate with

dn

dt + 3 Hn = − σ ann v (n 2 − n 2

eq )

xf ≈ 24 + ln

m χ

100GeV + ln

σ ann v

10 − 9 GeV − 2 −

1

2 ln

g ∗

100

dn 1

dt + 3 Hn 1 = −

4

i =1

d3 pi

(2π )3 2E i|M (12 → 34)| 2 (2π )4 δ 4 ( p1 + p2 − p3 − p4 )

[f 1 f 2 (1 ± f 3 )(1 ± f 4 ) − f 3 f 4 (1 ± f 1 )(1 ± f 2 )]

,h10-s

-; 10-7

caJ 10-aa

2

10-Q

p lo-‘9

lo-”

z 10-m

F o-‘3

10 100

x=m/T (time +)

Fig. 4. Comoving number density of a WIMP in the early Universe. The dashed curves are the actualthe solid curve is the equilibrium abundance. From [31].

thermal relic

WIMP



• A stable particle at the weak scale with “EM-strength” coupling naturally gives the correctabundance

• This is where we expect new particlesbecause of the hierarchy problem!

• Many candidates of this type: SUSY, little Higgswith T-parity, Universal Extra Dimensinos, etc

• If so, we may even create dark matter ataccelerators

WIMP

Mi i l M d l



Minimal Model• Dark Matter clearly a new degree of

freedom

•The smallest degree of freedom you canadd to the QFT is a real Klein-Gordon eldS:dof=1

• assign odd Z 2 parity to S, everything else

even• Most general renormalizable coupling LS =

1

2! µS ! µS −

1

2m2

S S 2 − k 2

| H | 2 S 2 − h4!

S 4 .

C i h k



Consistency check • correct Dark Matter abundance• evades direct detection limits• satises triviality/instability limits from RGE

•consistent with precision electroweak data

180

190

170

160

150

140

130

m h

( G e V

) m S

=1

8 0 0 G e V

1 0 0 0

3 0 0

2 0 5 0

7 5

7 5

h (m Z )=01.01.2 i nst a b i l i t y

t r iv ialit y of λ

t r i v i a l i t y o f k

5. 5

σ p

( c m 2 )

10 − 40

10 − 42

10 − 44

10 − 46

DAMA (3 σ )

C D M S - I I ( 9 0 % C L )

mh = 150GeV Ω

S h 2=0.11

C R E S S T I I

Z E P L I N 4 / MA X

C D M S - I I

E d e l w e i s s 2

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