Dark Matter and Dark EnergyDark Matter and Dark Energy

Rocky I: Evidence for dark matter and dark energy Rocky II: Dark matter candidatesRocky III: Dark energy ideas

SLAC Summer Institute, August 2003Rocky Kolb, Fermilab & The University of Chicago

Epicycle II – Dark matterEpicycle II Epicycle II –– Dark matterDark matterWhat is dark matter?

“In questions like this, truth is only to be had by laying together many variations of error.”

-- Virginia WolfA Room of Ones Own

Particle Dark Matter CandidatesParticle Dark Matter CandidatesParticle Dark Matter Candidates• neutrinos (hot dark matter)

• sterile neutrinos, gravitinos (warm dark matter)

• LSP (neutralino, sneutrino, …) (cold dark matter)

• LKP (lightest Kaluza-Klein particle)

• axions, axion clusters

• solitons (B-balls; Q-balls; Odd-balls,….)

•••

• supermassive relics

Supermassive relics(Nonthermal dark matter)

SupermassiveSupermassive relicsrelics((NonthermalNonthermal dark matter)dark matter)

Production Mechanisms:

• Bubble collisions Chung, Kolb, Riotto

• Preheating Chung

• Reheating Chung, Kolb, Riotto

• Gravitational Chung, Kolb, Riotto; Kuzmin & Tkachev

new application: dark matter(Chung, Kolb, & Riotto; Kuzmin & Tkachev)

• require (super)massive particle “X”• stable (or at least long lived)• initial inflationary era followed by radiation/matter

Arnowit, Birrell, Bunch, Davies, Deser, Ford, Fulling, Grib, Hu, Kofman, Lukash, Mostepanenko, Page, Parker, Starobinski, Unruh, Vilenkin, Wald, Zel’dovich,…

first application:

(Guth & Pi; Starobinski; Bardeen, Steinhardt, & Turner; Hawking; Rubakov; Fabbi & Pollack; Allen)

Expanding universe particle creationExpanding universe particle creationExpanding universe particle creation

density perturbations from inflationgravitational waves from inflation

It’s not a bug, it’s a feature!

Fourier modes [a(τ) = expansion scale factor]

Mode equation (τ = conforml time)

Particle creation in nonadiabatic region

2measure of nonadiabaticity or k

k

HH

ωω

′∝

3† *

3/ 2( , ) ( ) ( )(2 ) ( )

ik x ik xk k k k

d xX x a h e a h ea

τ τ τπ τ

⋅ − ⋅ = + ∫

( ) ( ) ( )( ) ( ) ( )

2 2 2

2

6 1 0

0k X k

k k k

h k M a a a h

h h

τ ξ τ

τ ω τ τ

′′ ′′ + + + − = ′′ + =

0

Scalar field X of mass MXScalar field X of mass MScalar field X of mass MXX

Background fields in chaotic inflationBackground fields in chaotic inflationBackground fields in chaotic inflation

nonadiabatic region: particle creation

preheating, reheating, …?HHMφ

Chung, Kolb& Riotto; Kuzmin & Tkachev

GeV10 to101for1 1510INFLATON ≈⇒≈≈Ω XXX MMM

INFLATONMMX

chaoticinflation

Particle productionParticle productionParticle production

• Inflaton mass (in principle measurable from gravitational wave background, guess ) may signal a new mass scale in nature.

• Other particles may exist with mass comparable to the inflaton mass.

• Conserved quantum numbers may render the particle stable.

GeV1012

Superheavy particlesSuperheavySuperheavy particlesparticles

Model explorationModel explorationModel explorationGravitational Production:• Fermions Kuzmin & Tkachev• Non-conformal couplings Kuzmin & Tkachev• Small-field models Crotty, Chung, Kolb, Riotto• Hybrid models Crotty, Chung, Kolb, Riotto

Model explorationModel explorationModel exploration

natural hybrid

( )IXXIX

RHXXIX

HMhHM

TMhHM

−∝Ω→≥

≈Ω→≤

exp GeV10GeV10

2

9

2

112

• supermassive: 109 - 1015 GeV (~ 1012 GeV ?)

• abundance may depend only on mass

• abundance may be independent of interactions

sterile?

electrically charged?

strong interactions?

weak interactions?

• unstable (lifetime > age of the universe)?

Wimpzilla characteristics:WimpzillaWimpzilla characteristics:characteristics:

Gravitino productionGravitinoGravitino productionproductionGiudice, Riotto, TkachevLinde, Kallosh, Kofman, Van ProeyenNilles, Peloso, SorboNilles, Olive, Peloso……

(perhaps it is a bug after all…)

WIMPZILLA footprints:WIMPZILLA footprints:WIMPZILLA footprints:

Isocurvature modes: CMB, Large-scale structureDecay: Ultra High Energy Cosmic RaysAnnihilate: Galactic Center, SunDirect Detection: Bulk, Underground Searches

WIMPZILLA decayWIMPZILLA decayWIMPZILLA decayX UHE cosmic rays

1013 GeV = 1022 eVKuzmin & Rubakov; Birkel & Sarkar; Ellis, Gelmini, Lopez, Nanopoulos & Sarkar; Berezinsky, Kachelriess, & Vilenkin;Benakli, Ellis, & Nanopoulos; Berezinsky, Blasi, & Vilenkin; Blasi; Berezinsky & Mikhaliov;Dubovsky & Tinyakov; Medina-Tanco & Watson;Blasi & Seth; Ziaeepour; Crooks, Dunn, & Frampton

Blasi ‘99Blasi ‘99

QCDQCDSUSY QCDSUSY QCD

1013 GeV

1014 GeV

UHE cosmic rays mostly photons; characteristic spectrum; UHE neutrinos; lower-energy crud;

clumping anisotropies

τ ~ 1020 years

WIMPZILLA decayWIMPZILLA decayWIMPZILLA decay

GZK cutoff

Clustering of UHE eventsClustering of UHE eventsClustering of UHE events

probability fromisotropic distribution:<1%

model follows Navarro,Frenk, White dark matterdistribution

Blasi & Sheth astro-ph/0006316

UHE cosmic rays

SSI

Epicycle III – Dark EnergyEpicycle III Epicycle III –– Dark EnergyDark Energy

“In questions like this, truth is only to be had by laying together many variations of error.”

-- Virginia WolfA Room of Ones Own

What is the nature of dark energy

Mass density of space:

Cosmo-illogical constant?CosmoCosmo--illogical constant?illogical constant?

( ) ( )4 430 -3 4 310 g cm 10 eV 10 cmρ−− − −

Λ =

Cosmological constantCosmological constantCosmological constant

The unbearable lightness of nothing!( ) ( )2 229 338 10 cm 10 eVGπ ρ

− −ΛΛ = = =

Numerology:( )4 8 4

SUSY

3 45

exp 2

10 eV 10 cmV W V PlM M M

m Rν

ρ α ρ− −

= − =

= =

Cosmic coincidenceCosmic coincidenceCosmic coincidence

BBNEWKGUT

ΛΩ

M RΩ + Ω

RECDM B B VISIBLE B DARK υρ ρ ρ ρ ρ ρΛ − −∼ ∼ ∼ ∼ ∼

Cosmic Coincidence?

Every party represented!

Anything interesting at z~1?Anything interesting at z~1?Anything interesting at z~1?W

ebb et al.

1. No unbroken symmetry demands Λ=02. Nothing sets the scale3. Scale seems unrelated to any other energy scale

. . . seems to require

. . . fifth-force experiments?

4. Deal with it!

Non l’avrei giammai creduto;Ma faro quel che potro.

Mozart/Da Ponte, Don Giovanni, Act II

` `

Λ: the uninvited guestΛΛ: the uninvited guest: the uninvited guest

33~ 10 eVm −

Fourier modes of all fields are harmonic oscillators with a zero-point energy

Quantum uncertaintyQuantum uncertaintyQuantum uncertainty

classical

0E =quantum

12E ω=

3 2 2

all particlesd k k mρ = ± +∑ ∫

3 2 2 3 4C

all particles all particles

d k k m d k kρΛ

= ± + ±∑ ∑∫ ∫

Quantum uncertaintyQuantum uncertaintyQuantum uncertainty

( )( )

4

44 28

44 12

3

: bad prediction

: 10 eV

: 10 eV

10 eV: Observed

C

C Pl Pl

C SUSY SUSY

C

M M

M M

ρ

ρ

ρ

ρ

Λ

Λ

Λ

−Λ

Λ = ∞ = ∞ =

Λ = = =

Λ = = =

Λ = =

Photons couple to virtual particlesLamb shift

Gravitons couple to virtual particlesCosmological constant

e+

e-

γ

e+

e-

g

Spontaneous symmetry breakingSpontaneous symmetry breakingSpontaneous symmetry breaking

φ15 4 3 4

2 4 -1 4

-12 4

GUT: (10 GeV) SUSY: (10 GeV)EWK: (10 GeV) CHIRAL: (10 GeV)

OBSERVED: (10 GeV)

high-temperature

low-temperature

V(φ)

Balancing other contributionsBalancing other contributionsBalancing other contributions• Many possible contributions. • Why then is total so small?• Perhaps unknown dynamics sets globalvacuum energy equal to zero……but we’re not there yet!

V(φ)

φ0

Λ

V(φ)

φ0

Λ

Frieman, Freese, Hill, Olinto, …..

Universe hung up Universe rolling along

Balancing other contributionsBalancing other contributionsBalancing other contributions• But why now?• Tracker potentials, relate dark

energy to other contributions.*

• Why now?….. “close to matter domination”• Why now?….. “it’s just that time”

Wetterich; Ratra & Peebles; …

, ,ne φ φ− − …

Field equation for tracker:

( )2

3 08

3 M

H dV dGH φ

φ φ φπ ρ ρ

+ + =

= + +…

Can have ρφ track (stalk) ρM - effective mass of the fielddecreases as H: close but no cigar

Punctuated vacuum dominationPunctuated vacuum dominationPunctuated vacuum domination

Dodelson, Kaplinghat, Stewart

dark energydestiny≠

ΛΩ

φ

( )( ) 1 sinV e φφ α φ−= +

For now…parameterizeFor now…parameterizeFor now…parameterize

1 for constant 1 1 3 for dynamicaldark energy

V Vw pw

w

ρ== − Λ

− < ≤ −

SNIa combinedclusters

Perlmutter, Turner, White

For now…parameterizeFor now…parameterizeFor now…parameterizeH

igh-z supernova team

w < −1 ?ww < < −−1 1 ??• null dominant energy condition: energy doesn’t propagate

outside the light cone

• model with w < −1: negative kinetic energy scalar field

• instability cured with higher derivative terms?

p pρ ρ ρ≤ ⇒ − ≤ ≤

( )2 2expL φ φ= − − −

Aether of the 21st century?AetherAether of the 21of the 21stst century?century?

• It’s an infrared issue!

• Scalars (quintessence, trackers, ….)?

• Tensors (gravity at large distances)?

Braneless cosmologyBranelessBraneless cosmologycosmology• Old Friedmann law

200 00

2 23Pl

Pl

G M T

H M ρ

−

−

=

=

Friedmann (1921)

SNIa evidence for dark energy:

( )dzH z∫

Brane cosmologyBrane cosmologyBrane cosmology• Israel junction condition (Israel 1966)

An

: unit vector normal to the brane: the induced metric

: the extrinsic curvature

A

AB AB A BC

AB A C B

nh g n n

h nκ

= −

= ∇

iii

3*

BRANEM Tµν µνκ − = −

[ ].... discontinuity across the brane=

[ ] ( )discontinuity in second derivative of scale factor

a a a yδ′′ ′′ ′= +

the

brane

Brane cosmologyBrane cosmologyBrane cosmology• New Friedmann law Binetruy, Deffayet, Langlois (2000)

62 2*

46 36 ( , 0)M cH

a t yρ

−Λ= + +

=

• Possible solution Randall & Sundrum (2000)

Introduce a tension σ on the brane ρ ρ σ→ +6 6 6

2 2 2* * *46 36 18 36 ( , 0)

M M M cHa t y

σ σρ ρ− − − Λ

= + + + + =

unconventialcorrections

cosmological constant

(cancels?)Friedmannequation

6* 8

18 3M Gπσ

−

=

Brane cosmologyBrane cosmologyBrane cosmology• Friedmann equation modified today

• Gravitational force law modified at large distance

• Tired gravitons

• Gravity repulsive at cosmological distance

• n=1 KK graviton mode very light

• 3+1 Lorentz invariance broken

Freese & Lewis( ) 12cutoff1 nH Aρ ρ ρ − = +

Five-dimensional at cosmic distances Deffayet, Dvali & Gabadadze

Gravitons metastable - leak into bulk Gregory, Rubakov & SibiryakovDvali, Gabadadze & Porrati

Kogan, Mouslopoulos, Papazoglou, Ross & Santiago( ) 1Gpcm −∼

Chung, Kolb & Riotto

Csaki, Erlich, Hollowood & Terning

In the IR!

GpcR ∼

44 41

16 MS d x g R d x g LG R

µπ

= − − + −

∫ ∫

Carroll, Duvvuri, Turner, Trodden – dark energy

Modify gravityModify gravityModify gravity

( )4 2 4116 MS d x g R R d x g L

Gα

π= − + + + −∫ ∫…

Starobinski - inflation

How do we sort it out?How do we sort it out?How do we sort it out?

• Something is established-ΛCDM too good to ignoreSNIaSubtractionAgeLarge-scale structure…..

• Is it “just” a cosmological constant? Is ?• If what is the dynamics? 1w ≠ −

1w = −

How do we sort it out?How do we sort it out?How do we sort it out?

Cosmology in the “precision” eraCosmology in the “precision” eraCosmology in the “precision” era• ΛCDM is a most predictive cosmological model

• Fundamental parts are a mystery

• nature of dark matter• nature of dark energy• dynamics of inflation

• The best is yet to come!

ν

ν

ν

Heavy Elements: Ω=0.0003

Cold Dark Matter: Ω=0.25

Dark Energy (Λ): Ω=0.70

Stars:Ω=0.005

Free H & He:Ω=0.04

CRITICAL

TOTAL 1i iρ ρΩ ≡

Ω =

Cosmic PieCosmic PieCosmic Pie

ΛCDMΛΛCDMCDM

Neutrinos (ν): Ω=0.0047