What is our universe What is our universe made of ?made of ?

quintessence !fire , air,

water, soil !

Dark Energy Dark Energy dominates the Universedominates the Universe

Energy - density in the Energy - density in the UniverseUniverse

==

Matter + Dark EnergyMatter + Dark Energy

25 % + 75 %25 % + 75 %

What is Dark Energy ?

Composition of the Composition of the universeuniverse

Atoms : Atoms : ΩΩb b = 0.045= 0.045

Dark Matter : Dark Matter : ΩΩdmdm= = 0.2250.225

Dark Energy : Dark Energy : ΩΩh h = 0.73= 0.73

critical densitycritical density ρρcc =3 H² M² =3 H² M² critical energy density of the critical energy density of the

universe universe ( M : reduced Planck-mass , H : Hubble ( M : reduced Planck-mass , H : Hubble

parameter )parameter )

ΩΩbb==ρρbb//ρρcc

fraction in baryons fraction in baryons energy density in baryons over energy density in baryons over

critical energy densitycritical energy density

Abell 2255 Cluster~300 Mpc

Matter : Everything that clumpsMatter : Everything that clumps

Dark MatterDark Matter ΩΩmm = 0.23 total “matter” = 0.23 total “matter” Most matter is dark !Most matter is dark ! So far tested only through gravitySo far tested only through gravity Every local mass concentration Every local mass concentration

gravitational potentialgravitational potential Orbits and velocities of stars and Orbits and velocities of stars and

galaxies measurement of gravitational galaxies measurement of gravitational potential potential

and therefore of local matter distributionand therefore of local matter distribution

gravitational lens , HST

ΩΩmm= 0.27= 0.27

Gravitationslinse,HST

Gravitationslinse,HST

Gravitationslinse,HST

bullet clusterbullet cluster

Dark MatterDark Matterin collisionin collision

Abell 2255 Cluster~300 Mpc

Matter : Everything that clumpsMatter : Everything that clumps

ΩΩmm= 0.27= 0.27

Dark Energy : Dark Energy : Energy density that does Energy density that does not clumpnot clump

Photons , gravitons : Photons , gravitons : insignificantinsignificant

spatially flat universespatially flat universe

theory (inflationary universe )theory (inflationary universe )

ΩΩtottot =1.0000……….x =1.0000……….x

observation ( WMAP )observation ( WMAP )

ΩΩtottot =1.02 (0.02) =1.02 (0.02)

ΩΩtottot = 1 = 1

Picture of the big bangPicture of the big bang

Anisotropy of background Anisotropy of background radiationradiation ::

size of hot and cold spotssize of hot and cold spots

Size of temperature fluctuationsSize of temperature fluctuationsin dependence on size of in dependence on size of

anisotropies ( angle )anisotropies ( angle )

ca 1 degreeca 1 degreeca 10 degreesca 10 degrees angleangle

contrastcontrast

Acoustic oscillations in plasmaAcoustic oscillations in plasma

ca 1 degreeca 1 degreeca 10 degreeca 10 degree

acoustic waves acoustic waves in the early Universe in the early Universe

lengthlengthcompu-compu-tabletable

ΩΩtottot=1=1

spatially flat Universespatially flat Universe

ΩΩtottot = = 11

ΩΩtottot=0.25=0.25ΩΩtottot = 1 = 1

WMAP 2006WMAP 2006

Polarization

ΩΩtottot=1=1

Dark EnergyDark Energy

ΩΩmm + X = 1 + X = 1

ΩΩmm : 25% : 25%

ΩΩhh : 75% : 75% Dark Dark

EnergyEnergyh : homogenous , often ΩΛ instead of Ωh

Space between clumpsSpace between clumps is not empty : is not empty :

Dark Energy !Dark Energy !

Dark Energy :Homogeneously distributed

Dark Energy density isDark Energy density isthe same at every point of the same at every point of

space space

“ homogeneous “ “ homogeneous “

No force in absence of No force in absence of matter –matter –

“ In what direction should it “ In what direction should it draw ? “draw ? “

Einstein’s equations :Einstein’s equations :almost static Dark Energy almost static Dark Energy

predicts accelerated expansion predicts accelerated expansion of Universe of Universe

Predictions for dark energy Predictions for dark energy cosmologiescosmologies

The expansion of the Universe

accelerates today !

Structure formation : Structure formation : OneOne primordial fluctuation primordial fluctuation

spectrumspectrum

Waerbeke

CMB agrees with

Galaxy distribution

Lyman – α

and

GravitationalLensing !

Power spectrum Power spectrum Baryon - PeakBaryon - Peak

SDSSSDSS

galaxy – galaxy – correlation –correlation –functionfunction

Structure Structure formation : formation : OneOne primordial primordial fluctuation- fluctuation- spectrumspectrum

M.Tegmark + …M.Tegmark + …

Dark Energy :Dark Energy :observations fit together !observations fit together !

consistent cosmological model !

Composition of the Composition of the UniverseUniverse

ΩΩb b = 0.045 = 0.045 visible visible clumpingclumping

ΩΩdmdm= 0.2 = 0.2 invisibleinvisible clumpingclumping

ΩΩh h = 0.75 = 0.75 invisibleinvisible homogeneoushomogeneous

Dark Energy –a cosmic mystery

What is Dark Energy ?

Cosmological Constant or Quintessence ?

Cosmological ConstantCosmological Constant- Einstein -- Einstein -

Constant Constant λλ compatible with all compatible with all symmetriessymmetries

No time variation in contribution to No time variation in contribution to energy densityenergy density

Why so small ? Why so small ? λλ/M/M44 = 10 = 10-120-120

Why important just today ?Why important just today ?

Cosmological mass scalesCosmological mass scales Energy densityEnergy density

ρρ ~ ( 2.4×10 ~ ( 2.4×10 -3-3 eV )eV )- 4- 4

Reduced Planck Reduced Planck massmass

M=2.44M=2.44×10 ×10 2727 eV eV Newton’s constantNewton’s constant

GGNN=(8=(8ππM²)M²)

Only ratios of mass scales are observable !Only ratios of mass scales are observable !

homogeneous dark energy: homogeneous dark energy: ρρhh/M/M44 = 6.5 = 6.5 10ˉ¹²¹10ˉ¹²¹

matter: matter: ρρmm/M/M4= 3.5 10ˉ¹²¹= 3.5 10ˉ¹²¹

Time evolutionTime evolution

ρρmm/M/M4 4 ~ aˉ~ aˉ³ ³ ~~

ρρrr/M/M4 4 ~ aˉ~ aˉ44 ~ ~ t t -2-2 radiation dominated universeradiation dominated universe

Huge age small ratioHuge age small ratio

Same explanation for small dark Same explanation for small dark energy?energy?

tˉ² matter dominated universe

tˉ3/2 radiation dominated universe

Cosm. Const. | Quintessence static | dynamical

QuintessenceQuintessence Dynamical dark Dynamical dark energy ,energy ,

generated by generated by scalarscalar fieldfield

(cosmon)(cosmon)C.Wetterich,Nucl.Phys.B302(1988)668, C.Wetterich,Nucl.Phys.B302(1988)668, 24.9.8724.9.87P.J.E.Peebles,B.Ratra,ApJ.Lett.325(1988)L17, P.J.E.Peebles,B.Ratra,ApJ.Lett.325(1988)L17, 20.10.8720.10.87

Prediction :Prediction :

homogeneous dark energy homogeneous dark energyinfluences recent cosmologyinfluences recent cosmology

- of same order as dark - of same order as dark matter -matter -

Original models do not fit the present observationsOriginal models do not fit the present observations……. modifications. modifications

QuintessenceQuintessence

Cosmon – Field Cosmon – Field φφ(x,y,z,t)(x,y,z,t)

similar to electric field , but no direction similar to electric field , but no direction ( scalar field )( scalar field )Homogeneous und isotropic Universe : Homogeneous und isotropic Universe :

φφ(x,y,z,t)=(x,y,z,t)=φφ(t)(t)

Potential und kinetic energy of the cosmon -Potential und kinetic energy of the cosmon -fieldfield

contribute to a dynamical energy density of contribute to a dynamical energy density of the Universe ! the Universe !

CosmonCosmon Scalar field changes its value even Scalar field changes its value even

in the in the presentpresent cosmological epochcosmological epoch Potential und kinetic energy of Potential und kinetic energy of

cosmon contribute to the energy cosmon contribute to the energy density of the Universedensity of the Universe

Time - variable dark energy : Time - variable dark energy :

ρρhh(t) decreases with time !(t) decreases with time !

Evolution of cosmon fieldEvolution of cosmon field

Field equationsField equations

Potential V(Potential V(φφ) determines details of the ) determines details of the modelmodel

V(V(φφ) =M) =M4 4 exp( - exp( - αφαφ/M )/M )

for increasing for increasing φφ the potential the potential decreases towards zero !decreases towards zero !

CosmonCosmon Tiny massTiny mass

mmcc ~ H (depends on time ! ) ~ H (depends on time ! )

New long - range interactionNew long - range interaction

““Fundamental” Fundamental” InteractionsInteractions

Strong, electromagnetic, weakinteractions

gravitation cosmodynamics

On astronomical length scales:

graviton

+

cosmon

observation will decide !observation will decide !

Time dependence of dark Time dependence of dark energyenergy

cosmological constant : Ωh ~ t² ~ (1+z)-3

M.Doran,…

Observational bounds on Observational bounds on ΩΩhh

G.RobberG.Robbers , s , M.Doran ,M.Doran ,……

exponential potentialexponential potentialconstant fraction in dark constant fraction in dark

energyenergy

can explain can explain order order

of magnitude of magnitude

of dark energy !of dark energy !

ΩΩh h = 3/= 3/αα22 V(V(φφ) =M) =M4 4 exp( - exp( - αφαφ/M )/M )

Cosmic AttractorsCosmic Attractors

Solutions independent of initial conditions

typically V~t -2

φ ~ ln ( t )

Ωh ~ const.

details depend on V(φ)or kinetic term

early cosmology

realistic quintessencerealistic quintessence

fraction in dark energy has fraction in dark energy has to to

increase in “recent time” !increase in “recent time” !

Quintessence becomes Quintessence becomes important “today”important “today”

Key questions for Key questions for quintessencequintessence

Why does cosmon potential vanish for Why does cosmon potential vanish for infinite time ? infinite time ? V(V(φφ) =M) =M4 4 exp( - exp( - αφαφ/M )/M )

Why is time variation of fundamental Why is time variation of fundamental couplings small ? couplings small ? ( e.g. fine structure ( e.g. fine structure constant , electron-proton mass ratio )constant , electron-proton mass ratio )

Why does Dark Energy dominate only in Why does Dark Energy dominate only in recent cosmology ( Why now ? – recent cosmology ( Why now ? – problem )problem )

Key questions for Key questions for quintessencequintessence

Why does cosmon potential vanish for infinite Why does cosmon potential vanish for infinite time ? time ? V(V(φφ) =M) =M4 4 exp( - exp( - αφαφ/M )/M )

Dilatation symmetry in higher dimensions – not Dilatation symmetry in higher dimensions – not todaytoday

Why is time variation of fundamental couplings Why is time variation of fundamental couplings small ? small ? ( e.g. fine structure constant , electron-proton ( e.g. fine structure constant , electron-proton mass ratio )mass ratio )

Fixed point behavior – not todayFixed point behavior – not today

Why does Dark Energy dominate only in recent Why does Dark Energy dominate only in recent cosmology ( Why now ? – problem )cosmology ( Why now ? – problem )

Growing neutrino mass - Growing neutrino mass - todaytoday

coincidence problemcoincidence problem

What is responsible for increase of What is responsible for increase of ΩΩhh for z < 6 ? for z < 6 ?

Why now ?Why now ?

Neutrinos in cosmologyNeutrinos in cosmology

only small fraction of energy only small fraction of energy densitydensity

only sub-leading role ?only sub-leading role ?

Cosmon – neutrino Cosmon – neutrino couplingcoupling

Can be somewhat stronger than Can be somewhat stronger than gravitational couplinggravitational coupling

Neutrino mass depends on value of Neutrino mass depends on value of cosmon fieldcosmon field

In contrast : cosmon – atom coupling must In contrast : cosmon – atom coupling must be weaker than gravitybe weaker than gravity

Masses and coupling constants are determined by properties of vacuum !Similar to Maxwell – equations in matter

Fundamental couplings Fundamental couplings in quantum field theoryin quantum field theory

Spontaneous symmetry Spontaneous symmetry breaking to be confirmed breaking to be confirmed

at the LHCat the LHC

Have coupling constants in the early Universe other values ?Yes !

Restoration of symmetryRestoration of symmetryat high temperature at high temperature in the early Universein the early Universe

High THigh TSYM SYM <<φφ>=0>=0

Low TLow TSSBSSB<<φφ>=>=φφ00 ≠≠ 0 0

high T :high T :Less orderLess orderMore More symmetrysymmetry

Example:Example:MagnetsMagnets

In hot plasma In hot plasma of early Universe :of early Universe :

masses of electron und masses of electron und muon muon

not different!not different!

similar strength of similar strength of electromagnetic and weak electromagnetic and weak

interactioninteraction

Particle masses in Particle masses in quintessence cosmologyquintessence cosmology

can depend on value of can depend on value of cosmon fieldcosmon field

similar to dependence on value of Higgs fieldsimilar to dependence on value of Higgs field

Varying couplingsVarying couplings

only question :only question :

How strong is How strong is presentpresent variation of variation of couplings ?couplings ?

Cosmon – atom coupling Cosmon – atom coupling inducesinduces

violation of equivalence violation of equivalence principleprincipleDifferent couplings Different couplings

of cosmon to of cosmon to proton and neutronproton and neutron

Differential Differential accelerationacceleration

““Violation of Violation of equivalence equivalence principle”principle”

earth

p,n

p,n

cosmon

only apparent : new “fifth force” !only apparent : new “fifth force” !

growing neutrinogrowing neutrinoquintessencequintessence

growing neutrino mass growing neutrino mass triggers transition to triggers transition to

almost static dark energyalmost static dark energy

growinggrowingneutrinoneutrinomassmass

L.Amendola, M.Baldi,…L.Amendola, M.Baldi,…

effective cosmological effective cosmological triggertrigger

for stop of cosmon for stop of cosmon evolution :evolution :

neutrinos get non-neutrinos get non-relativisticrelativistic

this has happened recently !this has happened recently ! sets scales for dark energy !sets scales for dark energy !

connection between dark connection between dark energy energy

and neutrino propertiesand neutrino properties

present present equationequationof state given of state given bybyneutrino mass neutrino mass !!

present dark energy density given by neutrino masspresent dark energy density given by neutrino mass

= 1.27= 1.27

cosmological selectioncosmological selection

present value of dark energy density present value of dark energy density set by cosmological event :set by cosmological event :

neutrinos become non – relativistic neutrinos become non – relativistic

not given by ground state properties !not given by ground state properties !

cosmon coupling to cosmon coupling to neutrinosneutrinos

basic ingredient :basic ingredient :

Cosmon coupling to Cosmon coupling to neutrinosneutrinos

can be large !can be large !

interesting effects for cosmology if interesting effects for cosmology if neutrino mass is growingneutrino mass is growing

growing neutrinos can stop the growing neutrinos can stop the evolution of the cosmonevolution of the cosmon

transition from early scaling solution transition from early scaling solution to cosmological constant dominated to cosmological constant dominated cosmologycosmology

L.Amendola,M.Baldi,…L.Amendola,M.Baldi,…

Fardon,Nelson,WeinerFardon,Nelson,Weiner

dark energy fraction dark energy fraction determined by neutrino determined by neutrino

massmass

constant neutrino - cosmon coupling constant neutrino - cosmon coupling ββ

variable neutrino - cosmon couplingvariable neutrino - cosmon coupling

cosmon evolutioncosmon evolution

scaliscalingng

““stopped”stopped”

stopped scalar fieldstopped scalar fieldmimicks amimicks a

cosmological constantcosmological constant( almost …)( almost …)

rough approximation for dark energy :rough approximation for dark energy : before redshift 5-6 : scaling ( dynamical ) before redshift 5-6 : scaling ( dynamical ) after redshift 5-6 : almost static after redshift 5-6 : almost static

( cosmological constant )( cosmological constant )

growing neutrinos growing neutrinos change cosmon evolutionchange cosmon evolution

modification of conservation equation for neutrinosmodification of conservation equation for neutrinos

effective stop of cosmon effective stop of cosmon evolutionevolution

cosmon evolution almost stops cosmon evolution almost stops onceonce

neutrinos get non –relativisticneutrinos get non –relativistic ß gets largeß gets large

This alwaysThis alwayshappens happens for for φφ → → φφt t !!

crossover to dark energy crossover to dark energy dominated universedominated universe

starts at time when “neutrino force” becomes starts at time when “neutrino force” becomes important for the evolution of the cosmon fieldimportant for the evolution of the cosmon field

cosmological selection !cosmological selection !

Tests for growing Tests for growing neutrino quintessenceneutrino quintessence

Hubble parameterHubble parameteras compared to as compared to ΛΛCDMCDM

Hubble parameter ( z < Hubble parameter ( z < zzc c ))

only small only small differencedifferencefrom from ΛΛCDM !CDM !

bounds on average neutrino bounds on average neutrino massmass

Can time evolution of Can time evolution of neutrino mass be neutrino mass be

observed ?observed ?Experimental determination of neutrino mass Experimental determination of neutrino mass

may turn out higher than cosmological upper may turn out higher than cosmological upper bound in model with constant neutrino massbound in model with constant neutrino mass

( KATRIN, neutrino-less double beta decay )( KATRIN, neutrino-less double beta decay )

GERDAGERDA

neutrino fluctuationsneutrino fluctuations

neutrino structures become nonlinear neutrino structures become nonlinear at z~1 for supercluster scalesat z~1 for supercluster scales

stable neutrino-cosmon lumps exist stable neutrino-cosmon lumps exist N.Brouzakis , N.Tetradis ,…N.Brouzakis , N.Tetradis ,…

D.Mota , G.Robbers , V.Pettorino , …D.Mota , G.Robbers , V.Pettorino , …

Formation of neutrino Formation of neutrino lumpslumps

N- body simulation M.Baldi et N- body simulation M.Baldi et alal

ConclusionsConclusions

Cosmic event triggers qualitative Cosmic event triggers qualitative change in evolution of cosmonchange in evolution of cosmon

Cosmon stops changing after Cosmon stops changing after neutrinos become non-relativisticneutrinos become non-relativistic

Explains why nowExplains why now Cosmological selectionCosmological selection Model can be distinguished from Model can be distinguished from

cosmological constantcosmological constant

SummarySummary

o ΩΩhh = 0.73 = 0.73

o Q/Q/ΛΛ : dynamical und static dark energy will be : dynamical und static dark energy will be distinguishabledistinguishable

o growing neutrino mass can explain why now growing neutrino mass can explain why now problemproblem

o Q : time varying fundamental coupling Q : time varying fundamental coupling “constants” “constants”

violation of equivalence principleviolation of equivalence principle

EnEndd

varying neutrino – cosmon varying neutrino – cosmon couplingcoupling

specific modelspecific model can naturally explain why neutrino – can naturally explain why neutrino –

cosmon coupling is much larger than cosmon coupling is much larger than atom – cosmon coupling atom – cosmon coupling

neutrino massneutrino mass

seesaw seesaw andandcascadecascademechanismechanismm

omit generation omit generation structurestructure

triplet expectation value ~ doublet squaredtriplet expectation value ~ doublet squared

cascade mechanismcascade mechanism

triplet expectation value ~triplet expectation value ~

M.Magg , …M.Magg , …G.Lazarides , Q.Shafi , …G.Lazarides , Q.Shafi , …

cascadecascade

varying neutrino massvarying neutrino mass

triplet mass depends on cosmon field triplet mass depends on cosmon field φφ

neutrino mass depends on neutrino mass depends on φφ

εε ≈≈ -0.05 -0.05

cascade mechanismcascade mechanism

triplet expectation value ~triplet expectation value ~

““singular” neutrino masssingular” neutrino mass

triplet mass vanishes for triplet mass vanishes for φφ → → φφtt

neutrino mass diverges for neutrino mass diverges for φφ → → φφtt

strong effective strong effective neutrino – cosmon neutrino – cosmon

coupling coupling for for φφ → → φφtt

typical present value : typical present value : ββ ≈≈ 50 50 cosmon mediated attraction between neutrinoscosmon mediated attraction between neutrinosis about 50is about 5022 stronger than gravitational attraction stronger than gravitational attraction

crossover fromcrossover fromearly scaling solution to early scaling solution to

effective cosmological effective cosmological constantconstant

early scaling solution ( tracker early scaling solution ( tracker solution )solution )

neutrino mass unimportant in early cosmologyneutrino mass unimportant in early cosmology

effective cosmological effective cosmological triggertrigger

for stop of cosmon for stop of cosmon evolution :evolution :

neutrinos get non-neutrinos get non-relativisticrelativistic

this has happened recently !this has happened recently ! sets scales for dark energy !sets scales for dark energy !

dark energy fraction dark energy fraction determined by neutrino determined by neutrino

massmass

constant neutrino - cosmon coupling constant neutrino - cosmon coupling ββ

variable neutrino - cosmon couplingvariable neutrino - cosmon coupling

cosmon evolutioncosmon evolution

scaliscalingng

““stopped”stopped”

Equation of stateEquation of state

p=T-V pressure p=T-V pressure kinetic energykinetic energy

ρρ=T+V energy density=T+V energy density

Equation of stateEquation of state

Depends on specific evolution of the scalar Depends on specific evolution of the scalar fieldfield

Negative pressureNegative pressure

w < 0 w < 0 ΩΩh h increases increases (with decreasing z (with decreasing z

))

w < -1/3 expansion of the Universe isw < -1/3 expansion of the Universe is

acceleratingaccelerating

w = -1 cosmological constantw = -1 cosmological constant

late universe withlate universe withsmall radiation small radiation component :component :

A few referencesA few references

C.Wetterich , Nucl.Phys.B302,668(1988) , received 24.9.1987C.Wetterich , Nucl.Phys.B302,668(1988) , received 24.9.1987

P.J.E.Peebles,B.Ratra , Astrophys.J.Lett.325,L17(1988) , received 20.10.1987P.J.E.Peebles,B.Ratra , Astrophys.J.Lett.325,L17(1988) , received 20.10.1987

B.Ratra,P.J.E.Peebles , Phys.Rev.D37,3406(1988) , received 16.2.1988B.Ratra,P.J.E.Peebles , Phys.Rev.D37,3406(1988) , received 16.2.1988

J.Frieman,C.T.Hill,A.Stebbins,I.Waga , Phys.Rev.Lett.75,2077(1995)J.Frieman,C.T.Hill,A.Stebbins,I.Waga , Phys.Rev.Lett.75,2077(1995)

P.Ferreira, M.Joyce , Phys.Rev.Lett.79,4740(1997)P.Ferreira, M.Joyce , Phys.Rev.Lett.79,4740(1997)

C.Wetterich , Astron.Astrophys.301,321(1995)C.Wetterich , Astron.Astrophys.301,321(1995)

P.Viana, A.Liddle , Phys.Rev.D57,674(1998)P.Viana, A.Liddle , Phys.Rev.D57,674(1998)

E.Copeland,A.Liddle,D.Wands , Phys.Rev.D57,4686(1998)E.Copeland,A.Liddle,D.Wands , Phys.Rev.D57,4686(1998)

R.Caldwell,R.Dave,P.Steinhardt , Phys.Rev.Lett.80,1582(1998)R.Caldwell,R.Dave,P.Steinhardt , Phys.Rev.Lett.80,1582(1998)

P.Steinhardt,L.Wang,I.Zlatev , Phys.Rev.Lett.82,896(1999)P.Steinhardt,L.Wang,I.Zlatev , Phys.Rev.Lett.82,896(1999)