Growing neutrinosand cosmological selection

QuintessenceQuintessence

C.WetterichC.Wetterich

A.Hebecker, M.Doran, M.Lilley, J.Schwindt,A.Hebecker, M.Doran, M.Lilley, J.Schwindt,C.MC.Müüller, G.Schller, G.Schääfer, E.Thommes,fer, E.Thommes,R.Caldwell, M.Bartelmann,R.Caldwell, M.Bartelmann,K.Kharwan, G.Robbers,T.Dent, S.Steffen,K.Kharwan, G.Robbers,T.Dent, S.Steffen,L.Amendola, M.BaldiL.Amendola, M.Baldi

Why now ?Why now ?

coincidence problemcoincidence problem

Why does dark energy become Why does dark energy become important important

in present cosmological epoch ?in present cosmological epoch ?

Cosm. Const. | Quintessence static | dynamical

QuintessenceQuintessenceDynamical dark energy ,Dynamical dark energy , generated by scalargenerated by scalar fieldfield

(cosmon)(cosmon)

C.Wetterich,Nucl.Phys.B302(1988)668, C.Wetterich,Nucl.Phys.B302(1988)668, 24.9.87 24.9.87P.J.E.Peebles,B.Ratra,ApJ.Lett.325(1988)LP.J.E.Peebles,B.Ratra,ApJ.Lett.325(1988)L17, 20.10.8717, 20.10.87

Prediction :Prediction :

homogeneous dark energy homogeneous dark energyinfluences recent cosmologyinfluences recent cosmology

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

Original models do not fit the present Original models do not fit the present observationsobservations……. modifications. modifications

here : cosmon coupling to neutrinoshere : cosmon coupling to neutrinos

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 !

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

exponential potentialexponential potentialconstant fraction in dark constant fraction in dark

energyenergy

can explain order of can explain order of magnitude magnitude

of dark energy !of dark energy !

ΩΩh h = n/= n/αα22

realistic quintessencerealistic quintessence

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

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

cosmic coincidencecosmic coincidence

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

No reason why w shouldNo reason why w shouldbe constant in time !be constant in time !

coincidence problemcoincidence problem

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

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

almost static dark energyalmost static dark energy

growinggrowingneutrinoneutrinomassmass

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 !

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

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 coupling to cosmon coupling to neutrinosneutrinos

basic ingredient :basic ingredient :

Cosmon coupling to Cosmon coupling to atomsatoms

Tiny !!!Tiny !!! Substantially weaker than gravity.Substantially weaker than gravity. Non-universal couplings bounded by Non-universal couplings bounded by

teststests

of equivalence principle.of equivalence principle. Universal coupling bounded by tests of Universal coupling bounded by tests of

Brans-Dicke parameter Brans-Dicke parameter ωω in solar in solar system.system.

Only very small influence on cosmology.Only very small influence on cosmology.

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,…

growing neutrinosgrowing neutrinos

end of matter end of matter dominationdomination

growing mass of neutrinosgrowing mass of neutrinos

at some moment energy density of at some moment energy density of neutrinos becomes more important than neutrinos becomes more important than energy density of dark matterenergy density of dark matter

end of matter dominated periodend of matter dominated period similar to transition from radiation similar to transition from radiation

domination to matter dominationdomination to matter domination this transition happens in the recent pastthis transition happens in the recent past

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

cascade mechanismcascade mechanism

triplet expectation value ~triplet expectation value ~

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

triplet expectation value ~ triplet expectation value ~ doublet squareddoublet squared

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

““singular” neutrino masssingular” neutrino mass

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

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

strong effective strong effective neutrino – cosmon neutrino – cosmon

coupling coupling for for φφ → → φφtt

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

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 !!

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 !

effective cosmological effective cosmological constantconstant

realistic value realistic value forforαα φφt t / M ≈ 276/ M ≈ 276

effective cosmological effective cosmological constantconstant

linked to neutrino masslinked to neutrino massrealistic value realistic value αα φφt t / M ≈ 276 :/ M ≈ 276 :needed for neutrinos to become non-needed for neutrinos to become non-relativistic in recent past -relativistic in recent past -as required for observed mass range as required for observed mass range of neutrino massesof neutrino masses

adjustment of one dimensionless parameteradjustment of one dimensionless parameterin order to obtain for the present time the in order to obtain for the present time the correct ratio between dark energy and neutrinocorrect ratio between dark energy and neutrinoenergy densityenergy density

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

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 !

cosmon evolutioncosmon evolution

neutrino fraction neutrino fraction remains smallremains small

mmνν = 0.45 eV = 0.45 eV

ΩΩνν

zz

equation of stateequation of state

present equationpresent equationof state given byof state given byneutrino mass !neutrino mass !

oscillating neutrino massoscillating neutrino mass

crossing timecrossing time

from matching between from matching between

early solution and late early solution and late solutionsolution

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 !

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

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

mass may turn out higher than upper mass may turn out higher than upper bound in model for cosmological constant bound in model for cosmological constant

( KATRIN, neutrinoless double beta decay ( KATRIN, neutrinoless double beta decay ))

How can quintessence be How can quintessence be distinguished from a distinguished from a

cosmological constant ?cosmological constant ?

Time dependence of dark Time dependence of dark energyenergy

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

M.Doran,…

effects of early dark effects of early dark energyenergy

modifies cosmological evolution (CMB)modifies cosmological evolution (CMB) slows down the growth of structureslows down the growth of structure

interpolation of interpolation of ΩΩhh

G.Robbers,G.Robbers,M.Doran,…M.Doran,…

bounds on bounds on Early Dark EnergyEarly Dark Energyafter WMAP’06after WMAP’06

G.Robbers,M.Doran,…G.Robbers,M.Doran,…

Cluster number relative to ΛCDM Two models

with 4% Dark Energy during structure formation

Fixed σ8

( normalization dependence ! )

Little Early Dark Energy can make Little Early Dark Energy can make large effect !large effect !

Non – linear enhancementNon – linear enhancement

More clusters at high redshift !

Bartelmann,Doran,…Bartelmann,Doran,…

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

EnEndd

Quintessence and Quintessence and solution of solution of

cosmological constant cosmological constant problem should be problem should be

related !related !

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)

approximate late approximate late solutionsolution

variables :variables :

approximate smooth solution approximate smooth solution ( averaged over oscillations )( averaged over oscillations )

dark energy fractiondark energy fraction

neutrino fluctuationsneutrino fluctuations

time when neutrinos become non – time when neutrinos become non – relativisticrelativistic

sets free streaming scalesets free streaming scale

neutrino equation of neutrino equation of statestate

cosmon equation of statecosmon equation of state

fixed point behaviour :fixed point behaviour :apparent tuningapparent tuning