Have neutrinos to do with Dark Energy ?

Why neutrinos may play Why neutrinos may play a rolea role

Mass scales :Mass scales :

Dark Energy density : Dark Energy density : ρρ ~ ( 2×10 ~ ( 2×10 -3-3 eV ) eV )- 4- 4..

Neutrino mass : eV or below.Neutrino mass : eV or below.

Cosmological trigger : Cosmological trigger : Neutrinos became Neutrinos became non-relativistic only in the late non-relativistic only in the late Universe .Universe .

Neutrino energy density Neutrino energy density not much not much smaller than Dark Energy density .smaller than Dark Energy density .

Neutrinos can have substantial Neutrinos can have substantial coupling coupling to Dark Energy.to 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

What do we know about Dark Energy ?

Dark Energy Dark Energy dominates the Universedominates the Universe

Energy - density in the Energy - density in the UniverseUniverse

==

Matter + Dark EnergyMatter + Dark Energy

30 % + 70 %30 % + 70 %

Composition of the Composition of the universeuniverse

Atoms : Atoms : ΩΩb b = = 0.0450.045

Dark Matter : Dark Matter : ΩΩdmdm= = 0.250.25

Dark Energy : Dark Energy : ΩΩh h = 0.7= 0.7

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

Photons , gravitons : Photons , gravitons : insignificantinsignificant

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

Dark Energy !Dark Energy !

Dark Energy :Homogeneously distributed

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

predicts accelerated expansion predicts accelerated expansion of Universe of Universe

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

Observational bounds on Observational bounds on ΩΩhh

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

Why now problemWhy now problem

Why does fraction in Dark Why does fraction in Dark Energy increase Energy increase in present cosmological epoch ,in present cosmological epoch ,and not much earlier or much and not much earlier or much later ?later ?

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 = 7 = 7 10ˉ¹²¹10ˉ¹²¹

matter: matter: ρρmm/M/M4= 3 10ˉ¹²¹= 3 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 !

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 !

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 )

Neutrinos in cosmologyNeutrinos in cosmology

only small fraction of energy only small fraction of energy densitydensity

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

Neutrino cosmon Neutrino cosmon couplingcoupling

Strong bounds on atom-cosmon coupling from Strong bounds on atom-cosmon coupling from tests of equivalence principle or time variation tests of equivalence principle or time variation of couplings.of couplings.

No such bounds for neutrino-cosmon coupling.No such bounds for neutrino-cosmon coupling.

In particle physics : Mass generation In particle physics : Mass generation mechanism for neutrinos differs from charged mechanism for neutrinos differs from charged fermions. Seesaw mechanism involves heavy fermions. Seesaw mechanism involves heavy particles whose mass may depend on the value particles whose mass may depend on the value of the cosmon field. of the cosmon field.

neutrino massneutrino mass

seesaw seesaw andandcascadecascademechanismechanismm

omit generation omit generation structurestructure

triplet expectation value ~ doublet squaredtriplet expectation value ~ doublet squared

neutrino massneutrino mass

cascade cascade ( seesaw II )( seesaw II )mechanismmechanism

M.Magg, C.W. M.Magg, C.W. 1980 1980

( ? ) ….( ? ) ….C.Wetterich, Nucl.Phys.B187 (1981) C.Wetterich, Nucl.Phys.B187 (1981) 343343

Neutrino cosmon Neutrino cosmon couplingcoupling

realized by dependence of neutrino realized by dependence of neutrino massmass on value of cosmon field on value of cosmon field

β ≈ 1 β ≈ 1 : cosmon mediated attractive force : cosmon mediated attractive force between neutrinos has similar strength between neutrinos has similar strength as gravityas gravity

growing neutrinogrowing neutrinoquintessencequintessence

growing neutrinos growing neutrinos change cosmon evolutionchange cosmon evolution

modification of conservation equation for neutrinosmodification of conservation equation for neutrinos

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

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 )

cosmon evolutioncosmon evolution

scaliscalingng

““stopped”stopped”

neutrino lumpsneutrino lumps

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 ,… ; O.Bertolami ; Y.Ayaita , N.Brouzakis , N.Tetradis ,… ; O.Bertolami ; Y.Ayaita , M.Weber,…M.Weber,…

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

N-body code with fully N-body code with fully relativistic neutrinos and relativistic neutrinos and

backreactionbackreaction

Y.Ayaita,M.WebY.Ayaita,M.Weber,…er,…

one has to resolve local value of one has to resolve local value of cosmon fieldcosmon fieldand then form cosmological and then form cosmological average;average;similar for neutrino density, dark similar for neutrino density, dark matter and matter and gravitational fieldgravitational field

Formation of neutrino Formation of neutrino lumpslumps

Y.Ayaita,M.Weber,…Y.Ayaita,M.Weber,…

backreactionbackreactioncosmon field inside lumps does cosmon field inside lumps does not follow not follow cosmological evolutioncosmological evolution

neutrino mass inside lumps neutrino mass inside lumps smaller than smaller than in environment in environment L.Schrempp, L.Schrempp, N.Nunes,…N.Nunes,…

importance of backreaction :importance of backreaction :cosmological average of cosmological average of

neutrino massneutrino mass

Y.Ayaita , Y.Ayaita , E.Puchwein,…E.Puchwein,…

importance of importance of backreaction :backreaction :

fraction in Dark Energyfraction in Dark Energy

neutrino lumpsneutrino lumps

behave as non-relativistic behave as non-relativistic fluid with fluid with effective coupling to effective coupling to cosmoncosmon Y.Ayaita,Y.Ayaita,

M.Weber,M.Weber,……

φφ - dependent neutrino – - dependent neutrino – cosmon couplingcosmon coupling

neutrino lumps form and are disrupted by neutrino lumps form and are disrupted by oscillations in neutrino massoscillations in neutrino masssmaller backreaction smaller backreaction

oscillating neutrino massoscillating neutrino mass

oscillating neutrino oscillating neutrino lumpslumps

small oscillations in dark small oscillations in dark energyenergy

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

Small induced enhancement Small induced enhancement of dark matter power of dark matter power

spectrum at large scalesspectrum at large scales

Enhanced bulk velocitiesEnhanced bulk velocities

Enhancement of Enhancement of gravitational potentialgravitational potential

Test of allowed parameter space by Test of allowed parameter space by ISW effectISW effect

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

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

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

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

neutrino mass unimportant in early cosmologyneutrino mass unimportant in early cosmology

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

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 !!