Growing Neutrinosas a solution of thewhy now problemof 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
Dark EnergyDark Energyand theand the
Why now problemWhy now problem
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 %
MatterMatter : everything that clumps : everything that clumps
----------------------------------------
Dark EnergyDark Energy density is density isthe same at every point of space the same at every point of space
“ homogeneous ““ homogeneous “
Space between clumps is not Space between clumps is not
emptyempty
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 ?
Cosm. Const | Quintessence static | dynamical
Why now problemWhy now problem
Why is dark energy important now Why is dark energy important now and not in the past ?and not in the past ?
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=2.44×10×101818GeVGeV 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
connection between dark connection between dark energy energy
and neutrino propertiesand neutrino properties
present dark energy density given by neutrino masspresent dark energy density given by neutrino mass
= 1.27= 1.27
Energy density : Energy density : ρρ1/41/4 ~ ~ 2.4×10 2.4×10 -3-3 eV eV
neutrino masses andneutrino masses anddark energy densitydark energy density
depend on time !depend on time !
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
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 - of same order as dark matter -matter -
Original models do not fit the present observationsOriginal models do not fit the present observations……. modifications. modifications
CosmonCosmon Scalar field changes its value even Scalar field changes its value even
in the in the present present 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 !
V(V(φφ) =M) =M44 exp( - exp( - αφαφ/M )/M )
““Fundamental” Fundamental” InteractionsInteractions
Strong, electromagnetic, weakinteractions
gravitation cosmodynamics
On astronomical length scales:
graviton
+
cosmon
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 = 3(4)/= 3(4)/αα22
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”
No reason why w shouldNo reason why w shouldbe constant in time !be constant in time !
ww
ΩΩ
cosmic coincidencecosmic coincidence
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 ?
A new role forA new role forneutrinos neutrinos
in cosmology ? in cosmology ?
growing neutrino mass growing neutrino mass triggers transition to triggers transition to
almost static dark energyalmost static dark energy
growinggrowingneutrinoneutrinomassmass
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 !
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 )
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
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 cosmon plays crucial rolecosmon plays crucial role
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
= 1.27= 1.27
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
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
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 !
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”
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
Hubble parameterHubble parameteras compared to as compared to ΛΛCDMCDM
mmνν=0.45 eV=0.45 eV
Hubble parameter ( z < Hubble parameter ( z < zzc c ))
only small only small differencedifferencefrom from ΛΛCDM !CDM !
mmνν=0.45 =0.45 eVeV
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 Experimental determination of
neutrino mass may turn out higher neutrino mass may turn out higher than upper bound in model for than upper bound in model for cosmological constant cosmological constant
( KATRIN, neutrino-less double beta ( KATRIN, neutrino-less double beta decay )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 , …
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
two key featurestwo key features
1 ) Exponential cosmon potential and 1 ) Exponential cosmon potential and
scaling solutionscaling solution
V(V(φφ) =M) =M44 exp( - exp( - αφαφ/M ) /M )
V(V(φφ →→ ∞ ) → 0 ! ∞ ) → 0 !
2 ) Stop of cosmon evolution by 2 ) Stop of cosmon evolution by
cosmological triggercosmological trigger
EnEndd
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,…
small early and large small early and large presentpresent
dark energydark energy fraction in dark energy has fraction in dark energy has
substantially increased since end of substantially increased since end of structure formationstructure formation
expansion of universe accelerates in expansion of universe accelerates in present epochpresent epoch
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,M.Doran,…G.Robbers,M.Doran,…
Early quintessence slows down Early quintessence slows down the the
growth of structuregrowth of structure
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.
time variation of time variation of “fundamental constants”“fundamental constants”
M.Mueller , G.Schaefer , T.Dent , S.Steffen ,…M.Mueller , G.Schaefer , T.Dent , S.Steffen ,…
How to distinguish Q How to distinguish Q from from ΛΛ ? ?
A) Measurement A) Measurement ΩΩhh(z) H(z)(z) H(z)
i) i) ΩΩhh(z) at the time of(z) at the time of structure formation , CMB - structure formation , CMB -
emissionemission or nucleosynthesisor nucleosynthesis
ii) equation of state wii) equation of state whh((todaytoday) > -1) > -1B) Time variation of fundamental B) Time variation of fundamental
“constants”“constants”C) Apparent violation of equivalence C) Apparent violation of equivalence
principleprincipleD) Possible coupling between Dark Energy D) Possible coupling between Dark Energy
and Dark Materand Dark Mater
Quintessence and Quintessence and Time dependence of Time dependence of
“fundamental constants”“fundamental constants”
Fine structure constant depends on Fine structure constant depends on value ofvalue of
cosmon field : cosmon field : αα((φφ))
(similar in standard model: couplings depend (similar in standard model: couplings depend on value of Higgs scalar field)on value of Higgs scalar field)
Time evolution of Time evolution of φφ Time evolution of Time evolution of αα
Jordan,…Jordan,…
baryons :
the matter of stars and humans
ΩΩbb = 0.045 = 0.045
primordial abundances primordial abundances for three GUT modelsfor three GUT models
T.Dent,T.Dent,S.Stern,…S.Stern,…
present present observatioobservations : 1ns : 1σσ
HeHe
DD
LiLi
three GUT modelsthree GUT models unification scale ~ Planck scaleunification scale ~ Planck scale 1) All particle physics scales ~1) All particle physics scales ~ΛΛQCDQCD
2) Fermi scale and fermion masses ~ 2) Fermi scale and fermion masses ~ unification scaleunification scale
3) Fermi scale varies more rapidly than 3) Fermi scale varies more rapidly than ΛΛQCDQCD
ΔαΔα//αα ≈ 4 10 ≈ 4 10-4 -4 allowed for GUT 1 and 3 , allowed for GUT 1 and 3 , larger for GUT 2larger for GUT 2
ΔΔln(Mln(Mnn/M/MPP) ≈40 ) ≈40 ΔαΔα//αα ≈ 0.015 allowed ≈ 0.015 allowed
time varying Fermi scaletime varying Fermi scale
yields triplet expectation value yields triplet expectation value as function of doubletas function of doublet
t =t =
insert :insert :
time varying electron time varying electron massmass
time variation of quantities time variation of quantities not related to tripletnot related to triplet
Time variation of coupling constants must be tiny –
would be of very high significance !
Possible signal for Quintessence
Quintessence and Quintessence and solution of solution of
cosmological constant cosmological constant problem should be problem should be
related !related !
EnEndd
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)
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 of as required for observed mass range of neutrino massesneutrino massesφφt t / M : essentially determined by present / M : essentially determined by present neutrino mass neutrino mass 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
no fine tuning !no fine tuning !