Growing neutrinos and cosmological selection. Quintessence C.Wetterich A.Hebecker, M.Doran,...
-
date post
19-Dec-2015 -
Category
Documents
-
view
215 -
download
0
Transcript of Growing neutrinos and cosmological selection. Quintessence C.Wetterich A.Hebecker, M.Doran,...
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 ?
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” !
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 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,…
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 !
equation of stateequation of state
present equationpresent equationof state given byof state given byneutrino mass !neutrino mass !
crossing timecrossing time
from matching between from matching between
early solution and late early solution and late solutionsolution
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
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
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 )
neutrino fluctuationsneutrino fluctuations
time when neutrinos become non – time when neutrinos become non – relativisticrelativistic
sets free streaming scalesets free streaming scale