Neutrino lumps. connection between dark energy and neutrino properties present equation of state...

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Neutrino lumps

Transcript of Neutrino lumps. connection between dark energy and neutrino properties present equation of state...

Page 1: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

Neutrino lumps

Page 2: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

connection between dark connection between dark energy energy

and neutrino propertiesand neutrino properties

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

present dark energy density computablepresent dark energy density computablein terms of neutrino massin terms of neutrino mass

= 1.27= 1.27

Page 3: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

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

Page 4: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

connection between dark connection between dark energy energy

and neutrino propertiesand neutrino properties

present dark energy density computablepresent dark energy density computablein terms of neutrino massin terms of neutrino mass

= 1.27= 1.27

Energy density : Energy density : ρρ1/41/4 ~ ~ 2.4×10 2.4×10 -3-3 eV eV

Page 5: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

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 ?

Page 6: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

neutrino masses andneutrino masses anddark energy densitydark energy density

depend on time !depend on time !

Page 7: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

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

Page 8: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

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

Page 9: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

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 !

Page 10: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

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

Page 11: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

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

Page 12: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

realistic quintessencerealistic quintessence

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

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

Page 13: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

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

Page 14: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

cosmic coincidencecosmic coincidence

Page 15: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

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 ?

Page 16: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

A new role forA new role forneutrinos neutrinos

in cosmology ? in cosmology ?

Page 17: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

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

almost static dark energyalmost static dark energy

growinggrowingneutrinoneutrinomassmass

Page 18: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

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 !

Page 19: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

cosmon evolutioncosmon evolution

scaliscalingng

““stopped”stopped”

Page 20: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

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 )

Page 21: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

cosmon coupling to cosmon coupling to neutrinosneutrinos

basic ingredient :basic ingredient :

Page 22: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

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

Page 23: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

growing neutrinosgrowing neutrinos

Page 24: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

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

Page 25: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

cascade mechanismcascade mechanism

triplet expectation value ~triplet expectation value ~

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

Page 26: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

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

Page 27: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

““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

Page 28: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

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

Page 29: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

crossover fromcrossover fromearly scaling solution to early scaling solution to

effective cosmological effective cosmological constantconstant

Page 30: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

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

neutrino mass unimportant in early cosmologyneutrino mass unimportant in early cosmology

Page 31: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

growing neutrinos growing neutrinos change cosmon evolutionchange cosmon evolution

modification of conservation equation for neutrinosmodification of conservation equation for neutrinos

Page 32: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

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 !!

Page 33: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

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 !

Page 34: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy 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

Page 35: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

cosmon evolutioncosmon evolution

scaliscalingng

““stopped”stopped”

Page 36: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

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 ,…BertolamiN.Brouzakis , N.Tetradis ,…Bertolami

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

Page 37: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.
Page 38: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

How to compute the How to compute the CMB ?CMB ?

Page 39: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

Linear approximation Linear approximation breaks downbreaks down

Page 40: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

cosmon attractioncosmon attraction

much stronger than gravitational attractionmuch stronger than gravitational attraction neutrino mass changes with timeneutrino mass changes with time

new methods need to be developednew methods need to be developed non-linear hydro-dynamical equationsnon-linear hydro-dynamical equations N-body simulations for coupled quintessenceN-body simulations for coupled quintessence renormalization group improved renormalization group improved

resummationsresummations

Pettorino, Wintergerst, Mota , Amendola , Baldi, Catena ,Pettorino, Wintergerst, Mota , Amendola , Baldi, Catena ,Schrempp, Nunes , …Schrempp, Nunes , …

Page 41: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

non-linear fluid non-linear fluid equationsequations

local scalar potential : 2ßlocal scalar potential : 2ß22 stronger stronger than gravitational potentialthan gravitational potential

Page 42: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

evolution of single evolution of single neutrino lumpneutrino lump

Wintergerst, Pettorino, Mota,…Wintergerst, Pettorino, Mota,…

Page 43: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

virializationvirialization

Page 44: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

shrinking of radiusshrinking of radius

Page 45: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

density profiledensity profile

normalized to 1 in the center of the lumpnormalized to 1 in the center of the lump

Page 46: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

gravitational potentialgravitational potential

Page 47: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

cosmological gravitational cosmological gravitational potentialpotential

induced by neutrino lumpsinduced by neutrino lumps

Page 48: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

time evolution of linear and time evolution of linear and

non-linear gravitational non-linear gravitational potentialpotential

Page 49: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

backreactionbackreaction neutrino-mass inside lump different from neutrino-mass inside lump different from

cosmological neutrino-mass ( smaller )cosmological neutrino-mass ( smaller ) effective coupling ß smallereffective coupling ß smaller freezing of growthfreezing of growth

criterion for backreaction effects : criterion for backreaction effects : local ß local ß δΦδΦ order one order one cosmological ß cosmological ß δΦδΦ order 10 order 10-3-3

stop growth of a k-modes with k<kstop growth of a k-modes with k<kb b ifif kkb b

hits boundhits bound

Page 50: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

time evolution of linear and time evolution of linear and

non-linear gravitational non-linear gravitational potentialpotential

at z = 1.7 at z = 1.7 backreactionbackreactionsets insets in

Page 51: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

cosmological gravitational cosmological gravitational potentialpotential

induced by neutrino lumpsinduced by neutrino lumps

Page 52: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

Linear approximation Linear approximation breaks downbreaks down

Page 53: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

enhanced peculiar velocities enhanced peculiar velocities in bulk flowin bulk flow

modification of ISW modification of ISW correlationscorrelations

chances for observationchances for observation

Page 54: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

bounds on average neutrino bounds on average neutrino massmass

Page 55: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

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

Page 56: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

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

Page 57: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

EnEndd

Page 58: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

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

Page 59: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

““Fundamental” Fundamental” InteractionsInteractions

Strong, electromagnetic, weakinteractions

gravitation cosmodynamics

On astronomical length scales:

graviton

+

cosmon

Page 60: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

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 )

Page 61: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

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

Page 62: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

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 !

Page 63: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

neutrino massneutrino mass

seesaw seesaw andandcascadecascademechanismechanismm

omit generation omit generation structurestructure

triplet expectation value ~ doublet squaredtriplet expectation value ~ doublet squared

Page 64: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

cascade mechanismcascade mechanism

triplet expectation value ~triplet expectation value ~

Page 65: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

equation of stateequation of state

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

Page 66: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

Hubble parameterHubble parameteras compared to as compared to ΛΛCDMCDM

mmνν=0.45 eV=0.45 eV

Page 67: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

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

only small only small differencedifferencefrom from ΛΛCDM !CDM !

mmνν=0.45 =0.45 eVeV

Page 68: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

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

cosmological constant ?cosmological constant ?

Page 69: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

Time dependence of dark Time dependence of dark energyenergy

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

M.Doran,…

Page 70: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

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

Page 71: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

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

Page 72: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

interpolation of interpolation of ΩΩhh

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

Page 73: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

Early quintessence slows down Early quintessence slows down the the

growth of structuregrowth of structure

Page 74: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

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.

Page 75: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

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 ,…

Page 76: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

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

Page 77: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

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,…

Page 78: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

baryons :

the matter of stars and humans

ΩΩbb = 0.045 = 0.045

Page 79: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

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

Page 80: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

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

Page 81: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

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 :

Page 82: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

time varying electron time varying electron massmass

time variation of quantities time variation of quantities not related to tripletnot related to triplet

Page 83: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

Time variation of coupling constants must be tiny –

would be of very high significance !

Possible signal for Quintessence

Page 84: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

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)

Page 85: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.

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 !

Page 86: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.
Page 87: Neutrino lumps. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density.