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Cosmological model : Cosmological model Cosmological model Cosmological model : : : : Cosmological model Cosmological model Cosmological model Cosmological model : : : from initial conditions from initial conditions from initial

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SLIDE 1
  • V. N.
  • V. N. Lukash

Lukash

Astro Astro Space Centre of P.N. Space Centre of P.N. Lebedev Lebedev Physics Physics Institute of the Russian Academy of Sciences Institute of the Russian Academy of Sciences

Cosmological model Cosmological model Cosmological model Cosmological model Cosmological model Cosmological model Cosmological model Cosmological model : : : : : : : :

from initial conditions from initial conditions from initial conditions from initial conditions from initial conditions from initial conditions from initial conditions from initial conditions to structure formation to structure formation to structure formation to structure formation to structure formation to structure formation to structure formation to structure formation

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SLIDE 2
  • Identificationproblem

Identificationproblem

  • EarlyandlateUniverse

EarlyandlateUniverse

  • Generation of

Generation of initialconditions initialconditions

  • Darkside

Darksideof matter

  • f matter
  • On

Onthe the eveofnewphysics eveofnewphysics

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SLIDE 3

2 x x b

h , Ω = ω ≈ ω + ω = ω

  • 0.15

c m

Astronomersseestructures unknowntophysicists

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SLIDE 4

DMnoninteractedwithradiation DMnoninteractedwithradiation

howeverlightiswhereDM howeverlightiswhereDM

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SLIDE 5
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SLIDE 6

Whatweseeisstructurecreated Whatweseeisstructurecreated frominitialconditions+evolution frominitialconditions+evolution

  • bservationalseparationof
  • bservationalseparationof

theearlyandlateUniverse theearlyandlateUniverse

the model

no theory of

  • rigin of matter

no model

theory of origin of initial conditions

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SLIDE 7

GeometryoftheUniverse GeometryoftheUniverse

  • zeroorder

zeroorder Hubble diagram Hubble diagram

  • firstorder

firstorder S S-

  • mode

mode (

(density perturbations density perturbations) )

T T-

  • mode

mode (gravitational waves)

(gravitational waves)

V V-

  • mode

mode (vortex perturbations)

(vortex perturbations)

Cosmologicalmodelinfourfunctions Cosmologicalmodelinfourfunctions

(t) a

) k ( S

) k ( V ) k ( T

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SLIDE 8
  • Hubbleparameter

Hubbleparameter h = 0.65 h = 0.65÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷0.7 0.7

  • RelicCMBR

RelicCMBR T = 2.725 K T = 2.725 K

  • Eucleadian

Eucleadian space space Ω Ω Ω Ω Ω Ω Ω Ω = 1 = 1

  • Darkbaryons

Darkbaryons Ω Ω Ω Ω Ω Ω Ω Ωb

b= 0.5

= 0.5

  • Colddarkmatter

ColddarkmatterΩ Ω Ω Ω Ω Ω Ω Ωc

c= 0.23

= 0.23

  • Darkenergy

Darkenergy Ω Ω Ω Ω Ω Ω Ω ΩΛ

Λ Λ Λ Λ Λ Λ Λ= 0.7

= 0.7

  • Theoryofstructureformation

Theoryofstructureformation

notheoryof notheoryof matterorigin matterorigin

zeroorder: zeroorder:lateUniverse lateUniverse

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SLIDE 9
  • Smalldensityperturbations

Smalldensityperturbations

  • LinearGaussianfield

LinearGaussianfield

  • Scale

Scale( (invariantspectrum( invariantspectrum(n nS

S=1)

=1)

  • Gravitationalwaves(T/S<0.2)

Gravitationalwaves(T/S<0.2)

  • Theoryofinitialconditions

Theoryofinitialconditions nomodelofearly nomodelofearly Universe(H& Universe(H&γ γ γ γ γ γ γ γ) )

firstorder: firstorder:earlyUniverse earlyUniverse

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SLIDE 10

S S →seedsforLSSstructure S S+ +T T+ +V V → imprintedinCMBstructure

(anisotropy andpolarization)

Initialconditions Initialconditions

(galaxies,clusters,voids..)

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SLIDE 11

S+T+V S+T+V

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SLIDE 12

Tegmark, Zaldarriaga 2002

  • nly S
  • nly S
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SLIDE 13

All values All values All values All values (

( ( ( ( ( ( (T+V)/S T+V)/S> 0.2 > 0.2 > 0.2 > 0.2 > 0.2 > 0.2 > 0.2 > 0.2 are

are are are excluded as in this case amplitude excluded as in this case amplitude excluded as in this case amplitude excluded as in this case amplitude

  • f S
  • f S
  • f S
  • f S-
  • mode is insufficient for the

mode is insufficient for the mode is insufficient for the mode is insufficient for the formation of the structure formation of the structure formation of the structure formation of the structure T+ + + + S+V= = = = (10 (10 (10 (10-

  • 5

5 5 5)

) ) ) 2

2 2 2 ⇒

⇒ ⇒ ⇒ fixed by CMB fixed by CMB fixed by CMB fixed by CMB

We live in the Universe with small We live in the Universe with small T

T&V V

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SLIDE 14

Т Тheoretical heoretical physics physics

Tismorefundamental than S! Tisnotsmall,canbedetected

Т Т – – acluetothemodelofearlyUniverse acluetothemodelofearlyUniverse V V( ( nonconsideredtoday(unknownseeds) nonconsideredtoday(unknownseeds)

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SLIDE 15

Originofcosmological Originofcosmological perturbations perturbations

quantum gravitational creation of quantum gravitational creation of massless massless fields under the action of non fields under the action of non-

  • stationary

stationary intensive gravity (parametric coupling), intensive gravity (parametric coupling), seeds seeds – – quantum fluctuations quantum fluctuations

  • Creation of matter

Creation of matter (

(particles particles, , Grib

Grib, , Starobinsky Starobinsky… …1970 1970s s)

)

  • Generation of

Generation of Т Т-

  • mode

mode (

(gravitational waves gravitational waves, , Grishchuk

Grishchuk 1974 1974)

)

  • Generation of

Generation of S S-

  • mode

mode (

(density perturbations density perturbations, , V N L

V N L 1980 1980 )

)

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SLIDE 16

GenerationofT and S modesinFriedmann cosmologyisaquantum(mechanicalproblem

  • felementaryoscillators

qk(η

η η η)[

  • = а/k,

ω ω ω ω=β

β β βk] intheMinkowski space(timeinthe externalparametricfieldα

α α α=α α α α(η η η η),η η η η=∫dt/a

( )

2 2 2 3 2 k k k

q q k 2 L , d L S ω − ′ α = η = ∫

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SLIDE 17

T

q

  • transverse-traceless component
  • f gravitational field

S

q

  • gauge-invariant superposition of

longitudinal gravitational potential and the velocity potential of matter multiplied by the Hubble parameter

1 8

2

= = β π α , G / a2

T

) a / a H , H / H ( c / c , G / a

s S

  • =

− = = =

2 2 2 2

4 γ β β π γ α

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SLIDE 18

q ) U ( q

2

= = = = − − − − ω ω ω ω + + + + ′ ′ ′ ′ ′ ′ ′ ′

q ˆ q k q

/ 2 1 −

= = β α

Evolutionofelementaryoscillators Evolutionofelementaryoscillators

2 2 2 2

2 ) aH )( ( U const ~ q : U const ~ q : U γ ω ω ω − ≈ = < >

  • adiabaticzone

adiabaticzone parametriczone parametriczone creation creation moment moment

) q p ( ) q q ( k L

2 2 2 2 2 3 2

2 2

  • −

= − ′ = ω ω α

α α ′ ′ = ′ ∂ ∂ ≡ U , q L p

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SLIDE 19
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SLIDE 20

Phaseinformation Phaseinformation:onlygrowing

:onlygrowing modeofperturbationsiscreated modeofperturbationsiscreated

κ κ κ κ κ κ κ κ + + + + κ κ κ κ κ κ κ κ = = = = = = = = cos C sin C q : U

2 1

  • )

~ ( η η η η a

growingmode growingmode decayingmode decayingmode vacuum: vacuum:

, C C

2 1

  • =

= = =

aftercreation: aftercreation:

2 1

C C >> >> >> >> ωη ωη ωη ωη = = = = κ κ κ κ

  • 200

3

rec p

≅ ≅ ≅ ≅ η η η η η η η η π π π π ≅ ≅ ≅ ≅ πη πη πη πη = = = =

  • firstpeak:

firstpeak:

π π π π = = = = κ κ κ κ

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SLIDE 21

weseethesound!

In the beginning was the Sound In the beginning was the Sound And the Sound was of the Big Bang And the Sound was of the Big Bang

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SLIDE 22

Amplitudeinformation:

initialconditionsforelementaryoscillators

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SLIDE 23

initialvacuumstate,

2 S 2 T

q S , q 2 T ≡ ≡

  • two polarizations of gravitational wave

2 q p

2 2

  • =

= = = = = = =

Uniqueness of the ground state in Uniqueness of the ground state in the the Friedmann Friedmann geometry geometry (

(VNL VNL 2006) 2006)

theminimallevelofexcitationsofan elementaryoscillatorinadiabaticzone

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SLIDE 24

GeneralscenarioofearlyUniverse

Vacuumisdeterminedinadiabaticzone,η η η η<η η η η0

2 q p

2 2

  • =

=

Parametriczone,η η η η>η η η η0

β α β α

η η η η 2 2 2 2 2 2

2 k q k q

  • =

≈

≤ ≥

βγ α α β

η η

4 2 2

2 2 2

≅         = ≡

> T S S T

q q S T

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SLIDE 25

Universalresult Universalresult

S T , M H ) ( T

P

γ γ π 4 2 4

2

=         − =

Expected Expected (

(T/S T/S <0.2): <0.2):

05 . γ , Gev 10 H

13

< < < < < < < <

  • Big Bang = Inflation (

Big Bang = Inflation (γ γ < 1 < 1) ! ) !

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SLIDE 26

T T is not negligible

is not negligible !

!

Power Power-

  • law inflation on massive field:

law inflation on massive field: the amplitude of T-mode is only five times less than amplitude of S-mode

Detection is possible ! Detection is possible !

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SLIDE 27

Darksideofmatter: Darksideofmatter:

where/whatwesearchfor? where/whatwesearchfor?

”Gothere,don’tknowwhere ”Gothere,don’tknowwhere Bringmethat,don’tknowwhat” Bringmethat,don’tknowwhat” /fromRussianfairytale/ /fromRussianfairytale/

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SLIDE 28

Only hypotheses Only hypotheses, , no theory no theory

Originofmatter Originofmatter

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SLIDE 29

MessagefromtheearlyUniverse MessagefromtheearlyUniverse DMmystery DMmystery isrelated isrelated tobaryonicasymmetry tobaryonicasymmetry

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SLIDE 30

Weliveinmatterworld Weliveinmatterworld

Prompt: Prompt:ε

εb

b ≅

≅ ≅ ≅ ≅ ≅ ≅ ≅ ε εDM

DM nowandearly

nowandearly

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SLIDE 31

Otherprompt:

coincidence ofLSSandCMBscales

3 1100 3200

2

z z

rec eq DM B

≅ ≅ =         η η

eq DM

k η 1 =

rec rec S B

c k η η 3 1 ≅ =

K K K Keq

eq eq eq

  • 1

1 1 1

DM DM DM DM

K K K Krec

rec rec rec

  • 1

1 1 1

B B B B ρ ρ ρ ρ

x

LSS: LSS: LSS: LSS:

CMB:

: : :

1 3 = =

eq rec B DM

k k η η

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SLIDE 32

WhereisDMmatter WhereisDMmatter? ?

Visible Visible: :

* *starsandgasingalaxies starsandgasingalaxies * *gasinclusters gasinclusters ( (Т Т~ ~keV keV ) )

Darkbaryons: Darkbaryons:

* *intergalacticgas intergalacticgas ( (Т Т~ ~0.1 0.1keV keV) ) * *MACHO(BH MACHO(BH, ,NS NS, ,WD WD, ,BD BD, ,jupiters jupiters, , а аsteroids steroids) )

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SLIDE 33

in galactic halo in galactic halo -

  • nomore

nomore than than20% 20%of

  • fМА

МАCHO CHO

therest therest 80% 80%( ( nonbaryonic nonbaryonic DM DM

Upperboundongalaxy UpperboundongalaxyМА МАCHOobjects(EROS) CHOobjects(EROS)

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SLIDE 34

Whereelseisnon Whereelseisnon( (baryonicDM? baryonicDM?

* *largevelocitydispersioninclusters largevelocitydispersioninclusters( (1930 1930) )

* * flatrotationcurvesinspiralgalaxies

flatrotationcurvesinspiralgalaxies (1970) (1970) * *galaxyclusters galaxyclusters’ ’ massesdetermined massesdetermined (1980) (1980) → → → → → → → → X X( (raygas raygas ( (Т Т~ ~ keV keV) ) → → → → → → → → gravitationallenses gravitationallenses

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SLIDE 35

theanswer: theanswer:non

non( (baryonicDMis baryonicDMis ingravitationallyboundsystems ingravitationallyboundsystems

weaklyinteracting weaklyinteracting particles particles donotdissipateasbaryons donotdissipateasbaryons

Baryonscooldown Baryonscooldownradiationally radiationally andresidetocenters andresidetocenters

  • fdarkmatterhalosgettingrotationalequilibrium
  • fdarkmatterhalosgettingrotationalequilibrium

Darkmatterremainsassemblingaround Darkmatterremainsassemblingaround visiblematteratscale~ visiblematteratscale~200 200 к кpc pc

( (themassofLocalGroup~ themassofLocalGroup~ 2 2 · · 10 1012

12 М

М

  • abouthalfinMilkyWayandA

abouthalfinMilkyWayandAndromeda ndromeda) )

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SLIDE 36

Matterbudgetissmall, Matterbudgetissmall,Ω Ωm

m<0.3!

<0.3!

(equivalently:smallpeculiarvelocities, (equivalently:smallpeculiarvelocities, time time7 7dependent dependentgrav grav.potential) .potential) Taking into account the Taking into account the flat 3 flat 3-

  • geometry

geometry ( (CMB CMB), we see that the rest 70% of the ), we see that the rest 70% of the full energy budget is in the form that full energy budget is in the form that took no part in gravitational clustering: took no part in gravitational clustering: * * we call it “dark energy” we call it “dark energy” * * it’s all we know about it it’s all we know about it * * far perspective of physics far perspective of physics

Ιε Ιε+p +pΙ Ι << << ε ε

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SLIDE 37
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SLIDE 38

Hypotheses Hypotheses ofnon

  • fnon(

(baryonicDM baryonicDM

10 10-

  • 21

21 eV

eV 10 10-

  • 5

5 eV

eV 10 10 keV keV 1 1 GeV GeV 100 100 GeV GeV 10 1013

13 GeV

GeV 10 1019

19 GeV

GeV 10 10-

  • 16

16-

  • 10

10-

  • 7

7 М

М

  • Gravitons

Gravitons Axions Axions Sterileneutrinos Sterileneutrinos Mirrorparticles Mirrorparticles Ма Маssive ssive particles particles Supermassive Supermassive particles particles Мо Моnopoles nopoles, ,defects defects Primordialblackholes Primordialblackholes mass mass candidats candidats

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SLIDE 39

BasicDMversion BasicDMversion

( (tobeverifiedin tobeverifiedinLHC LHC, , 2008 2008) )

– – unknownparticles unknownparticles (

(WIMPs WIMPs) )

( ( mass ~ 100 mass ~ 100 ГэВ, ГэВ, oneparticle

  • neparticle inaglass

inaglass 7 7 stable stable, , neutral neutral, ,weaklyinteracting weaklyinteracting(

(neutralino neutralino) )

New New physics physics! !

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SLIDE 40

Gain in the annihilation signal > 10 Probability for Earth to be in minihalo ~ 10% Excess of DM particles in minihalo ~ 10

Independentverification: Independentverification:WIMP

WIMPminihalos minihalos

Cuspproblem Cuspproblem– – akeytoDMphysics akeytoDMphysics

* *predictedinsimulations predictedinsimulations ... ... * *unobservedindwarfgalaxies unobservedindwarfgalaxies .. .. * *possibleconnectionwithmassive possibleconnectionwithmassiveBHs BHs

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SLIDE 41

DMalternative DMalternative– – modificationofgravity modificationofgravity

example: example: massive gravitons massive gravitons ( (gravitational creation gravitational creation in early Universe in early Universe, , monochromatic signal for LISA monochromatic signal for LISA) )

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SLIDE 42

Constraintsonparametersof Constraintsonparametersof а

а а а а а а аxion xion xion xion xion xion xion xion

allowed masses allowed masses conversion conversion а аxion xion-

  • photon

photon

  • а

аxion xion in magnetic field in magnetic field

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SLIDE 43

Largescalecorrelationofthe Largescalecorrelationofthe QSO polarization QSO polarization positionangle positionangle

mayariseinextragalacticmagneticfield mayariseinextragalacticmagneticfield duetoconversionofphotonsto duetoconversionofphotonstoaxions axions

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SLIDE 44

Constraints on Constraints on sterileneutrino

sterileneutrino sterileneutrino sterileneutrino sterileneutrino sterileneutrino sterileneutrino sterileneutrino

( DM is not dark because of massive neutrino decay ) ( DM is not dark because of massive neutrino decay )

remaining region for remaining region for 10 10 keV keV neutrinos neutrinos

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SLIDE 45

Conclusions Conclusions

  • Independent determination of

Independent determination of late and early Universe late and early Universe

T/S –

– a clue to very early Universe a clue to very early Universe

  • Stable predictions

Stable predictions: :

n nS

S ≅

≅ ≅ ≅ ≅ ≅ ≅ ≅ 1, 1, Ω Ω Ω Ω Ω Ω Ω Ωκ

κ κ κ κ κ κ κ ≅

≅ ≅ ≅ ≅ ≅ ≅ ≅ 0, 0, Ω Ω Ω Ω Ω Ω Ω ΩΛ

Λ Λ Λ Λ Λ Λ Λ ≅

≅ ≅ ≅ ≅ ≅ ≅ ≅ 0.7 0.7 SCM SCM: : f fb

b ~ 17%,

~ 17%, Ω Ω Ω Ω Ω Ω Ω Ωm

m ~ 0.3, h~ 0.7

~ 0.3, h~ 0.7

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SLIDE 46

Theoryisexhausted Theoryisexhausted

presentingalist presentingalist where/how where/how tosearchforDMparticles tosearchforDMparticles

Experiment’sturn Experiment’sturn

The situation reminds great historical The situation reminds great historical moments: moments: quarks

quarks, , W W-

  • Z

Z-

  • bosons

bosons, , neutrino neutrino

  • scillations
  • scillations,

, CMB CMB anisotropy, polarization anisotropy, polarization

WhyNatureisgeneroustous anddisclosesitssecrets?