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 V. N. Lukash Lukash V. N. Astro Space Centre of P.N. Space Centre of P.N. Lebedev Lebedev Physics Physics Astro Institute of the Russian Academy of Sciences Institute of the Russian Academy of Sciences
� Identification�problem Identification�problem � � Early�and�late�Universe���� Early�and�late�Universe���� � initial�conditions Generation of initial�conditions � Generation of � � Dark�side� Dark�side� of matter of matter � � On� On� the the eve�of�new�physics eve�of�new�physics �
Astronomers�see�structures unknown�to�physicists 0.15 � ����� 2 , h ω = ω + ω ≈ ω = Ω m c b x x
DM�non�interacted�with�radiation� DM�non�interacted�with�radiation� however�light�is�where�DM however�light�is�where�DM
What�we�see�is�structure�created� What�we�see�is�structure�created� from�initial�conditions�+�evolution from�initial�conditions�+�evolution observational�separation�of� observational�separation�of� the�early�and�late�Universe the�early�and�late�Universe no model the model theory of origin of no theory of initial conditions origin of matter
Geometry�of�the�Universe Geometry�of�the�Universe a (t) � zero�order� zero�order� Hubble diagram Hubble diagram � � first�order first�order � S- -mode mode ( S (density perturbations density perturbations) ) S ( k ) T- -mode mode (gravitational waves) T (gravitational waves) T ( k ) V- -mode mode (vortex perturbations) V (vortex perturbations) V ( k ) Cosmological�model�in�four�functions Cosmological�model�in�four�functions
zero�order:�late�Universe late�Universe zero�order:� � Hubble�parameter Hubble�parameter ÷ ÷ ÷ ÷ 0.7 h = 0.65 ÷ ÷ ÷ ÷ 0.7 h = 0.65 � � Relic�CMBR� Relic�CMBR� T = 2.725 K T = 2.725 K � � Eucleadian Eucleadian space space Ω Ω = 1 Ω Ω Ω Ω Ω Ω = 1 � � Dark�baryons Dark�baryons Ω Ω Ω Ω b Ω Ω Ω Ω = 0.5 b = 0.5 � � Cold�dark�matter���� Cold�dark�matter���� Ω Ω Ω c Ω Ω Ω Ω Ω = 0.23 c = 0.23 � � Dark�energy Dark�energy Ω Ω Λ Ω Ω Ω Ω Ω Ω = 0.7 Λ = 0.7 � Λ Λ Λ Λ Λ Λ � Theory�of�structure�formation Theory�of�structure�formation � no�theory�of� no�theory�of� matter�origin matter�origin
first�order:�early�Universe early�Universe first�order:� � Small�density�perturbations Small�density�perturbations � � Linear�Gaussian�field Linear�Gaussian�field � � Scale Scale( (invariant�spectrum�( invariant�spectrum�(n n S =1) S =1) � � Gravitational�waves�(T/S�<�0.2) Gravitational�waves�(T/S�<�0.2) � � Theory�of�initial�conditions Theory�of�initial�conditions � no�model�of�early� no�model�of�early� Universe��(H�&� γ ) Universe��(H�&� γ ) γ γ γ γ γ γ
Initial�conditions Initial�conditions S →��� seeds�for�LSS�structure S (galaxies,�clusters,�voids..) S+ +T T+ +V V → imprinted�in�CMB�structure S (anisotropy and�polarization)
S+T+V S+T+V
only S only S Tegmark, Zaldarriaga 2002
T & V V We live in the Universe with small T We live in the Universe with small T+V)/S > 0.2 ( T+V)/S ( ( ( > 0.2 are > 0.2 > 0.2 > 0.2 All values All values ( ( ( ( > 0.2 > 0.2 > 0.2 are All values All values 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 of S of S- of S of 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 = 2 ⇒ ⇒ ⇒ fixed by CMB ⇒ (10 - - -5 - 5 5 5 ) ) 2 2 2 + + = (10 = = (10 (10 ) ) fixed by CMB fixed by CMB fixed by CMB
Тheoretical heoretical physics� physics� Т T�is�more�fundamental than S�! T�is�not�small,�can�be�detected� Т – – a�clue�to�the�model�of�early�Universe a�clue�to�the�model�of�early�Universe Т V�( ( non�considered�today�(unknown�seeds) non�considered�today�(unknown�seeds) V�
Origin�of�cosmological� Origin�of�cosmological� perturbations perturbations quantum gravitational creation of massless massless quantum gravitational creation of fields under the action of non- -stationary stationary fields under the action of non intensive gravity (parametric coupling), intensive gravity (parametric coupling), seeds – – quantum fluctuations quantum fluctuations seeds � Creation of matter Creation of matter ( � (particles particles, , Grib ) s ) Grib, , Starobinsky Starobinsky… …1970 1970s Т - Generation of Т � Generation of -mode mode ( � (gravitational waves gravitational waves, , Grishchuk ) 1974 ) Grishchuk 1974 � Generation of Generation of S S- -mode mode ( � (density perturbations density perturbations, , V N L 1980 ) ) V N L 1980
Generation�of� T and S modes�in�Friedmann cosmology�is�a�quantum(mechanical�problem� q k ( η of�elementary�oscillators η )���[ � � = а/k, η η � � ω ω =� β ω ω β k] in�the�Minkowski space(time�in�the� β β α = α α ( η η ),� η external�parametric�field� α α α α α η η η = ∫ dt/a η η 2 α ( ) = ∫ ������ ′ 2 2 2 S L d , L q q η = − ω k k k 2 k 3
q - transverse-traceless component T of gravitational field 2 8 1 α = π β = a 2 / G , T q - gauge-invariant superposition of S longitudinal gravitational potential and the velocity potential of matter multiplied by the Hubble parameter 2 2 4 2 α = γ π β β = a / G , c / c S s � 2 γ = − = � ( H / H , H a / a )
Evolution�of�elementary�oscillators Evolution�of�elementary�oscillators α ′ ′ α ∂ � L 1 / 2 − ≡ = = = β ˆ p , U q q q � ′ ∂ α q k 2 α ω � − � ′ 2 2 2 2 2 = − ω = L ( q q ) ( p q ) 2 3 2 k ′ ′ ′ ′ ′ ′ ′ ′ 2 q ( U ) q 0 + + ω ω − − = = + + ω ω − − = = � adiabatic�zone� adiabatic�zone� 2 ω > U : q ~ const 2 ω < parametric�zone� parametric�zone� U : q ~ const 2 2 2 ω = ≈ − γ creation moment moment creation U ( )( aH )
Phase�information :�only�growing� Phase�information :�only�growing� mode�of�perturbations�is�created mode�of�perturbations�is�created sin cos κ κ κ κ κ κ κ κ ����� U 0 : q C C = = = = = = = = + + + + 1 2 κ κ κ κ κ κ κ κ a ( ~ ) η η η η κ κ κ κ = = = = ωη ωη ωη ωη growing�mode decaying�mode growing�mode decaying�mode � C C , C >> C = = >> = = >> >> vacuum: after�creation: vacuum: after�creation: 1 2 1 2 κ κ κ κ = = = = π π π π first�peak: first�peak: 3 π π π π η η η η � �� 200 = = = = πη πη πη πη ≅ ≅ ≅ ≅ 0 ≅ ≅ ≅ ≅ � p 0 η η η η rec
we�see�the�sound�! 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
Amplitude�information: initial�conditions�for�elementary�oscillators
2 2 �������� T 2 q , S q ≡ ≡ T S two polarizations of gravitational wave initial�vacuum�state , the�minimal�level�of�excitations��of�an� elementary�oscillator�in�adiabatic�zone � � � p 2 q 2 = = = = = = = = 2 Uniqueness of the ground state in Uniqueness of the ground state in the Friedmann Friedmann geometry geometry ( the (VNL VNL 2006) 2006)
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