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Quantum Origin of the Universe Structure
V. Mukhanov ASC, LMU, München
Blaise Pascal Chair, ENS, Paris
There exists background radiation with the temper 2.725ature T K= °
Penzias, Wilson 19652.725K Blackbody Spectrum of the CMB
€
2009
€
Planck
€
???End 2012
€
Hubble law
rrvr
comaχ=r&
Rate of expansion
vr( ) comr a t χ=rr
The Universe expands
t r
v 13,7bil. years
Expanding Universe: FactsThe Universe is homogeneous and
isotropic on scales from 300 millions up to 13 billions light
Today:
-yearsThere exist structure on small scales:Planets, Stars, Galaxies, Clusters of galaxiesSuperclusters ....
There is nd heavy elements in ve
7ry
5% , 25% small amounts
aH He: :
There exist Dark Matter and Dark Energy
In past the Universe was VERY hot
5
When the Universe was about 1000 times smaller, it was extremely homogeneous
and isotropic in scales l 10a l δεε
−:
a
aλ ∝1Ta
∝
When the Universe was 1000 times smallerits temperature was about 2725 K°
RecombinationNucleosynthesis
Neutrinos decoupling,Electron-Positron pairsannihilation ( 1 sek):-4
Quark-gluon phase transition
10 sec:1010
Electro-weak phase transition
t −:
???
Very homogeneous Inhomogeneous
€
???
INFLATION
310 cmL −:
3310 cmcl−:
In 1090 causally disconnected regions δε / ε ≤ 10−5
.!!!
Why?
c
Ll 0
iaa
≈&&
Initial speed of expansion
speed of expansion today
Gravitation is attractiveReason fo: rce 0
1iaa
a&
t0t0a&
it
ict
decelerated Friedmann Expansion
ia&INFLATION
Predictionof inflation !
Ω0 ≡
E0pot
E0kin 1=
Ekin = 3E pot = −9
+1000000000
−1000000000
10000000091000000003
=
How gravity can become "repulsive"?43Ga aπ ε= −&& ( )3p aε +
accelerationenergydensity pressure
"antigravity" +3 0 0 Only if p aε < > ≡⇒ &&
Scenarios
Which concrete scenario was realized ???
???????????????????????????????????????????Energy density pressure , pε
( ) equation of s e tatp ε −for inflat ionp ε ε+ =
p ε≈ −
Quantum Fluctuations and Galaxies
Inflation "wash out" all existing classical inhomogeneities and leaves classical desert
Where the ihhomogeneities come from?
There always exist unavoidable Quantum Fluctuations
Quantum fluctuations in the density distribution are large (10-5 )
only in extremely small scales ( 10-33 cm),
but very small ( 10-58 ) on galactic scales ( 1025 cm)Can we transfer the large fluctuations from extremely small scales to large scales???
p x hΔ Δ ≥
!!!Yes only if in past the Universe went throughthe stage of accelerated expansion (inflatbut
ion)
( )Consider plane wave pertur ,bati eon: xp comik xδϕ Φ ∝r r
1
For given and the change of the amplitude with time depends on how big is
compared to the curvature scale (size of Einstein l
, ( ) / ( )
/ift)
com ph com
phys
k cm a k a t
H a a
λ
λ−
∝ ∝
= &
1H −
1H −
1 1/ 2H ε− −∝ 1 1/ 2H ε− −∝
Gravity waves
Scalar perturbations
( )1/ 21 / ,phδϕ ε+ + Φ
physλ
2 3
2 3
k
k
k
h k
Φ
( )2 3 111 /k Pl k Ha
k Op
εε ε
≈
⎛ ⎞Φ = ⎜ ⎟+ ⎝ ⎠
1 3 1 3 1lnS k Ha k Ha
p d pndε ε ε≈ ≈
⎛ ⎞ ⎛ ⎞− = − + + +⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠0< 0< 0.95 < nS < 0.97
( )1/ 2
1 1 k HaT pOS ε
≈⎛ ⎞= +⎜ ⎟⎝ ⎠
ln λ / λγ( )∝ λ1−nS or nS = 0.96
Power
-- ΛCDM
Small-scale spectrum: summer 2011
€
Ω = 1± 0.02Dark Matter & Dark Energy
• All predictions so far consistent with CMB. Big goal: is index
TE
E
CURRENT OBSERVATIONS
PLANCK FORECAST
"In models with the initial superdense de Sitter state ... such a large amount of relic gravitational waves is generated...that ... the very existence of this state can be experimentally"verified in the near future.(Starobinsky, 1980)