new quantum origin of the universe structure v. mukhanov · 2012. 5. 23. · there always exist...
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Quantum Origin of the Universe Structure
V. Mukhanov ASC, LMU, München
Blaise Pascal Chair, ENS, Paris
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There exists background radiation with the temper 2.725ature T K= °
Penzias, Wilson 19652.725K Blackbody Spectrum of the CMB
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€
2009
€
Planck
€
???End 2012
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€
Hubble law
rrvr
comaχ=r&
Rate of expansion
vr( ) comr a t χ=rr
The Universe expands
t r
v 13,7bil. years
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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: :
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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
−:
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a
aλ ∝1Ta
∝
When the Universe was 1000 times smallerits temperature was about 2725 K°
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RecombinationNucleosynthesis
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Neutrinos decoupling,Electron-Positron pairsannihilation ( 1 sek):-4
Quark-gluon phase transition
10 sec:1010
Electro-weak phase transition
t −:
???
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Very homogeneous Inhomogeneous
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€
???
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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
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Gravitation is attractiveReason fo: rce 0
1iaa
-
a&
t0t0a&
it
ict
decelerated Friedmann Expansion
ia&INFLATION
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Predictionof inflation !
Ω0 ≡
E0pot
E0kin 1=
Ekin = 3E pot = −9
+1000000000
−1000000000
10000000091000000003
=
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How gravity can become "repulsive"?43Ga aπ ε= −&& ( )3p aε +
accelerationenergydensity pressure
"antigravity" +3 0 0 Only if p aε < > ≡⇒ &&
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Scenarios
Which concrete scenario was realized ???
???????????????????????????????????????????Energy density pressure , pε
( ) equation of s e tatp ε −for inflat ionp ε ε+ =
p ε≈ −
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Quantum Fluctuations and Galaxies
Inflation "wash out" all existing classical inhomogeneities and leaves classical desert
Where the ihhomogeneities come from?
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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)
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( )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−
∝ ∝
= &
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1H −
1H −
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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
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Power
-- ΛCDM
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Small-scale spectrum: summer 2011
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Ω = 1± 0.02Dark Matter & Dark Energy
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• All predictions so far consistent with CMB. Big goal: is index
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TE
E
CURRENT OBSERVATIONS
PLANCK FORECAST
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"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)
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