11/28/03 chris pearson : fundamental cosmology 7: big bang ...€¦ · 11/28/03 chris pearson :...
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11/28/03 Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003
1
BIG BANG COSMOLOGY
“"In the beginning the Universe was created.This has made a lot of people very angry and been widely regarded as a bad move.”
The Hitch Hiker's Guide to the Galaxy—!Douglas Adams (1952-2001), British writer
““""In the beginning the Universe was created.In the beginning the Universe was created.This has made a lot of people very angry and been widely regarded as a bad move.This has made a lot of people very angry and been widely regarded as a bad move.””
The Hitch Hiker's Guide to the GalaxyThe Hitch Hiker's Guide to the Galaxy—!—!Douglas Adams (1952-2001), British writerDouglas Adams (1952-2001), British writer
Fundamental Cosmology: 7.Big Bang CosmologyFundamental Cosmology: 7.Fundamental Cosmology: 7.Big Bang CosmologyBig Bang Cosmology
PART IPART I
11/28/03 Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003
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BIG BANG COSMOLOGY
7.1: The 4 pillars of Standard Cosmology7.1: The 4 pillars of Standard Cosmology• The story so far
• Expansion of the Universe• Universe began in a BIG BANG about 13.7billion years ago• The Universe is expanding• The Universe is Isotropic and Homogeneous on the largest scales
• Origin of the cosmic background radiation• The CMB is the fossil of the Hot Big Bang Fireball• The surface of last scattering is the last time the bulk of the background radiationinteracted with normal matter• The temperature of that radiation has cooled from 3000K to 2.7K
• Nucleosynthesis of the light elements• Nucleons synthesized into the light elements in the first few minutes of the Big Bang• The Big Bang correctly predicts the ratio of Helium to Hydrogen ~25%
•Formation of galaxies and large-scale structure• Structure formation commences at the time of matter-radiation decoupling• The Big Bang provides the framework from which matter condenses to form large scalestructure
11/28/03 Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003
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BIG BANG COSMOLOGY
7.2: The Timeline of the Universe7.2: The Timeline of the UniverseTHE HOT BIG BANG
a = Radiation constantG = Newton’s Gravitational Constantc = speed of light
†
R2•
=8pGr
3R2 =
8pGro
3Ê
Ë Á
ˆ
¯ ˜
Ro4
R2 =8pGaTo
4
3c 2
Ê
Ë Á
ˆ
¯ ˜
Ro4
R2
The Friedmann Equation for radiation dominated universe
†
lo
l=
Ro
R= (1+ z)
redshift
integrating
†
R2
2Ro2 =
8pGaTo4
3c 2 t or RRo
=32pGa
3c 24 To t1/ 2
†
lmaxT = constantWiens Law
How does the temperature of the early Universe evolve ?
†
RoTo = RT 1
†
e = aT 4 = rc 2Energy density of radiation32
†
T =32pGa
3c 2
Ê
Ë Á
ˆ
¯ ˜
-1/ 4
t-1/ 2 ª1.5x1010 t-1/ 2
1
Temperature evolution in early Universe depends ONLY on Nature’s fundamental constants!Temperature evolution in early Universe depends ONLY on Nature’s fundamental constants!
11/28/03 Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003
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BIG BANG COSMOLOGY
7.2: The Timeline of the Universe7.2: The Timeline of the Universet=0T=∞
Atoms
Mat
ter
Clu
mpi
ngHen
nn
nm-
m+q-
q+W±
Zo?
InitialSingularity
Form
atio
n of
Sol
ar S
yste
m a
nd B
irth
of
Life
1010yrs2.73K
Epoc
h of
Gal
axy
Form
atio
n
109yrs30K
Firs
t St
ars
and
Gala
xies
(re-
ioni
zati
on)
107yrs300K
Epoc
h of
Rec
ombi
nati
on
3x105yrs3000K
Prim
ordi
al N
ucle
osyn
thes
is
3mins109K
n-p
rati
o fr
eeze
s
4s5x109K
n e de
coup
le, e
± ann
ihila
te
1s109K
Had
ron-
Lept
on R
eact
ions
shi
ft ->
Pro
ton
0.01s1011K
m- m
+ an
nihi
lati
on
10-4s1012K
quar
k - a
ntiq
uark
ann
ihila
tion
10-6s1013K
E-W
Pha
se T
rans
itio
n
10-12s1015K
Infl
atio
n10-35s1027K
Plan
ck T
ime
10-43s1031K
11/28/03 Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003
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BIG BANG COSMOLOGY
7.2: The Timeline of the Universe7.2: The Timeline of the UniverseEpochs of the Universe
Acceleration phase of the Universe
Structure Formation, first galaxies
Nucleosynthesis, Decoupling
Rapid Expansion/cooling (leptons/photons equilibrium)
Matter Anti Matter Asymmetry
Free Quarks in Thermal Equilibrium
Symmetry Breaking -> Exponential Expansion
String Theory / Quantum Cosmology
Birth of the Universe ?
<10-273presentAcceleration Era
<10-19<3000>106yrMatter Era
>10-19>3000<106yrRadiation Era
>108>1010<100sLepton Era
>1017>1012<10-4sHadron Era
>1058>1022<10-23sQuark Era
>1027<10-35sInflation Era
>1097>1031<10-43sPlanck Era
••0Big Bang
r (kg/m3)To(K)TimeEpoch
11/28/03 Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003
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BIG BANG COSMOLOGY
7.3: The Planck Time and Initial Singularity7.3: The Planck Time and Initial Singularity• In the Beginning……Planck era = 0 - 10-43 s after Big Bang
Running Time backwards
†
t Æ 0R Æ 0T Æ •
r Æ •
Ï
Ì Ô Ô
Ó Ô Ô
¸
˝ Ô Ô
˛ Ô Ô
Initial singularity - The Creation Event
• t<10-43s known as the Planck Era• Quantum Effects become important• Einstein’s Theory of gravity breaks down
Planck time can be defined via the Heisenberg Uncertainty Principle
†
DEDt ª h ª mpc2t p ª rp (ctp )3c 2t p ª
c 5t p4
Gtp2
From Plank time tp define
• Planck length lpª ctp• Planck density rpª 1/Gtp
2
• Planck mass mpª rp lp3
†
tp ªhGc 5
Ê
Ë Á
ˆ
¯ ˜
1/ 2
ª10-43 s lp ªhGc 3
Ê
Ë Á
ˆ
¯ ˜
1/ 2
ª1.7x10-35 m rp ªc 5
hG2 ª1096 kgm-3
mp ªhcG
Ê
Ë Á
ˆ
¯ ˜
1/ 2
ª 2.5x10-8 kg EP = mpc2 ª
hc 5
GÊ
Ë Á
ˆ
¯ ˜
1/ 2
ª1019GeV TP =EP
kB
ªhc 5
kB2G
Ê
Ë Á
ˆ
¯ ˜
1/ 2
ª1032K
11/28/03 Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003
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BIG BANG COSMOLOGY
7.3: The Planck Time and Initial Singularity7.3: The Planck Time and Initial Singularity• In the Beginning……What is the Planck scale ??
Quantum fluctuations of spacetime, of scale equal to Planck length, are of cosmic magnitude
For any particle of mass, m, Scale at which quantum effects become important is given by the Compton Wavelength
†
lc =h
mc
Scale at which self gravity of particle becomes important is the Schwarzchild Radius
†
RS =2Gm
c 2
Compton Wavelength & Schwarzchild Radius are comparable
For a particle of mass, mP = the Planck Mass
†
lc ª RSlC
RS
11/28/03 Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003
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BIG BANG COSMOLOGY
7.3: The Planck Time and Initial Singularity7.3: The Planck Time and Initial Singularity• In the Beginning……Before the Planck time ?? • Require Quantum Theory of Gravity ?
• (1) Quantum Gravity•Path Integrals (sum over possible histories) successful in Quantum Mechanics
• For gravity, sum over possible geometries
• Very complicated mathematical process · simplify · instantons.
• Assume most of 4D geometries in the path integral · very small contributions · can be neglected
• Path integral can be calculated but considering few geometries with largest contributions = instantons
•(2) Super Gravity• A quantum theory of elementary particles based on particle symmetry known as supersymmetry.• Naturally includes gravity along with other fundamental forces (electromagnetic, weak & strong nuclear)• Predicts quanta of gravity - graviton with spin 2 and its fermionic partner, the gravitino, spin 3/2.• Neither has yet been observed.
11/28/03 Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003
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BIG BANG COSMOLOGY
7.3: The Planck Time and Initial Singularity7.3: The Planck Time and Initial Singularity• In the Beginning……Before the Planck time ??
• (3) SUPERSTRING THEORY
quark
graviton
photon
• String theory + supersymmetry = Superstring Theory
•Sub quantum scales - Universe composed of strings - fundamental building blocks
•Requires ~10 dimensions with 6 being curled up at every point in space (Calabi-Yau Manifolds and Orbifolds)
•Think of different modes of vibration as representing different particles
•Predicts a massless spin 2 particle !
11/28/03 Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003
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BIG BANG COSMOLOGY
7.3: The Planck Time and Initial Singularity7.3: The Planck Time and Initial Singularity• In the Beginning……Before the Planck time ??
• (4) M THEORY• Problem with String theories are that there is simply too much freedom
• Bosonic String Theory (just decribes bosons)• Superstring (1,2) fundemental building block are closed strings• Superstring (3) fundemental building blocks are open strings• Bosonic String Theory + Superstring Theory = Heterotic String Theories (4,5)
• Too many parameters• Like exploring 5 different planets !!
• M theory• Superstring Theories not 5 different planets … •BUT rather 5 islands on the same planet!• Different aspects of some greater underlying pattern or order
• M- Theory (The Mother of all String Theories ??) formualted in 1 higher dimension ? (11 dimensions)
CURRENTLY OUR BEST BET FOR A THEORY OF EVERYTHING (TOE)
The superstring Planetary System
http://www.damtp.cam.ac.uk/
11/28/03 Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003
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BIG BANG COSMOLOGY
7.4: The Inflationary Era7.4: The Inflationary Era• Problems with the Hot Big Bang ModelInflationary Era = 10-43 - 10-35 s after Big Bang
1.1.THE HORIZON PROBLEMTHE HORIZON PROBLEM
ß the isotropy of the apparent causally disconnected regions of the CMB
2.2.THE FLATNESS PROBLEMTHE FLATNESS PROBLEM
ß the apparent remarkable closeness of W to 1
3.3.THE RELIC PROBLEMTHE RELIC PROBLEM
ß the apparent absence of relics from the Big Bang in our Universe
11/28/03 Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003
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BIG BANG COSMOLOGY
7.4: The Inflationary Era7.4: The Inflationary Era• The Horizon Problem
Speed of light is finite - define particle HORIZON
x
y
t
Area within light cone: dS2>0This is a timelike interval ‡ communication possible.
Area outside light cone: dS2<0Events that are causally disconnected from observer.
spacelike intervals ‡ no communication possible.
†
ds2 = c 2dt 2 - (dx 2 + dy 2 + dz2)Recall: SR Metric
HORIZON - distance, for a given time, over which information can be exchanged
(measure the same temperature in CMB)(surface of last scattering- last time matter and radiation were in equilibrium)
1800
Earth
11/28/03 Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003
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BIG BANG COSMOLOGY
7.4: The Inflationary Era7.4: The Inflationary Era• The Horizon Problem
HORIZON distance (dH) is the proper distance (dP) travelled by a photon since t=0 › tH
†
dH = dP t= 0t= t H = R(tH )r = R(t) c
R(t)dt
0
t HÚ
†
dS2 = c 2dt 2 - R2(t) dr2
1- kr2 + r2(dq 2 + sin2 qdf 2)Ê
Ë Á
ˆ
¯ ˜ R-W Metric
†
=3ctH R µ t 2 / 3 (matter dominated)2ctH R µ t1/ 2 (radiation dominated)
Ï Ì Ó
¸ ˝ ˛
ª c tH
(measure the same temperature in CMB)(surface of last scattering- last time matter and radiation were in equilibrium)
1800
Horizon at the surface of last scattering (tSLS~3x105yrs ~1013s) dH (t=tSLS) ~ 0.3Mpc
The (angular diameter) distance to the surface of last scattering dA ~ 13Mpc
†
dA =dP (to)1+ z( )
= dP (te ) angular diameter distance not equal to proper distance NOW but rather theproper distance at the time the light was emitted te (for our example te=tSLS) !
11/28/03 Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003
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BIG BANG COSMOLOGY
7.4: The Inflationary Era7.4: The Inflationary Era• The Horizon Problem
1800
Horizon at surface of last scattering dH (tSLS)~0.3Mpc
The angular diameter distance dA~13Mpc
dA
dH
qH
The horizon distance of the surface of last scattering subtends and angle of
†
qH =dH (tSLS )
dA
ª0.313
ª1.3o
• CMB is highly isotropic -looking in opposite directions To is identical to 1 part in 10,000 )• These opposite regions appear never to have been in causal contact• But opposite points in CMB are ~90 horizon distances apart !!• So how do they know that they should be at the same temperature??• This apparently violates causality
11/28/03 Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003
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BIG BANG COSMOLOGY
7.4: The Inflationary Era7.4: The Inflationary Era• The Flatness Problem
WMAP CMB Observations: The Universe is almost flat today: Wo~1± 0.02How about in the past ?
†
W -1 =k c 2
R2H 2†
˙ R 2
R2 = H 2 =8pGr
3-
kc 2
R2 = WH 2 -kc 2
R2Friedmann eqn.
Matter dominated Era:
†
R µ t 2 / 3 fi R2H 2 = ˙ R 2 µ t-2 / 3
Radiation dominated Era:
†
R µ t1/ 2 fi R2H 2 = ˙ R 2 µ t-1
†
W -1 t
W -1 to
=R2H 2( )to
R2H 2( )t
Evolution of W
11/28/03 Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003
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BIG BANG COSMOLOGY
7.4: The Inflationary Era7.4: The Inflationary Era• The Flatness Problem
to~ 13.7Gyr=4x1017s ‡ Wo~1± 0.02
†
W -1 t
W -1 to
=tto
Ê
Ë Á
ˆ
¯ ˜
matter
2 / 3
=tto
Ê
Ë Á
ˆ
¯ ˜
radiation
teq~ 106yr = 1013s ‡ |1-W| < 5x10-7Matter Radiation Equality
tBBN~ 3mins = 180s ‡ |1-W| < 10-18Big Bang Nucleosynthesis
tP~ 10-43s ‡ |1-W| < 10-63Planck Time
• Why is the Universe so FLAT
• Fine Tuning to > 1 part in 1060
• Why did the Universe not expand - contract back to a big crunch very quickly
• Why did the Universe not expand so quickly that galaxies and life were unable to form
• Do we live in a very special part of the Cosmological Parameter Space
• Anthropic Principle ?
11/28/03 Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003
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BIG BANG COSMOLOGY
PHASE TRANSITION
7.4: The Inflationary Era7.4: The Inflationary Era• The Relic Problem
GravityGravityGravity
Weak NuclearWeak NuclearWeak Nuclear
ElectromagneticElectromagneticElectromagnetic
Strong NuclearStrong Nuclear
STRENGTH
GUT
TOEELECTROWEAK
t=10-43sT=1031KE=1019GeV
t=10-35sT=1027KE=1015GeV
t=10-12sT=1015KE=102GeV
• At high energies the forces of nature unify
• Symmetry · Forces become indistinguishable from each other
• Universe cools · temperature drops · symmetry breaks · phase transition
• Like water freezing into ice · defects appear on cooling
11/28/03 Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003
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BIG BANG COSMOLOGY
7.4: The Inflationary Era7.4: The Inflationary Era• The Relic Problem
• Phase transition · loss of symmetry · topological defects• Predicted for GUT (strong/electroweak unification) t=10-35s, T=1027K, E=1015GeV• Compare with freezing water
• different ice nucleation sites• different axes (domains) of symmetry · topological defects
• 0D point like defects = Magnetic Monopoles (isolated North/South poles)• formed when spherical symmetry is broken
• 1D linear defects = Cosmic Strings• formed when axial / cylindrical symmetry is broken
• 2D sheet like defects = Textures• formed when higher symmetries are broken
Magnetic Monopole rest energy ~ 1015GeV · E=mc2 · mass ≡ bacterium
VERY BIG!!
11/28/03 Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003
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BIG BANG COSMOLOGY
7.4: The Inflationary Era7.4: The Inflationary Era• The Relic Problem• Magnetic Monopoles
THE MAGNETIC MONOPOLE SONGMarian McKenzie, 2-01
(To the tune “Toplady”,which is usually used for the hymn “Rock of Ages”)
As the day requires the night,
As the left requires the right,
So are north and south entwined.
Then be sure to bear in mind --
As you strive for physics goals --
NO MAGNETIC MONOPOLES!
Recording (As performed by the choir of St. James United Church of Christ, Havertown PA):
11/28/03 Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003
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BIG BANG COSMOLOGY
7.4: The Inflationary Era7.4: The Inflationary Era• The Relic Problem
• Phase Transition · symmetry breaking · topological defects• Symmetry survives were areas of Universe are in equilibrium• Therefore, expect one topological defect / horizon distance
Horizon distance at tGUT
†
dH = 2c tGU T
Number density of Monopoles
†
1dH
3 ª10146 Mpc-3
with energy density
†
mc 2
dH3 ª10161GeVMpc-3
†
eg = aT 4 ª10170GeVMpc-3Still small compared to radiation energy density
†
a = 4.2x1061GeV Mpc-3K-4 = radiation constant
• BUT: Monopoles become non-relativistic at early times eµR-3 (c.f., radiation eµR-4)• t~10-12s · Dominate the energy density and CLOSE the Universe• However…. We are here ….. So where are the Monopoles ????
11/28/03 Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003
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BIG BANG COSMOLOGY
7.4: The Inflationary Era7.4: The Inflationary Era• Problems with the Hot Big Bang ModelInflationary Era = 10-43 - 10-35 s after Big Bang
1.1.THE HORIZON PROBLEMTHE HORIZON PROBLEMß the isotropy of the apparent causally disconnected regions of the CMB
2.2.THE FLATNESS PROBLEMTHE FLATNESS PROBLEMß the apparent remarkable closeness of W to 1
3.3.THE RELIC PROBLEMTHE RELIC PROBLEMß the apparent absence of relics from the Big Bang in our Universe
The Cure ?The Cure ?
11/28/03 Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003
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BIG BANG COSMOLOGY
7.4: The Inflationary Era7.4: The Inflationary Era• InflationInflationary Era = 10-43 - 10-35 s after Big Bang
Inflationary Epoch
t 1980s, Alan Guth - Inflation Theory -t Period between 10-36 and 10-34 st Small portion of Universe balloons outward to become today’s visible Universe.t Can solve horizon, flatness, relic problems !!
11/28/03 Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003
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BIG BANG COSMOLOGY
7.4: The Inflationary Era7.4: The Inflationary Era• InflationInflationary Era = 10-43 - 10-35 s after Big Bang
• During inflation the Universe accelerates• Need negative pressure, or large, positive L
†
R2•
R2 = H 2 =8pGr
3-
kcR2
2
+L3
fiL3
†
R••
= -4pGr
3R +
LR3
fiLR3
Friedmann Equations become
†
R µeL1/2
3t= eHt
De Sitter expansion
注意: Hubble Parameter during inflation is constant =(L/3)1/2
Universe expands exponentially
11/28/03 Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003
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BIG BANG COSMOLOGY
7.4: The Inflationary Era7.4: The Inflationary Era• Inflation - A Possible Mechanism ?
•GUT symmetry breaking
• t<10-36s · Universe dominated by a scalar field f
• GUT theories Higgs Field mediated by Higgs Boson pervades all of space-time, at high temperatures, f =0• Higgs Boson responsible for the particle masses ?
• For the symmetry to break and the forces to separate, the Higgs field must acquire a non-zero value
Spontaneous Symmetry Breaking important aspect of particle physics gauge theories
In the language of group theory:
†
SU(5) Æ SU(3) x SU(2) x U(1)GUT QCD EW EMschematically
11/28/03 Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003
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BIG BANG COSMOLOGY
7.4: The Inflationary Era7.4: The Inflationary Era• Inflation - A Possible Mechanism ?
• In the ordinary vacuum, Higgs field is non-zero
• This is lowest (degenerate) energy state or TRUE VACUUM
• f =0 state = meta-stable state
• Shape of the Higgs field has unique characteristic
• Phase transition is slow compared to cooling of Universe
• Regions of Universe supercool without breaking symmetry
• Like water super cooling 253K without turning to ice
• Supercooled regions in a state known as FALSE VACUUM
• Higgs field finally reaches lowest state- symmetry breaks, domains of true vacuum eat into false vacuum
• True vacuum represents lowest energy density state · pressure =0
• For true vacuum to expand into false vacuum, pressure of false vacuum must be negative · Repulsive Force
• False Vacuum acts like a Cosmological Constant L
• Symmetry breaks - latent heat stored in Higgs Field released and re-heats the Universe - inflation ends
11/28/03 Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003
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BIG BANG COSMOLOGY
7.4: The Inflationary Era7.4: The Inflationary Era• Inflation - The Mechanics
Assume an inflation scalar field f and corresponding potential V
If inflation field changes only very slowly with time
†
˙ f 2 << V fi r ª -P ª V
Inflation can drive expansion if there is a period of
• Large V such that the potential dominates energy density of the Universe
†
˙ f • small
• The Higgs Mechanism
†
ef =12
˙ f 2 + V (f)
†
pf =12
˙ f 2 -V (f)Gives a pressure and a energy density of the inflation field1 2
SEMINAR 3 :Fluid Equation
†
˙ e + 3H(e + P) = 0 1
2
†
˙ ̇ f + 3H ˙ f = -dVdf
Equation of motion of a particle being accelerated by a force µ dV/df and being impeded by a frictional force µ particle speed (the Hubble Friction)
The Expansion of the Universe provides the Hubble Friction term that slows the transition of the Inflation Field
†
3H ˙ f
11/28/03 Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003
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BIG BANG COSMOLOGY
7.4: The Inflationary Era7.4: The Inflationary Era• Inflation - The Cure for the Problems
1. THE HORIZON PROBLEM1. THE HORIZON PROBLEMß the isotropy of the apparent causally disconnected regions of the CMB
• Inflate from a small sub horizon region•Seemingly causally disconnected points today would’ve been in causal contact before inflation• Inflation creates bubble Universes seperated by domain walls of order of Horizon
Horizon
Today’sObservableUniverse
Pre-inflationary universe
11/28/03 Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003
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BIG BANG COSMOLOGY
7.4: The Inflationary Era7.4: The Inflationary Era• Inflation - The Cure for the Problems
2. THE FLATNESS PROBLEM2. THE FLATNESS PROBLEMß Can make the Universe arbitrarily flat
• During inflation, H is constant: W is driven relentlessly towards unity
†
W -1 =k c 2
R2H 2 Æ 0
• We needed flatness to ~10-63
• ‡ need >1031 inflation
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BIG BANG COSMOLOGY
7.4: The Inflationary Era7.4: The Inflationary Era• Inflation - The Cure for the Problems
3. THE RELIC PROBLEM3. THE RELIC PROBLEMß the apparent absence of relics from the Big Bang in our Universe
• Inflation pushes domain boundaries beyond our horizon distance• The density of relics is diluted
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BIG BANG COSMOLOGY
7.4: The Inflationary Era7.4: The Inflationary Era• INFLATION - SUMMARY
• Require Flatness 1031
• Require Horizon ~100• For Relics depends on details of the physics
• For inflation from t1=10-36 (1/H1) to t2=10-34 s · 100 e foldings !
40
20
0
-20
-40
-60 inflation
Standard big bang
-40 -30 -20 -10 0 10lg(t) {s}
lg(R
) {m
}
†
R µeL1/2
3t= eHt
Inflation of quantum fluctuations · macroscopic scales · the seeds of STRUCTURE FORMATION
†
R2 /R1 = et2-t1
t1 = e99 =1043
During the inflationary era
†
T2 /T1 =10-43
But energy in Higgs Field reheats
11/28/03 Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003
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BIG BANG COSMOLOGY
“"In the beginning the Universe was created.This has made a lot of people very angry and been widely regarded as a bad move.”
The Hitch Hiker's Guide to the Galaxy—!Douglas Adams (1952-2001), British writer
““""In the beginning the Universe was created.In the beginning the Universe was created.This has made a lot of people very angry and been widely regarded as a bad move.This has made a lot of people very angry and been widely regarded as a bad move.””
The Hitch Hiker's Guide to the GalaxyThe Hitch Hiker's Guide to the Galaxy—!—!Douglas Adams (1952-2001), British writerDouglas Adams (1952-2001), British writer
Fundamental Cosmology: 7.Big Bang CosmologyFundamental Cosmology: 7.Fundamental Cosmology: 7.Big Bang CosmologyBig Bang Cosmology
PART IIPART II
11/28/03 Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003
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BIG BANG COSMOLOGY
7.5: The Evolution of the Big Bang7.5: The Evolution of the Big Bang Thermal Equilibrium in the Early Universe
GUT(Higgs?)
LEPTONS
QUARKS
e+e-
nn
q
q
e-
n
qqq
g
g
g
• For any particle X of mass, m, there will be an epoch where kT~mc2
†
g + g ¤ X + X • Creation of particle anti-particle pair creation becomes favourable
• For kT>mc2 : number of particles ~ number of photons
• For kT<mc2 : pairs can no longer be created fi annihilation & freeze out
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BIG BANG COSMOLOGY
7.5: The Evolution of the Big Bang7.5: The Evolution of the Big Bang THE QUARK ERA• 3 Quarks for Muster Mark (Finnegan’s Wake)Quark era = 10-34 - 10-23 s after Big BangThe Primordial Soup :
• 10-34s inflationary period ends• Energy in inflation field released•Universe reheats to 1022 Kfi primordial soup in thermal equilibrium
• photons• free quarks, antiquarks, exchange particles
†
q + q ´ g + g
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BIG BANG COSMOLOGY
7.5: The Evolution of the Big Bang7.5: The Evolution of the Big Bang THE QUARK ERA• Brief Review of Particle Physics
_ http://www.fnal.gov/pub/inquiring/physics/discoveries/pr/top_news_release.html
http://CPEPweb.org
1995年 発見した!_1995年 発見した!_
FUNDEMENTALFUNDEMENTAL
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BIG BANG COSMOLOGY
7.5: The Evolution of the Big Bang7.5: The Evolution of the Big Bang• THE HADRON ERAHadron era = 10-23 - 10-4 s after Big Bang
• 10-12 s ElectroWeak Symmetry breaking (g, W±, Z0) · E-M and Weak Nuclear Force• 4 fundamental forces of nature now distinct• Expansion of Universe cools Big Bang Fireball ~1013K (10-6s) ≡ 1GeV• Quarks bond to form individual Baryons · Quark Confinement · Baryogenesis
1) Why are there so many photons in the Universe ?2) Why is there no antimatter in the Universe ?
1) Photon Background produced from matter/antimatter anihilation
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BIG BANG COSMOLOGY
7.5: The Evolution of the Big Bang7.5: The Evolution of the Big Bang• THE HADRON ERAMATTER ANTIMATTER ASYMMETRY
Assume some tiny tiny asymmetry between quarks & anti quarks (matter & antimatter)
†
dq =nq - nq
nq + nq
After matter & antimatter anihilation: small excess of quarks remain
†
dq ªnq
ng
• How large is dq ?•From CMB and Wbaryon estimate Baryon to photon ratio = h~5x10-10
•Since 3 quarks bind to form a Baryon (Hadron) ‡ dq~ 10-10
Baryons
CMB
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BIG BANG COSMOLOGY
7.5: The Evolution of the Big Bang7.5: The Evolution of the Big Bang• THE HADRON ERAORIGIN OF MATTER ANTIMATTER ASYMMETRY
• Where does the Matter - Antimatter Asymmetry come from ? • Particle Physics - Standard Model - 3 basic symmetries• Charge Conjugation (C)
• Replacing a particle by its antimatter counterpart.• Parity (P)
• Reverses all three coordinates.• Like a mirror where image is not only back-to-front, but also left-right swapped and upside-down.
• Time Reversal (T)• Interactions are independent of the arrow of time.
o CPT still believed to be conserved in all reactions i.e., antiparticle is indistinguishable from the mirror-image of a particle moving backwards in time
o Weak interactions, both P and C are individually broken. (neutrino chirality) but CP is conserved
o One case of combination of C and P also not conserved
CP-violation, detected by Cronin & Fitch in decay neutral KaonsC violated P violated
CP conserved
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BIG BANG COSMOLOGY
7.5: The Evolution of the Big Bang7.5: The Evolution of the Big Bang• THE HADRON ERACP VIOLATION AND THE ORIGIN OF MATTER ANTIMATTER ASYMMETRY
• 1964 Cronin and Fitch Experiment:• Measurement of decay of pions from neutral Kaon particles• Measure the decay rate at the end of 17m particle beam tube.• Kaon decay lifetimes different by factor of 100 for the two Kaon species
•Expect to see only the long-lived version at the end of the beam tube, • BUT found about 1 in 500 long lived kaons decayed to 2 pions• CP violation (in K mesons due to fact that KL contain ~0.3% more Ko than anti-Ko)
†
KL0 Æ p + + e- + n e
KL0 Æ p - + e+ + n e
CP{p + + e- + n e} = p - + e+ + n e
Neutral Kaons also have semi-leptonic decay mode (39%, compared to 34% for 3p mode)
• CP transforms one set of decay products into the other fi identical decay rates ?• Experiment fi positron decay mode more frequent than the electron decay mode.• CP violation with fractional excess is only 3.3 x 10-3
CP violation fi difference in kaon-antikaon deacy lifetimes
†
S d Ko
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BIG BANG COSMOLOGY
7.5: The Evolution of the Big Bang7.5: The Evolution of the Big Bang• THE HADRON ERAORIGIN OF MATTER ANTIMATTER ASYMMETRY
1967 Andrei Sakharov : 3 criterea for matter-antimatter assymetry• Baryon number must be violated - Proton is unstable (decays into mu-meson and two neutrinos 1030yrs)• P and CP must be violated• A departure from thermal equilibrium when the baryon number was being violated.
CP violation requires 3 families of quarks ¤ 3 families of quarks imply CP violation
• N.B., CP violation fi T violation (strong nuclear force magnetic orientation fi axion fi dark matter)
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BIG BANG COSMOLOGY
7.5: The Evolution of the Big Bang7.5: The Evolution of the Big Bang• THE LEPTON ERALepton era = 10-4 - 1s after Big Bang
• ~ equal numbers of g, e, n in thermal equilibrium• For every 109 photons, electrons, or neutrinos, ~ 1 proton or neutron exists • Lepton Era continues until T<~1010K neutrinos decouple forming their own ghost Universe
†
Se ± ,g Re ± ,g3 =
43
p30
ge ± ,gT3Re ± ,g
3
S0,g R0,g3 =
43
p30
g0,gT3R0,g
3
¸
˝ Ô
˛ Ô
fi ge ± ,gT3Re ± ,g
3 = g0,gT3R0,g
3
Thermal equilibrium, the second law of thermodynamics ‡ entropy, S, of the Universe remained constant‡As Universe expands SR3=constantConsider Entropy conservation before and after the electron/positron annihilation
•T<~1010K neutrinos decouple•T~109K electrons and positrons annihilate• Universe gets extra source of photons (heating) which neutrinos never “see” ‡ neutrino background colder• Can calculate difference between neutrino background and photon background temperatures
g = effective number of species in equilibrium
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BIG BANG COSMOLOGY
7.5: The Evolution of the Big Bang7.5: The Evolution of the Big Bang• THE LEPTON ERAThe Neutrino Background
†
ge ± ,gT3Re ± ,g
3 = g0,gT3R0,g
3
Contributions to g calculated as product of 3 factors
g (e±) = 2 x 2 x 7/8 = 7/2g (g) = 2 x 1 x 1 = 2
• 2 if particle has distinct antiparticle, 1 if not.• Number of possible orientations of the particle spin.• 7/8 if particle subject to Pauli exclusion principle, 1 if not.
Therefore; before e± annihilation ge±, g=7/2 + 2 = 11/2after e± annihilation g0, g = 2
†
TRe ± ,g
TR0,g
= (11/4)1/ 3 ª1.4
Since TR(v) for the neutrinos remains equal to TR(e±, g) before the annihilation
Tn = Tg/1.4= 2.725/1.4 ~ 1.95 Kand en~ 0.5eg ~ 0.11 MeV/m3
The present day Temperature of the neutrino background is given by
• Neutrino background very difficult detect directly• If neutrinoes have mass, then neutrinos dominate the density of the Universe
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BIG BANG COSMOLOGY
7.6: Big Bang 7.6: Big Bang NucleosynthesisNucleosynthesis• The Neutron - Proton ratio~ 0.1s after Big Bang
• After Quark/Hadron era - Neutrons & Protons (nucleons) present in equal numbers
• T~1010K >> mec2fi g + g ´ e- + e+
• Nucleons in thermal equilibrium with electrons and photons
†
(1) n ´ p + e- + n e(2) n + n e ´ p + e-
(3) n + e+ ´ p + n e
Number densities of nucleons given by Maxwell-Boltzmann Distribution
†
Nn = gnmnkT2ph2
Ê
Ë Á
ˆ
¯ ˜
3 / 2
e-
mnc 2
kT
N p = gpmpkT2ph2
Ê
Ë Á
ˆ
¯ ˜
3 / 2
e-
mpc 2
kT
¸
˝
Ô Ô
˛
Ô Ô
Nn
N p
=mn
mp
Ê
Ë Á Á
ˆ
¯ ˜ ˜
3 / 2
e-
(mn -m p )c 2
kT
Neutron Decay Mode
mn/mp=1.002~1
(mn-mp)c2=Q=1.29MeV
†
Nn
N p
= e-
QkT = e
-1.5x1010
T Neutron Proton ratio is decided by the temperature
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BIG BANG COSMOLOGY
7.6: Big Bang 7.6: Big Bang NucleosynthesisNucleosynthesis• The Neutron - Proton ratio
1011 1010 109
Temperature (K)
1
0.1
0.001
0.01
0.0001
Nn/N
p
Neutron freezeout
Thermal Equilibrium• T~9x109K : • electrons-positrons annihilate g + g ¨ e- + e+
• neutrinos decouple from nucleons• Small neutron-proton mass difference · reactions shift in favour of the lighter Proton
†
Nn
N p
= e-
1.5x1010
9x109 ª 0.2†
(1) n ´ p + e- + n e(2) n + n e ´ p + e-
(3) n + e+ ´ p + n e
Only neutron decay mode (1) remains
†
Nn (t) = Nn oe- t /t
t ~16mins decay time of free neutron
Neutrons are disappearing quickly !
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BIG BANG COSMOLOGY
7.6: Big Bang 7.6: Big Bang NucleosynthesisNucleosynthesis• The Formation of the Light Elements~ 1s - 3 minutes after Big Bang
Onset of nucleosynthesis locks up all the free neutrons in nuclei stopping the neutron decay
• Nucleosynthesis of the elements begins with Deuterium and ends with Helium (+ a little Lithium, Beryllium, Boron)• Number densities too low to directly make 2p + 2n fi 4He • Sequence of 2 body reactions
Weak Interaction because neutrinos are involved fi lower probability
Can also have …..
†
p + p ´ D + e+ + n
n + n ´ D + e- + n
Deuterium binding energy low = mn+mp+mD=2.22MeV fi Immediately destroyed Stability when ND~Nn fi Temperature drops ~ kT~0.07 = 7x108K (t~200s)
Neutron decay mode fiNn/Np~0.16 (nucleosynthesis will be quite an inefficient process)
†
n + p ´ D + g
FIRST STEP:- Deuterium 2H = D
2H
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BIG BANG COSMOLOGY
7.6: Big Bang 7.6: Big Bang NucleosynthesisNucleosynthesis• The Formation of the Light Elements~ 3 minutes after Big Bang
• Once significant amount of Deuterium has formed the heavier elements form very fast• All post-Deuterium reactions involve strong nuclear forces, large cross sections and high reaction rates• Reactions proceed quickly to Helium
†
n + p Æ D + g
D + n Æ 3H + g
D + p Æ 3He + g
D + D Æ 3H + pD + D Æ 3He + nD + D Æ 4He + g
4He
3H
3He
2H
†
3H + p Æ 4He + g3He + n Æ 4He + g3H + D Æ 4He + n3He + D Æ 4He + p
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BIG BANG COSMOLOGY
7.6: Big Bang 7.6: Big Bang NucleosynthesisNucleosynthesis• The Formation of the Light Elements
Most of 3H, 3He gets locked up in 4He - how about heavier elements ?
†
4He + D Æ 6Li + g4He+3H Æ 7Li + g4He+3He Æ 7Be + g4He+4He Æ 8Be
†
8Be Æ (unstable) Æ 4He+4He (t ~ 3x10-16 s)
4He
6Li
7Li
7Be 5 8
• No stable nuclei with atomic number 5 or 8• Unusually large binding energy of Helium
Universe runs out of steam production ceases with Helium
Fusion Fission
56Fe
56
• Binding energy/nucleon as a function of atomic number or number of nucleons per atom. •Decrease in binding energy beyond Iron as the nucleus gets bigger, strong force loses to electrostatic force.
•Peaks in binding energy at 4,16 & 24 nucleons from the stability of 4He combination of 2 protons/neutrons
•Maximum binding energy at iron ‡ means that elements lighter than Iron release energy when fused. •Elements heavier than iron only release energy when split
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BIG BANG COSMOLOGY
7.6: Big Bang 7.6: Big Bang NucleosynthesisNucleosynthesis• Light Element Abundances
Everything Else is made in Stars107-108 yrs later
Assumes h~5x10-10Only the very lightest elements aresynthesized in the Big Bang
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BIG BANG COSMOLOGY
7.6: Big Bang 7.6: Big Bang NucleosynthesisNucleosynthesis• Light Element Abundances
Abundance depends on Baryon to photon ration (h)
• High h ‡ higher density• ‡ nucleosynthesis starts earlier (higher T)• Helium production more efficient• Less D & 3He leftover
4He+3H(1)
7Be+e-(2)
Mass fraction of He ~ Nn/Np~0.16 so there are ~6 protons for every neutron
So for 2n + 2pÆ 4He ‡ 10 protons leftover ‡ H
Maximum allowedMass fraction He
†
4x number He nuclei( )4x number He nuclei( ) + number H nuclei( )
=4
4 +10= 28%
(1) Production of 7Li from 4He+3H ~ decreasing fn(h)
(2) Production of 7Li from 7Be+e- ~ increasing fn(h)
Mass fraction of Li
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BIG BANG COSMOLOGY
7.7: Recombination7.7: Recombination• THE RADIATION ERARadiation era = 1s - 106yrs after Big Bang
• Radiation more dense than matter, 108 kg/m3 compared to 100 kg/m3• Temperature 1010 K• Expanding space filled mostly with protons and neutrinos• Protons and neutrons combined to produce deuterium• Helium synthesized when universe some 200 seconds old• Universe between ~105 years old• Temperature 3000o K, electrons captured by protons to form hydrogen atoms• Electrons no longer scatter photons• Universe becomes transparent to radiation; decoupling epoch when radiation decouples from matter• Fireball that flooded expanding universe for first 106 years appears as CBR
Before Recombination photon mean free path is very short
Radiation and matter are thermally bound together
http://zebu. uoregon. edu
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BIG BANG COSMOLOGY
7.7: Recombination7.7: Recombination• Decoupling and Recombination
zT
tR
pe-
p pp
e-
e- e-
gg g
g•matter in thermal equilibrium withthe radiation. photons and electronsto interact via Thompson scattering
HH
H
Hg
gg
g
recombination •Temperature drops then p+e-ÆH ‡recombination
HHH
H
g
g
ggg
De-coupling• Eventually interactions stop
allowing the photons to flowfreely on scales of thehorizon ‡ de-coupling
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BIG BANG COSMOLOGY
7.7: Recombination7.7: Recombination• Decoupling and Recombination
Time of recombination depends on1. Ionization energy of Hydrogen =13.6eV2. The baryon/photon ratio, h~5x10-10
Simply equating the ionization energy to average photon energy ~3kT · TR ~50,000K
But since there are many more photons than protons, · even at lower temperatures there are enough photons with the ionization energy
Use Boltzmann distribution:
†
ng (> E) µe-E / kT fi T =13.6
3k9ln10ª 2500K
•Redshift of Recombination / Decoupling ~ z=Ro/RR=TR/To=2500/2.7~1000• more accurately z=1089 over redshift shell dz=195
•380,000 years after Big Bang over a time scale of ~ 118,000yr
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BIG BANG COSMOLOGY
7.7: Recombination7.7: Recombination• The Surface of Last Scattering
• After Recombination and Decoupling the photons are no longer bound to matter and can stream freely• Photons from the Big Bang fill the universe and we observe them as the 2.7K microwave background.• The redshifted relic or ashes of the Big Bang• Last time photons interacted ‡ SURFACE OF LAST SCATTERING•This also means that we can not observe the Universe when it was younger than ~400,000 years
BEFORE DECOUPLING: photons and matter coupled AFTER DECOUPLING: photons become free
http://zebu.uoregon.edu
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BIG BANG COSMOLOGY
7.8: The Matter Era7.8: The Matter Era• THE MATTER ERA • Before Recombination - Radiation coupled to matter ‡ Matter cannot cluster
• After recombination, radiation no longer influences the distribution of matter.• Matter can cluster and collapse around density enhancements• Form the structures of galaxies and clusters of galaxies we observe today
• Universe <106 years old•Density 1 H-atom/cm3
•No galaxies existed prior to 106 years
• Matter era, ~106 years after big bang•Quasars and clusters of galaxies condensing•Density 10-25 kg/m3
•Temperature > 3000o K•Universe flooded with brilliant yellow light
• Universe 109 years old• Density 100 H-atoms/m3• Galaxies coming into existence
• Present era, 13.7x 109 years after big bang• Density 1 H-atom/m3; ~1080 particles in observable universe• 109 photons and neutrinos for each baryon• Galaxies exist in billions; stars forming everywhere• CBR has redshift of 1000 and temperature of 2.7 K
• The Acceleration Era• Cosmological Constant term has turned on• What is the fate of the Universe ?
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BIG BANG COSMOLOGY
7.9: The Undiscovered Country7.9: The Undiscovered Country• The fate of the Universe?
Ruling law of Nature: Entropy - objects go from order to disorder - The Arrow of Time
HEAT FLOWT1 T2
T1>T2T3 T3 T1>T3>T2
• STELLAR ERA:•Energy of the Universe from thermonuclear fusion in Stars. Stellar era lasts until the last starshave used up their fuel. ~1014yrs for 0.1Mo Red Dwarf
• DEGENERATE ERA:•All stars in the form of stellar remnants - white/brown dwarfs/neutron stars /black holes.• Eventually all stars become black dwarves. Galaxies dissolve
• BLACK HOLE ERA:• Proton decays with lifetime of 1030yrs.• Only organized units are black holes.• Black Holes evaporate via Hawking Radiation over 10100 years for galactic sized systems.• Universe becomes a cold photon sea
• DARK ERA:• Universe consists of leptons + photons - ultimate disorder.• Cools to vacuum energy state
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BIG BANG COSMOLOGY
7.10: Summary7.10: Summary• Summary
At times prior to this our evidence is indirect
• Early Universe must consider Particle Physics
• TÆ0 a Quantum Theory of Gravity
• However the Big Bang Theory has had great success in predicting fine details of
• The expanding Universe
• Primordial Nucleosynthesis and the light element abundances
• The Relic Radiation from the fireball
• The beginning of structure formation
• However… we shall see that there are still many unsolved problems with this Standard Model
•Followed the evolution of the Universe from the Big Bang to the present and beyond
• The farthest back we can observe is the surface of last scattering
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BIG BANG COSMOLOGY
7.10: Summary7.10: Summary• Summary
Fundamental CosmologyFundamental Cosmology7. Big Bang Cosmology7. Big Bang Cosmology終終終
次:次:次:Fundamental CosmologyFundamental Cosmology
8. Dark Matter8. Dark Matter