11/28/03 Chris Pearson : Fundamental Cosmology 7: Big Bang ...€¦ · 11/28/03 Chris Pearson :...

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


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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


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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!


4

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


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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


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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


7

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


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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.


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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 !


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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/


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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


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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


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BIG BANG COSMOLOGY


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) !


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BIG BANG COSMOLOGY


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


15

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


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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 ?


17

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


18

BIG BANG COSMOLOGY


• 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!!


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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):


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BIG BANG COSMOLOGY


• 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 ????


21

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 ?


22

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 !!


23

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


24

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


25

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


26

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


27

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


28

BIG BANG COSMOLOGY


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


29

BIG BANG COSMOLOGY


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


30

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


31

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


32

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


33

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


34

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


35

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


36

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


37

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


38

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


39

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)


40

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


41

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


42

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


43

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 !


44

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


45

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


46

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


47

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


48

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


49

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


50

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


51

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


52

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


53

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 ?


54

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


55

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


56

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

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