Fundamental Cosmology: 6.Cosmological World Models

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Fundamental Cosmology 6.Cosmological World Models
This is the way the World ends,
Not with a Bang,
But a whimper T.S. Elliot
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6.1 Cosmological World Models

• What describes a universe ?
• We want to classify the various cosmological
  models

from Friedmann eqn.
Defined the density parameter W
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6.1 Cosmological World Models

• L0 World Models

• Lets think about life without Lambda

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6.2 Curvature Dominated World Models
Friedmann Equation

• The Milne Universe

• Special relativistic Universe
• negliable matter / radiation r0, Wmltlt1
• No Cosmological Constant L0, WL0
• Curvature, k-1

Universe expands uniformly and monotomically
R?t
Age toHo-1

• Useful model for
• Universes with Wmltlt1
• open Universes at late times

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6.3 Flat World Models
Friedmann Equation

• General Flat Models

• Flat, k0 universe
• Assume only single dominant component
• r ro(Ro/R)3(1-w)
• W1

• For spatially flat universe
• Universes with wgt-1/3 - Universe is younger than
  the Hubble Time
• Universes with wlt-1/3 - Universe is older than
  the Hubble Time

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6.3 Flat World Models
Friedmann Equation

• The Einstein De Sitter Universe

• Flat, k0 universe
• Matter dominated r ro(Ro/R)3
• No Cosmological Constant L0, WL0
• W1

Age to(2/3Ho )
Until relatively recently, the EdeS Universe was
the most favoured model
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6.4 Matter Curvature World Models

• Matter Curvature

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6.4 Matter Curvature World Models
Friedmann Equation

• The Einstein Lemaitre Closed Model

• Closed, k1 universe
• Matter dominated r ro(Ro/R)3
• No Cosmological Constant L0, WL0
• Wgt1

The Scale Factor has parametric Solutions

• q0 ? t0

For the case of W2, the Universe will be at half
lifetime at maximum expansion
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6.4 Matter Curvature World Models

• The Einstein Lemaitre Closed Model

• Closed, k1 universe
• No Cosmological Constant L0, WL0
• Wgt1

Age

• Models normalized at tangent to Milne Universe
  at present time

• High W? Age universe decreases (start point gets
  closer to Origin)

• Universe evolves faster for higher values of W

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6.4 Matter Curvature World Models
Friedmann Equation

• The Einstein Lemaitre open Model

• Open, k-1 universe
• Matter dominated r ro(Ro/R)3
• No Cosmological Constant L0, WL0
• Wlt1

The Scale Factor has parametric Solutions

• f0 ? t0

• f?? ? R ??

• Universe will become similar and similar to the
  Milne Model (W0) as t??

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6.4 Matter Curvature World Models

• The Einstein Lemaitre open Model

• Open, k-1 universe
• No Cosmological Constant L0, WL0
• Wlt1

Age

• Models normalized at tangent to Milne Universe
  at present time

• Low W ? Age universe increases (start point gets
  farther from origin)Oldest universe is Milne
  Universe

• Universe evolves faster for lower values of W

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6.4 Matter Curvature World Models

• Summary

Open Cosmologies
Closed Cosmologies
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6.4 Matter Curvature World Models

• Summary

Universe Type Parameters Parameters Parameters Parameters Parameters Fate Topology R / t
k W r q L
Milne Special Relativistic Open -1 0 0 0 0 Expand forever
Friedmann - Lemaitre open Hyperbolic Open -1 lt1 lt rc lt 0.5 0 Expand Forever
Einstein De Sitter Flat Closed 0 1 rc 0.5 0 t ?? R ??
Friedmann - Lemaitre closed Spherical Closed 1 gt1 gt rc gt 0.5 0 Re-contract Big Crunch
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6.5 L World Models

• L ? 0 World Models

• Lets think about life with Lambda

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6.5 L World Models

• Living with Lambda

The Friedmann Equations including Cosmological
Constant
L

• Modifies gravity at large distances
• Repulsive Force (Lgt0)
• Repulsion proportional to distance (from
  acceleration eqn.)

• Consider the following scenarios
• The Einstein Static Universe
• L lt 0 universes
• L gt 0 universes
• k lt 0, k0
• L gt LC
• L LC
• L lt LC

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6.5 L World Models

• The Einstein Static Universe
• (k1, rgt0, Lgt0)

For a static universe

• original assumed solution to field equations
• Problem
• no big bang
• no redshift

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6.5 L World Models

• Oscillating Models
• (L lt 0)

When RRC universe contracts

• Universe is Oscillatory
• Oscillatory independent of k

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6.5 L World Models

• The De Sitter Universe
• (k0, r0, Lgt0)

For k ? 0
Monotomically expanding Universe, at large R
De Sitter Model
Special Case k 0, r0

• Does have a Big Bang
• But is infinitely old

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6.5 L World Models

• k1 , Lgt0 World Models
• (k1, Lgt LC)

For k1, Lgt LC
Monotomically expanding Universe, at large R ? De
Sitter Universe
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6.5 L World Models

• k1 , Lgt0 Eddington Lemaitre Models
• (k1, L LC LCe) 3 Models

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6.5 L World Models

• k1 , Lgt0 Lemaitre Models
• (k1, L LC LCe) 3 Models

Long Coast period ? Concentration of objects at a
particular redshift (1zRo/Rcoast) (c.f. QSO
at z2)
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6.5 L World Models

• k1 , Lgt0 Oscillatory and Bounce Models
• (k1, 0ltL lt LC)

2 sets of solutions for 0ltL lt LC separated by
R1, R2 (R1ltR2) for which no real solutions
exist No solution R1ltRltR2 because (dR/dt)2lt0
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6.5 L World Models

• Summary of L models

L k Name Dynamics Evolution
lt0 ? k Oscillatory (1st kind) contract back to R0 (oscillatory)
gt0 ?0 monotomically expanding
gt0 0 De Sitter monotomically expanding
LC 1 Einstein Static Static ? t at RRE with L Lc
gtLC 1 monotomically expanding
LCe 1 Eddington Lemaitre (EL1) Big Bang ? Einstein Static universe
LCe 1 Eddington Lemaitre (EL2) expand from Einstein Static ??
LCe 1 Lemaitre Long coasting period at RRE
0ltL lt LC 1 Oscillatory (1st kind) contract back to R0 (oscillatory)
0ltL lt LC 1 Oscillatory (2nd kind) Universe bounces at RB
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6.5 L World Models

• Summary of L models

COLD DEATH
k1
k-1
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6.5 L World Models

• Summary of L models

• L lt0 models all have a big crunch
• L gt0 models depenent on k
• Expansion to ? if k ?0 L becomes dominant
• kgt0 and L gt 0 ? multiple solutions.
• Our Universe.?

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6.6 Alternative Cosmologies

• ?????

• There are a lot of strange theories out there !

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6.6 Alternative Cosmologies

• Steady State Cosmology

• Bondi Gold 1948 (Narliker, Hoyle)
• 1948 Ho-1 to lt age of Galaxies
• ?? Steady State ? Static

Recall PERFECT COSMOLOGICAL PRINCIPAL
The Universe appears Homogeneous Isotropic to
all Fundamental Observers At All Times
Density of Matter constant ? continuous
creation of matter at steady rate / volume
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6.6 Alternative Cosmologies

• Steady State Cosmology

Curvature 3D Gaussian (k/R(t)2) ? dependent on
t if k?0
10x mass found in galaxies ? Intergalactic
Hydrogen at creation rate 10-44 kg/m3/s
Problems
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6.6 Alternative Cosmologies

• Changing Gravitational Constant

• Milne, Dirac, Jordan (Brans Dicke, Hoyle
  Narliker)
• G decreases with time

• e.g. Earths Continents fitted together as
  Pangea G? as t? continents drift apart.
• Stars L?G7 G? as t? ? stars brighter in the
  past.
• Earth is moving away from the Sun if G? as t? ?
  T?t9n/4 inconsistent with Earth history
• G(t) ? Perturbations in moon planet orbits
  (constraints (dG/dt)/Glt3x10-11 yr-1 )
• Light Elements Abundance (dG/dt)/Glt3x10-12 yr-1

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6.6 Alternative Cosmologies

• Changing Gravitational Constant
• Brans Dicke Cosmology
• Variation on the variation of G Theory

• As well as the Gravitational Tensor field there
  is an additional Scalar field G(t)
• L0, Mach Principle G-1Sm/rc2

• coupling constant between scalar field and the
  geometry Such that Grt2 constant

Diracs original 1937 theory w-2/3

• nucleosynthesis ? wgt100
• ? Analysis of lunar data for Nordtvedt effect ?
  wgt29 ? dG/dt)/Glt10-12 yr-1

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6.6 Alternative Cosmologies

• Other Cosmological Theories
• Anisotropic Cosmologies

• Anisotropic Cosmologies
• Universe is homogeneous and isotropic on the
  largest scales (CMB)
• Obviously anisotropic on smaller scales ?
  Clusters

• Quiescent Cosmology
• Universe is smooth except for inevitable
  statistical fluctuations that grow

• Chaotic Cosmology (Misner)
• Whatever the initial conditions, the Universe
  would evolve to what we observe today
• Misner - neutrinos damp out initial
  anisotropies
• Zeldovich - rapidly changing gravitational
  fields after Planck time (10-43-10-23s) ?
  creation of particle pairs at expense of
  gravitational energy

But initial fluctuations HAVE been observed and
explainations are available !
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6.7 Our Universe - The Concordance Model

• What Kind of Universe do we live in then ?

• Lets think about
• Our Universe

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6.7 Our Universe - The Concordance Model

• What Universe do we live in ?
• Evidence 1 Supernova Cosmology Project

• Type Ia supernovae Absolute luminosity depends
  on decay time ? "standard candles
• Apparent magnitude (a measure of distance)
• Redshifts (recession velocity).
• Different cosmologies - different curves.

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6.7 Our Universe - The Concordance Model

• What Universe do we live in ?
• Evidence 1 Supernova Cosmology Project

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6.6 Our Universe - The Concordance Model

• What Universe do we live in ?
• Evidence 2 Hubble Key Project

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6.6 Our Universe - The Concordance Model

• What Universe do we live in ?
• Evidence 2 Hubble Key Project

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6.7 Our Universe - The Concordance Model

• What Universe do we live in ?
• Evidence 3 WMAP

Wilkinson Microwave Anisotropy Probe (2001 at L2)
Detailed full-sky map of the oldest light in
Universe. It is a "baby picture" of the
380,000yr old Universe

• Temperature fluctuations over angular scales in
  CMB correspond to variations in matter/radiation
  density

• Temperature fluctuations imprinted on CMB at
  surface of last scattering

• Largest scales sonic horizon at surface of
  last scattering

• Flat universe this scale is roughly 1 degree
  (l180)

• Relative heights and locations of these peaks ?
  signatures of properties of the gas at this time

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6.7 Our Universe - The Concordance Model

• What Universe do we live in ?
• Evidence 3 WMAP

http//map.gsfc.nasa.gov/

• WMAP - fingerprint of our Universe

• Flat Universe - sonic horizon 1sq. Deg.
  (l180)

• Open Universe - photons move on faster
  diverging pathes gt angular scale is smaller for
  a given size

• Peak moves to smaller angular scales (larger
  values of l)

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6.7 Our Universe - The Concordance Model

• What Universe do we live in ?
• Evidence 3 WMAP
• WMAP maps and geometry

http//map.gsfc.nasa.gov/
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6.7 Our Universe - The Concordance Model

• What Universe do we live in ?
• Evidence 4 WMAP SDSS

Tegmark et al. 2003
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6.7 Our Universe - The Concordance Model

• What Universe do we live in ?

• Approximately Flat (k0)
• CMB measurements
• WL0.6-0.7
• Type Ia supernovae
• There is also evidence that Wm0.3
• Structure formation, clusters
• H072 km s-1 Mpc-1
• Cepheid distances HST key program
• Currently matter dominated

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6.7 Our Universe - The Concordance Model

• The Evolution of the Concordance Model - The
  Evolution of Our Universe

Lgt0, k 0

• Early times Universe is decelerating
• Later times L dominates Universe accelerates

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6.7 Our Universe - The Concordance Model

• The Evolution of the Concordance Model - The
  Evolution of Our Universe

Why do we live at a special epoch ??
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6.7 Our Universe - The Concordance Model

• The Evolution of the Concordance Model - The
  Evolution of Our Universe

http//map.gsfc.nasa.gov/
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6.8 SUMMARY

• Summary

• Used the Friedmann Equations to derive
  Cosmological Models depending on the density W

• Have discovered a large family of cosmological
  World Models

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6.8 SUMMARY

• Summary

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Fundamental Cosmology 6. Cosmological World
Models
Fundamental Cosmology 7. Big Bang Cosmology
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