PHY 4460 RELATIVITY

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PHY 4460RELATIVITY

• K Young, Physics Department, CUHK
• ?The Chinese University of Hong Kong

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CHAPTER 11POOR MAN'S COSMOLOGY
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Objectives

• The problem of cosmology
• Observational evidence
• Kinematics
• Dynamics
• Belief in 1920s, 1960s, 21st century

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Observational Evidence
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Observational evidence

• Isotropic
• Principle of cosmology
• Homogeneous
• Expansion

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1. Universe is isotropic
YES
NO
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2. Our position is not special
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2. Our position is not special
NO
YES
Would not be isotropic from another observational
point
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Universe is homogeneous!
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3. Galaxies are receding from us
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4. Velocity ? distance s (for small distances)
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Hubble constantis not constant

• Although
• it does not mean velocity is uniform
• and in fact H is changing
• Present values denoted by subscript0

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Unit of H

• v km s-1
• s Mpc
• 1 pc 3.26 ly
• H km s-1 Mpc-1
• H v / s s-1
• H-1 s Gyr

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Value of H0

• Hubble 1930s 500 units
• Recent decades 50-100 units
• 2001 70 units (/- 10)
• WL Freedman et al

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Problem

• Determine s?
• Determine v?

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Determine s
L 100 W

• "Standard" sources Cepheids Know L
• Measure l
• Determine s

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Determine v
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Uniform motion? T age of universe?
NO !
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Kinematics
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Kinematics

• Co-expansion
• factorization
• Single parameter a(t)
• Expansion
• H(t)
• Deceleration
• q

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Co-expansion
Factorized
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v ? s does not imply uniform motion H?1 ? age of
universe
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Key Equations
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?
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If earlier H is larger, then decelerating (to be
qualified)
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How to express deceleration

• Dimensionless

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Example inNewtonian Gravity
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Stone
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• Escape KE gt PE q lt 1/2

Marginal KE PE q 1/2 Not escape KE lt PE q
gt 1/2
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Deceleration parameter

• How do we know whether expansion is

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In principle

• Measure H or T
• now
• 0.1 Gyr ago
• Find difference

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In practice?

• We do not have data from long time ago
• But light from distant galaxies
  came from long time ago

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• If earlier H is larger
• Then amount of deviation is a measure (q) of how
  much larger

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In practice?

• Slope of each part
• Tells us H at some time in past
• Can trace H(t)
• Actually dynamical model with a few parameters
• Fit diagram to determine parameters

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• Model

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Homogeneous and Isotropic Spatial Geometries
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Homogeneous and isotropic spatial geometries

• Flat

• Closed sphere

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Homogeneous and isotropic spatial geometries

• Open
• like a saddle

All described by a(t) ???