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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Dynamics
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Newtonian derivation
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(No Transcript)
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Vacuum repulsion

• Vacuum contains another density
• Repulsive

Equation of motion for a(t)
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Matter domination

4th power if radiation dominates
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Cosmological constant
Vacuum does not get thinned

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Both effects together
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Both effects together

• Inverse square force
• Hookian force, opposite sign

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Conservation of energy
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K' K ?1, 0!! Can only be derived from
Einstein's equations
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Meaning

• Time evolution is related to spatial
  structure
• Energy is positive if space is closed

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Simplify the equationsintroduce dimensionless
variables
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Acceleration eqn
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Velocity eqn
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Reduce to now
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Reduce to now
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Parameters
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Parameters

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Interpretation of parameters
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Interpretation of parameters
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Interpretation of parameters
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Interpretation of parameters
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Interpretation of parameters
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Big Question
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• What are the values of the parameters?

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The mass parameter

• Count the amount of matter ??

• But miss dark matter
• Only gives lower bound
• No longer used

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Other effects ofcosmological constant

• Normal gravity goes as inverse square
• Cosmological constant gives repulsion which is
  independent of distance
• Therefore cosmological constant not important for
  small system?
• Small ?