updates

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Lecture 17

• updates

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Themes for this lecture

1. How did roughness start?
2. Why does roughness grow?
3. Why does roughness depend in scale?

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Roughness ??/?
Roughness ??/?
Example
??
density
?
Roughness 1/12 8
position
4
Growth of Roughness ??/?
Growth of Roughness
Roughness ??/?
??
??
density
density
?
?
position
position
5
Roughness on different length scales
Position (e.g. light years)
Actual roughness
Super-horizon roughness
Density Roughness ????
Large wavelength component
Sub-horizon roughness
Small wavelength component
Position (e.g. light years)
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Super-Horizon Growth
Lower density
Higher density
C
A
B
Average
Horizon Size
Regions larger than the horizon
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Expansion Amplifies Density Variations
C lower density
B average density
A higher density
Region Size
Big Bang
Time
8
Sub-Horizon Growth
Lower density
Higher density
C
A
B
Average
Horizon Size
Regions within the horizon
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Roughness on different length scales
Density Roughness ????
Position (e.g. light years)
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Fourier Representation of Density Variations
Position (e.g light years)
600
800
1000
200
400
0
Density Variations
Roughness ????
Roughness spectrum P(k)
Power P
100
200
500
0
300
400
long waves
Short waves
Spatial Frequency k
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The Initial Power Spectrum
Position (light-years)
Density variations
Roughness ????
Roughness spectrum
P(k) ? k
Power P
long waves
short waves
Spatial Frequency k
12
Expansion of Different Sized Waves
Matter Era
Radiation Era
long
5
4
Horizon size c ? t
medium
Size
3
2
short
1
expansion
long
5
4
horizon envelopes wave
medium
3
2
1
short
Now
Equality
Big Bang
Time
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Growth of Roughness for Different Waves
medium
3
Matter Era
Radiation Era
2
4
short
1
Roughness P(k)
long
5
short
1
2
medium
3
4
5
long
Now
Equality
Big Bang
Time
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The Evolving Roughness Spectrum
Age/yr
1010
109
108
107
Matter era
Roughness P(k)
106
105
Radiation era
104
P(k) ? k
1000
100
short waves
long waves
Spatial Frequency k
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Todays Power Spectrum
Position (light-years)
Roughness ????
Density variations
Peak
P(k) ? k
Power P
P(k) ? 1/k2
short waves
long waves
Roughness spectrum
Spatial Frequency k
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peak
P(k) ? k
P(k) ? 1/k2