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Cosmology &The Big Bang Theory
Dr Alex Calverley
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222 dydxdl
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222 dydxdl 22
2222
ddr
drdrdl
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2,1,
2
ji
jiij dxdxgdl
10
01ijg
Cartesian coordinates
20
01
rgij
Polar coordinates
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3
0,
2
dxdxgds
1
1
1
1
g
Special relativity
22222 dzdydxdtds
ta
ta
tag
2
2
2
1
General relativity
22222222 dztadytadxtadtds
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T
c
GRgR
421 8
In 1915...
T
c
GgRgR
421 8
In 1917...
Using the GR metric from the last slide Friedmann solved the equation in 1922 to get...
33
8 2
2
22c
a
kcG
adtda
3
3
3
4 2
2
2
2
c
c
pG
adtad
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k > 0
k < 0
k = 0
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Demonstrating the relationship between comoving (i.e. coordinate) distances and physical distances
a = 1 today (a0), and a(t) < 1 at earlier times
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In 1929...
dHv 0
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However, in 1927...
If D(t) is the proper distance between two objects at time t and D0 is the proper distance now, then:
taDtD 0 tatD
D 0
and
dt
daD
dt
tDd0
Then combining these
tDHtDtadt
tDd dtda
taH dtda
dHv 0So Lemaître had predicted
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EVIDENCE FOR THE BIG BANG THEORY (1)
An expanding universe where the recessional speed is proportional to the distance away
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In 1948...
George Gamow predicts the ratio of light elements due to Big Bang Nucleosynthesis
Ralph Alpher and Robert Herman predict the glow from the Big Bang will still be visible in the microwave spectrum with a temperature of about 5 K
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Colours represent fluctuations of size ΔT/T ~ 10-5
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EVIDENCE FOR THE BIG BANG THEORY (2)
A near perfect blackbody spectrum at T ≈ 2.7 K, suggesting the Universe was once much hotter and denser
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xn
xnpn eXexHdx
dX 11
15.0xX n
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EVIDENCE FOR THE BIG BANG THEORY (3)
BB Nucleosynthesis can explain the observed ratios of light elements in pristine primordial gas
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In 1999...
The Universe’s expansion is accelerating!Need an extra component to the Friedmann equations called Dark Energy – which acts just like Einstein’s Λ term!
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Colours represent fluctuations of size ΔT/T ~ 10-5
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