Cosmology
Lecture 2
Summary from Lecture 1
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The cosmological principle
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Universe is isotropic
Universe is homogeneous
The universe is expanding, with its current rate
given by the Hubble constant

Hubble constant is the rate of change of the scale factor at
the current time.
Today - the impact of relativity
Relativity

Implications of relativity

Special
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Faster than light expansion
General
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Principle of equivalence
Space time curvature
More details on relativity later in course and in 4th year
Equivalence principle
a
g=a
Inertial Mass = Gravitational Mass
Space time curvature
Light follows a null geodesic
Newton
Mass tells gravity how to exert a force
Force tells mass how to accelerate
Einstein
Mass-energy tells space time how to curve
Curved space-time tells mass energy how to move
Curvature
Flat
Positive
Negative
Co-moving co-ordinates
Time
X=1
2
X=1 2 3
Real distance R = a(t) X
3
Curvature and scale factors
Scale factor
k>0
k=0
k>0
Time