# Cosmology Lecture 4 ```Cosmology
Lecture 4
Constituents
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Protons
Neutrons
Electrons
mass (Mev)
983.3
939.6
0.511
charge
+1
0
-1
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Photons
Neutrinos
0
?
0
0
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Dark matter
?
0
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Dark Energy

?
0
Overall, the universe is flat
Ω
4%
23%
73%
Cosmological constant
Contributes most of the energy of the universe?
What is the evidence for this?
What impact does it have on universal evolution?
Standard Candles
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Known luminosity =&gt; brightness gives
distance
“Standardized candles” - not quite
“standard”, but various relationships can
give true luminosity
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Cepheids - Period-Luminosity relation (visible to
z=0.01)
SN Ia - Peak magnitude - decay rate relation
(visible to z=1.5)
Type Ia Supernovae
The Philips relation
σ ~ 0.3 mag
σ ~ 0.07 mag
SN Ia Hubble Diagram
SN Ia at higher redshift
are too faint
Further away than we
expect
Universe is accelerating
- first evidence for
cosmological constant
This is a BIG suprise
Scale factor
k&lt;0
Λ
k=0
k&gt;0
Time
Back to the Friedman equation

Useful, but contains too many unknowns

Need some more equations to solve for
a(t), ε, k, Λ etc
The fluid equation

Comes from first law of thermodynamics
(essentially conservation of energy)
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The acceleration equation
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Combination of Fluid and Friedman
Equations
Not independent - unfortunately, we still
need more!
And finally……equations of state
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Equation of state links P and ε
Define equation of state parameter ω
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P=ωε
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ω = 0 - matter dominated universe
ω = 1/3 - radiation dominated universe
ω = -1 - cosmological constant dominated
universe
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Cosmological Models
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We are now (finally) in a position to
describe the evolution of a universe
consisting of
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Matter