Housekeeping
• Only 2008 past paper directly relevant
• Derivations: General rule, if derived in the
course it could be asked, but long derivations
would be guided.
• If a question is using (rather than deriving) a
relatively complex equation it will generally be
given (not necessarily true for simple
equations or those from basic physics).
• Friedman, Fluid and Acceleration equations
are on the front of the paper!
a α t1/2
ω = 1/3
Rotation curves flat:
Dark Matter Dominant:
Probably Cold
Hubble’s law obeyed in
local universe
D
H0
v=
velocity
MACHO and
WIMP
searches microlensing
+ gammaray
Radial distance
a α eHt
ω = -1
t2/3
aα
ω=0
Matter
Radiation
Energy densities
εΛ = const
εm α 1/a3
εr α 1/a4
Horizon size
Type Ia supernova searches
10 ~Gyr - Matter- Cosmological constant equality
a α eHt
ω = -1
On large scales universe is
homogeneous and isotropic
(Cosmological Principle)
velocity
10-36s - increase scale
factor by ~1040
Solves flatness problem horizon problem
Peak of star formation
Inflation
Matter-radiation equality
Big bang
Vacuum fluctuations?
Brane collisions?
Nucleosynthesis
N+p => D
D+p => 3He
D+D => 4He
Jeans mass ~105 Msol.
Stars/Galaxies form
First stars/galaxies
Jeans mass >1018 Msol.
Galaxies can’t collapse
~300,000 years Cosmic Microwave background (e+p => H + γ)
ΩΛ,0 = 0.73, Ωm,o = 0.27, Ωr,0 = 10-5
H0 = 72 km s-1 Mpc-1
Spatially flat Ω0 =1
Distance
The universe on a side of A4
Λ
Time (total age = 13.5 Gyr)
Friedman
Fluid
Acceleration
Observational challenges/facts
Key points/ideas
Key periods in Universe history
Inflation
Horizon problem
US
G1
G2
We are in causal contact with G1 and G2, but G1 is not in
contact with G2. How can it have the same temperature?
What inflation does
1- Ω(t) = e-2Ht
1- Ω(t) = 1- Ω0 a2 / Ωr,0 + a Ωm,0
inflation
Matter/radiation
|1-Ω|
0
time
• Solves flatness problem (of all values
available why would the universe be flat?)
Baryogenesis/Nucleosynthesis
•
•
•
•
Early universe equal in matter + antimatter
CP violation probably removes the antimatter
Protons and neutrons formed
When very hot protons and neutrons kept in
equilibrium via weak interaction
• As universe cools it undergoes freeze-out,
neutrons start to decay into protons
• Neutron to proton ratio fixed
.
Nucleosynthesis
• As universe cools nucleosynthesis create
Helium and small quantities of Li, Be and
heavier elements
• p+p => D
• D+p => 3He
• D+D => 4He
•
•
•
•
D+4He => 6Li
4He + 3He => 7Li
4He + 3He => 7Be
4He + 4He => 8Be
Cosmic Microwave Background
Caused by recombination: e+p => H + γ
Cosmic Microwave Background
• 1st peak in angular
correlation function
gives universe
flatness
ϑ
Closed
ϑ
Flat
ϑ
Open
Structure Formation
• As universe cools structure can form when
bound structures exceed the Jeans mass
• MJ = 4/3 π ρ λJ3
• λJ = 2 π cs tdyn
• MJ roughly 105 solar masses in early universe
(post CMB)
Dark Matter
• Dark Matter is dominant source of
matter dominating structure formation
• Evidence for dark matter in rotation
curves of galaxies (flat at large radii)
• Origin unknown, some is baryonic,
some likely non-baryonic
• Possible origins include
WIMPS,MACHOS,neutrinos etc
Cosmological Dynamics
Rate of change of scale factor / scale factor - relative growth
rate of universe
Depends on curvature
Depends on mass density
Solutions
• Matter only
– a(t) = (t/t0)2/3
• Radiation only
– a(t) = (t/t0)1/2
• Cosmological
Constant
– a(t) = exp(H0(t-t0))
• Curvature only
– a(t) = t/t0
Cosmological Constant
• As universe expands cosmological
constant becomes more important
(constant energy per unit volume).
• Evidence for cosmological constant
comes from type Ia SN, and yields our
benchmark model
SN Ia
• CMB provides evidence of flatness of
the universe
• SN Ia are standard candles (when using
relationship between peak brightness
and decay times - Philips relation),
provide evidence of universal
acceleration and cosmological constant
Benchmark Model (today)
H0 = 72 km s-1 Mpc-1
Ω0 = 1
ΩΛ = 0.73
Ωm = 0.27
Ωm,baryon = 0.04
Ωm,cold-dark-matter = 0.23
Ωr = 10-4
Age of universe = 13.7 Gyr
IMPORTANT: These are the properties today, different density
dependences for matter, radiation and cosmological constant
mean they are different in the past.
Fate of the Universe
2
Big Bounce
l
ΩΛ,0 1
ing
r
e
oit
Ω
m,
0+
0
Big Chill
Ω
Λ,
0=
1
k=+1
k=-1
-10
1
Ωm,0
Big Crunch
2
3
Local Universe: Hubble’s Law
• v=H0d => useful way of getting distances
Local Universe: Cosmological
Principle
• Universe is homogeneous and isotropic
– No preferred location
– No preferred direction
– Valid on large scales
a α t1/2
ω = 1/3
Rotation curves flat:
Dark Matter Dominant:
Probably Cold
Hubble’s law obeyed in
local universe
D
H0
v=
velocity
MACHO and
WIMP
searches microlensing
+ gammaray
Radial distance
a α eHt
ω = -1
t2/3
aα
ω=0
Matter
Radiation
Energy densities
εΛ = const
εm α 1/a3
εr α 1/a4
Horizon size
Type Ia supernova searches
10 ~Gyr - Matter- Cosmological constant equality
a α eHt
ω = -1
On large scales universe is
homogeneous and isotropic
(Cosmological Principle)
velocity
10-36s - increase scale
factor by ~1040
Solves flatness problem horizon problem
Peak of star formation
Inflation
Matter-radiation equality
Big bang
Vacuum fluctuations?
Brane collisions?
Nucleosynthesis
N+p => D
D+p => 3He
D+D => 4He
Jeans mass ~105 Msol.
Stars/Galaxies form
First stars/galaxies
Jeans mass >1018 Msol.
Galaxies can’t collapse
~300,000 years Cosmic Microwave background (e+p => H + γ)
ΩΛ,0 = 0.73, Ωm,o = 0.27, Ωr,0 = 10-5
H0 = 72 km s-1 Mpc-1
Spatially flat Ω0 =1
Distance
The universe on a side of A4
Λ
Time (total age = 13.5 Gyr)
Friedman
Fluid
Acceleration
Observational challenges/facts
Key points/ideas
Key periods in Universe history
Good luck!