Modern Cosmology
Continuing Education Course
The University of Sydney
Winter 2009
Week 4
Transformation of cosmology into
observational science:
• Dark Matter
• Discovery of CMB
• Observations of distant supernovae
• Dark Energy
Evolution of the Universe:
• Big Bang and the first three minutes
1
Measurements of Hubble Constant
 Uncertainties in distance measurements
Hubble time:
t0 =
1
H0
In general:
!
t0 =
1
F(")
H0
!
Latest value of H0 = 74.2 +/- 3.6 km/second/Mpc from the
SHOES project (Supernova H0 for the Equation of State) observations of Cepheids in galaxies which also had
supernovae type Ia in the past
Independent measurements of the age of
the Universe
･The age of the chemical elements.
Radioactive decay of elements in the oldest stars 14.5 +/- 2.8 Gyr
･The age of the oldest star clusters.
From the lifetime of stars in oldest clusters as a function of luminosity
11.5 +/- 1.3 Gyr
･The age of the oldest white dwarfs.
From estimates of their cooling time 12.8 +/- 1.1 Gyr
The t0 appears to be shorter than all the above for a
reasonable models with cosmological constant Λ
being zero.
2
Curvature of the Universe
"=
Ω>1
Ω=1
Ω<1
#TOT
#CRIT
k=1
k=0
k=-1
Density parameter - the ratio of the total
energy density to the critical energy
density in the universe
Positive spherical curvature, closed universe
Flat space, open infinite universe
Negative curvature, open infinite universe
!
The self-gravitation of the Universe acts to slow down the expansion with time
since the Big Bang (characterized by the deceleration parameter q0).
Shape of the Universe.
Can Ω be measured by direct observations?
The geometry and evolution of the universe depends on the contribution of
various types of matter and energy, radiation pressure and cosmological
constant and possibly vacuum energy term.
"TOT = "M + "R + "# + "k
Methods:
 Adding up all forms of matter (ΩM )
!
 Luminosity distances of galaxies
 Angular-size distances
 Number counts of galaxies
 Fluctuations in the Cosmic
Background Radiation (ΩTOT, Ωk, ΩR)
 Observations of extragalactic
supernovae (ΩΛ)
3
Standard candles
Astronomers cannot measure distances directly
but if the true luminosity of the object is known
its distance can be found by the inverse square
law.
 RR Lyrae
 Cepheids
 Supernovae
m " M = "5 + 5log DL
!
Distance-redshift
relationship
Remember - redshift is a measure of light ‘stretching’ in
expanding Universe.
Luminosity Distance (DL)
a young and distant galaxy at
redshift 15 appears to be about 560
billion light years from us as derived
from its observed luminosity
 Angular Diameter Distance (DA)
a galaxy at redshift 15, which we
see today, emitted the light about
2.2 billion light years ago.
 Light Travel Time Distance (DT)
the light from this galaxy traveled
for 13.6 billion years from the time it
was emitted
 Comoving Distance (DC)
this same galaxy today, if we could
see it, would be about 35 billion light
years from us.

These distances converge for the nearby Universe.
4
Hubble diagram
Brightness -from DL
Test of cosmological models, because the distance depend on
H0 and its derivative (deceleration parameter q0 )
Hubble diagram - measures brightness of a class of object
(‘a standard candle’) versus its redshift and its curvature
probes the expansion rate of the Universe
Forms of matter and energy in
ΩTOT
Both energy density and pressure contribute to the strength of
gravity in General Relativity.
Pressure is also a form of energy especially important in the hot Universe.
The Universe with pressure has increased gravity. E=mc2
Baryonic matter:
"ordinary matter" - protons, neutrons and electrons
- no pressure of cosmological importance
Dark matter:
"exotic" - non-baryonic matter that interacts only weakly with
ordinary matter (WIMPS) or neutrino
baryonic matter - MACHOs (Massive Astronomical Compact Halo Objects)
- no cosmologically significant pressure
Radiation:
massless or nearly massless particles that move at the speed of light
(photons and neutrinos)
- contribute large positive pressure
Dark energy:
either a bizarre form of matter, or a property of the vacuum itself
- has a large, negative pressure
The only form of matter that can cause the expansion of the universe to
accelerate, or speed up
5
Dark matter
 Observation of clusters of galaxies
- velocities of galaxies are higher than expected from the gravitational pull of visible
members (Fritz Zwicky was first to notice this in 1933)
- gravitational lensing
- in fact only 5% of mass in clusters is visible based on the movement of visible
galaxies
- dark matter dominates at larger scales
In Coma cluster there
is about 400 times
more unseen mass
than luminous mass.
Dark matter
 Most of the visible mass is locked in stars
we observe most stars orbiting Galaxy at the similar
speeds
but
V=(GM / r) ½
Vera Rubin
 Dynamical studies of galaxies indicate
the significant fraction of the mass in
the Universe is missing
Rotation curve of the Galaxy
6
Mean density of matter in the Universe
 Counts of luminous objects (stars, galaxies, galaxy clusters) give 0.5% of ρCRIT
 Gas (hydrogen, helium) - 4% of ρCRIT
 Dark matter evident from: dynamics of galaxies, measurements and simulation
of large scale structure, gravitational lensing - 25% of ρCRIT
Total mass density parameter
corresponds to ΩΜ=0.3
Not enough if the
Universe is flat (Ω=1)
Cosmic Microwave Background Radiation Prediction of the Big Bang model
For every matter particle in
the Universe there are 10
billion more photons.
Cosmic background
photons are the product of
matter/anti-matter
annihilation in the early
Universe. They were
formed as most energetic
gamma-rays.
During the
first 300000
years
(radiation era)
photons were
scattering off
particles.
The wavelength of
these photons
stretched during the
process of
expansion. Today
they are visible as
microwave photons.
When the Universe
cooled matter
recombined and
cosmic background
photons escaped from
the interaction with
matter to travel freely
through the Universe.
Most photons in the
Universe are cosmic
background radiation,
invisible to the eye
7
Observations by Wilson and Penzias
 Experiments with a very sensitive 6m horn antenna, with the receiver
cooled to -269o C
 Detection of the steady residual noise in all directions in the sky, at 7.3cm
 Independently Jim Peebles and collaborators at Princeton University were
ready to search actively for microwave radiation
 In 1978 Robert Wilson and Arno Penzias received Nobel Prize in Physics
Wrinkles in the CMBR
 Cosmic Background Explorer (COBE)
experiment launched in 1989:
mapping variations of the CMB over
various directions
measuring the spectrum of the CMB
 Results from COBE Differential
Microwave Radiometer (DMR)
mapped the full sky at 53 GHz and
90 GHz
 FIRAS confirmed that the observed
radiation has a blackbody spectrum
with a temperature:
2.735 K +/-12 µK,
8
Cosmic Background Fluctuations
Map with the equal area
projection
10 degrees resolution images
• Dipole due to the movement of the Solar
system relative to the distant matter in the
Universe
• Galactic emission from cosmic rays, electronion bremsstrahlung, diffuse ionized gas and dust
Fluctuations of the order of 1 part in 100000
WMAP
Wilkinson Microwave Anisotropy Probe
• Launched in 2001
• 13 arcminute resolution full sky map
• 45 times higher sensitivity than COBE
• Wavelengths between 3.2 and 13 mm
9
Large structure of the Universe
During gravitationally driven evolution the inhomogeneities in the
Cosmic Microwave Background gave rise to the observed
‘clumpiness’ of the Universe.
Large structure of the Universe
 Galaxies are grouped in clusters
 Clusters of galaxies form SUPERCLUSTERS
 Superclusters are arranged in filaments and strings on the surface of
‘bubbles’
 Regions within bubbles are voids - ‘spongy’ large scale structure
|<----300 billion ly -------->|
10
Simulations of large structure
Millennium Simulation (Springel et al.- the largest N-body
simulation carried out (more than 1010 particles).
Theoretical simulations can follow the growth of the
‘clumpiness’ for different curvatures of the Universe.
z=18.3 (t = 0.21 Gyr)
z=5.7 (t = 1.0 Gyr)
z=1.4 (t = 4.7 Gyr)
z=0 (t = 13.6 Gyr)
Geometry of the Universe
from WMAP data
Experiments like WMAP, BOOMERANG and MAXIMA find the angular scale
of fluctuations in the CMB to be about 1 degree.
Such result is expected for the flat Universe (ΩΤΟΤ~1).
If ΩΜ~0.3, what constitutes the rest?
11
Observations of Supernovae
Type Ia supernovae are best
‘standard candles’ for
independent measurements
of distances due to known
model constraints on their
luminosity evolution.
Observations of Supernovae
In 1998 the Supernova Cosmology and High-z Supernova teams used
Type Ia supernovae as ‘standard candles’ to construct a Hubble diagram
out to redshift of 1.
Both teams found that supernovae appear too dim for what is predicted from the
model of the Universe with ΩΜ=0.3.
The Universe
accelerates!
What causes this acceleration?
- Repulsive force
- Not an ordinary matter
- It contributes negative energy
pressure
12
Energy pressure
 Solutions to Einstein’s equations
express deceleration of the
Universe as dependent on pressure
P and energy density of mass ρ,
 Acceleration decreases with
increasing pressure and energy
density
After Einstein added
cosmological constant to his
solutions it took a role of a
negative pressure which
counteracts deceleration
Energy density of vacuum from the Heisenberg
Uncertainty Principle: ΔEΔt > h/2π
In a pair production process photon can transfer
enough energy to bring virtual particles to reality.
Vacuum has negative pressure, more space
corresponding to more pairs formed, which exert
more pressure.
Dark Energy
• Cosmological constant 10−29g/cm³
Why so small?
Vacuum energy (calculated from quantum physics
120 orders of magnitude too large)
• Quintessence - variable parameter- very light
dynamic field - not confirmed, its existence would
possibly affect fundamental constants
• Or general relativity fails on the largest scales of
the Universe
13
Concordance Cosmology Λ−CDM model
Λ- dark energy term causes current accelerating
expansion of the universe. Currently, ΩΛ=0.74,
implying 74% of the energy density of the present
universe is in this form.
Cold dark matter (its velocity is non-relativistic at the
epoch of radiation-matter equality), ΩDM=0.22
• possibly non-baryonic,
• dissipationless (can not cool by radiating photons)
• collisionless (interacts only through gravity)
H0 = 73.2 km/s/Mpc
T0 = 13.73 Gyr
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