Astro 101
Fall 2013
Lecture 12
Cosmology
T. Howard
Cosmology = study of the Universe as a whole
• ? What is it like overall?
• ? What is its history? How old is it?
• ? What is its future?
• ? How do we find these things out from what we can observe?
• In 1996, researchers
at the Space Telescope
Science Institute used
the Hubble to make a
very long exposure of
a patch of seemingly
empty sky.
Q: What did they find?
A: Galaxies “as far as
The eye can see …”
(nearly everything in
this photo is a galaxy!)
40 hour exposure
What do we know already (about the Universe) ?
•
•
•
•
Galaxies in groups; clusters; superclusters
Nearby universe has “filament” and void type of structure
More distant objects are receding from us (light is redshifted)
Hubble’s Law:
V = H0 x D
(Hubble's Law)
Structure in the Universe
What is the largest kind of structure in the universe? The ~100-Mpc
filaments, shells and voids? On larger scales, things look more uniform.
600 Mpc
Olbers’ Paradox
• Assume the universe is homogeneous, isotropic, infinte, and static
• Then:
 Why don’t we
see light
everywhere?
 Why is the
night sky
(mostly) dark?
Olbers’ Paradox (cont’d.)
• We believe the universe is homogeneous and isotropic
• So, either it isn’t infinite OR it isn’t static
• “Big Bang” theory – universe started expanding a finite time ago
Given what we know of structure in the universe, assume:
The Cosmological Principle
On the largest scales, the universe is roughly homogeneous (same at all
places) and isotropic (same in all directions). Laws of physics are
everywhere the same.
Hubble's Law might suggest that everything is expanding away from
us, putting us at center of expansion. Is this necessarily true?
If there is a center, there must be a boundary to define it => a finite
universe. If we were at center, universe would be isotropic (but only
from our location) but not homogeneous:
Finite volume of galaxies
expanding away from us
into...what, empty space?
Then part of universe has
galaxies and part doesn’t.
Us
But if we were not at center, universe would be neither isotropic nor
homogeneous:
Us
So if the CP is correct, there is no center, and no edge to the Universe!
Best evidence for CP comes from Cosmic Microwave Background
Radiation (later).
The Big Bang
At time zero, all separations were infinitely small. Universe then
expanded in all directions. Stars, galaxies formed as expansion
continued.
All galaxies now moving away from each other.
A galaxy twice as far away from us, is moving twice as fast (Hubble's
Law).
So, how old is the Universe?
Reversing the Hubble expansion, all separations go back to zero. How
long ago?
H0 gives rate of expansion. Assume H0 = 75 km / sec / Mpc. So galaxy at
100 Mpc from us moves away at 7500 km/sec. How long did it take to
move 100 Mpc from us?
time =
=
distance
velocity
100 Mpc
7500 km/sec
= 13 billion years
(Experts note that this time is just
We can do this same
calculation for
galaxies at other distances,
getting a similar answer.
Age of universe is related
to H0. Note, H0 may be
in range 65 – 75
km/sec/Mpc
1 ).
H0
The faster the expansion (the greater H0), the shorter the time to get to
the present separation.
Redshift vs. “Lookback Time”
• Astronomers (and physicists) denote redshift by “z”
= amount light has shifted relative to its (laboratory, at rest) wavelength
= direct measure of speed of recession of distant galaxies
z
light travel time
(Gyr)
Age at redshift
(Gyr)
0.037
0.075
0.254
0.488
1.04
1.74
6.54
10.13
0.5
1.0
3.0
5.0
8.0
10
13
13.38
13.360
12.860
10.860
8.860
5.860
3.860
0.860
0.480
1 Gyr = 1,000,000,000 years.
Time (now) since Big Bang = 13.860 Gyr
using H0 = 70 km/sec/Mpc
Flat universe
But this is not galaxies expanding through a pre-existing, static space.
That would be an explosion with a center and an expanding edge.
If CP is correct, space itself is expanding, and galaxies are taken
along for the ride. There is no center or edge, but the distance
between any two points is increasing.
A raisin bread analogy provides some insight:
But the bread has a center and edge. Easier to imagine having no center
or edge by analogy of universe as a 2-d expanding balloon surface (this
is only one possible analogy for our universe’s geometry):
Now take this analogy "up one dimension". The Big Bang occurred
everywhere at once, but "everywhere" was a small place.
(To understand what it would be like in a 2-d universe, read Flatland
by Edwin Abbott: www.ofcn.org/cyber.serv/resource/bookshelf/flat10 )
The Cosmic Microwave Background Radiation (CMBR)
A prediction of Big Bang theory in 1940's. "Leftover" radiation from
early, hot universe, uniformly filling space (i.e. isotropic,
homogeneous). Predicted to have perfect black-body spectrum.
Photons stretched as they travel and universe expands, but spectrum
always black-body. Wien's Law: temperature decreases as
wavelength of brightest emission increases => was predicted to be ~ 3
K now.
Found in 1964 by Penzias and Wilson. Perfect black-body spectrum at T
= 2.735 K. Uniform brightness (and thus temperature) in every direction.
Points are data on the spectrum of the CMBR
from the COBE satellite (1989). Curve is a
black-body spectrum at T=2.735 K.
1% of the
“snow” on a
blank TV
channel is this
radiation!
All-sky map of the CMBR temperature, constant everywhere to one part in
105 ! For blackbody radiation, this means brightness is very constant too
(Stefan’s law).
(WMAP satellite)
Deviations are -0.25 milliKelvin (blue) to +0.25 milliKelvin
(red) from the average of 2.735 Kelvin.
The Early Universe
The First Matter
At the earliest moments, the universe is thought to have been
dominated by high-energy, high-temperature radiation. Photons had
enough energy to form particle-antiparticle pairs. Why? E=mc2.
pair
production
annihilation
At time < 0.0001 sec, and T > 1013 K, gamma rays could form protonantiproton pairs.
At time < 15 sec, and T > 6 x 109 K, electron-positron pairs could form.
Annihilation occurred at same rate as formation, so particles coming in
and out of existence all the time.
As T dropped, pair production ceased, only annihilation. A tiny
imbalance (1 in 109) of matter over antimatter led to a matter universe
(cause of imbalance not clear, but other such imbalances are known to
occur).
Primordial Nucleosynthesis
Hot and dense universe => fusion reactions.
At time 100-1000 sec (T = 109 - 3 x 108 K), helium formed.
Stopped when universe too cool. Predicted end result: 75%
hydrogen, 25% helium.
Oldest stars' atmospheres (unaffected by stellar nucleosynthesis)
confirm Big Bang prediction of 25% helium.
We are now in a “Matter-dominated” epoch
Other Measurements Support the Big Bang Model of the Universe
(Detailed Big Bang theory predicts some things we can measure)
We can’t “see” all the way to the Big Bang
[we see its “echo”]
(Now)
…
< -- Time
…
(Early Universe)
Radiation and
Matter “decoupled”
Nuclei and electrons
combine to form
atoms (H, He)
More complex atoms
form later from
fusion
This explains CMB
Galaxies –
form around clumps
of Dark Matter ?
Opaque
Transparent
Computer simulations of structure formation around clumps of Dark Matter
predict a universe with shapes/sizes very similar to what we observe.
Time since
Big Bang.
Cosmic expansion timelines (1)
Big Bang cosmology + Dark Energy, WMAP values
Current mass density ratio 0.27 (incl. Dark Matter)
Current value of Dark Energy equivalent density ratio, 0.73
H0 ~ 71 km/s-Mpc
Era or Event
Time
Temp
Planck Era
Planck transition
** Grand unification era **
Grand unification of forces ends
Inflation
** Electro weak era **
Electroweak era ends
** Quark era **
Quark era ends
< 5x10-44
5 x 10-44
> 1019 GeV
1019 GeV
10-36
10-36 to 10-34
1015 GeV
1015 GeV
10-11
100 GeV
10-5
200 MeV
Cosmic expansion timelines (2)
Era or Event
Time
Temp
Neutrino decoupling
e- e+ annihilation ends
n-p ratio frozen
Deuterium formation begins
Matter-dominated era begins
** Matter era **
CMB visible
1st stars form
1st galaxies form
universal expansion accelerates
Dark Energy dominates
** Dark Energy era**
Today
0.1 s
1.3 s
1.8 s
176 s
55000 year
3 MeV
1 MeV
1010 K
109 K
8920 K
redshift
z = 3233
~300,000 yr
3000 K
200Myr – 1 Gyr
1 Gyr – 5 Gyr
~ 7.1 Gyr
z= 0.76, R =0.57
~ 9.5 Gyr
z = 0.39, R = 0.72
~ 13.7 Gyr
z = 0, R = 1
The Early Universe
Inflation
A problem with microwave background:
Microwave background
reaches us from all
directions.
Temperature of background in opposite directions nearly identical.
Yet even light hasn't had time to travel from A to B (only A to Earth),
so A can know nothing about conditions at B, and vice versa. So why
are A and B almost identical? This is “horizon problem”.
Solution: Inflation. Theories of the early universe
predict that it went through a phase of rapid expansion.
Separation
between two
points (m)
If true, would imply that points that are too far apart now were
once much closer, and had time to communicate with each other
and equalize their temperatures.
More on Dark Matter
•
Dark matter thought to be necessary in cosmology theory to explain
clumpy distributions of matter massive enough for galaxies to form
• Could have been either CDM or HDM
• CDM = non-relativistic (speed << c)
• HDM = relativistic (speed ~ c)
• Usual predictions of CDM candidates require modifications or
extensions to Standard Model of particles
• Non-baryonic candidates
• Neutrinos (neutrino oscillation  implies neutrino mass)
• WIMPs – hypothetical
• Possibly “heavy” neutrinos or something equally exotic
• Axions
Current Status
Dan Hooper - Closing In On Dark Matter
Evidence For Dark Matter
!
Galactic rotation curves
!
Gravitational lensing
!
Light element abundances
!
Cosmic microwave
background anisotropies
!
Large scale structure
Dan Hooper - Closing In On Dark Matter
Evidence For Dark Matter
!
There is a wide variety of
independent evidence that
dark matter exists
!
Each of these observations infer
dark matter’s presence through
its gravitational influence
!
Still no observations of dark
matter’s electroweak
interactions (or other
non-gravitational interactions)
Dan Hooper - Closing In On Dark Matter
What Happens to the Universe?
The Geometry of Curved Space
Net density
of matter
and
Fate of the
Universe are
related
The universe as
a curved space
Analogy using
the Earth’s surface
What Happens to the Universe?
The Geometry of Curved Space (cont’d.)
Possibilities:
1) Space curves back on itself (like a sphere). "Positive" curvature.
2) “Saddle-like”, with curvature in the opposite sense in different
dimensions: "negative" curvature.
3) A more familiar “flat” geometry.
In general relativity, the geometry of the universe depends on the total
mass and energy of the universe (including dark energy). Latest CMBR
measurements are consistent with flat, infinite universe (curved, finite
universe still possible, with enormous radius of curvature).
All-sky map of the CMBR temperature, constant everywhere to one part in
105 ! For blackbody radiation, this means brightness is very constant too
(Stefan’s law).
(WMAP satellite)
Deviations are -0.25 milliKelvin (blue) to +0.25 milliKelvin
(red) from the average of 2.735 Kelvin.
Sizes of patches in CMBR constrain geometry of universe.
Curvature of universe makes it act like lens or pair of glasses
measure this angle ( 1°)
some
known
size
we know this distance
Size of patches simply related to speed of light and age of universe
when CMBR photons started streaming freely. This we know quite
well. Also know how far away we are looking. Then angular size
of patches tells us how light has traveled to us => curvature of space.
Supernovae – extremely violent stellar explosions
• Several types & subtypes (called type “I”, “Ia”, “II”, etc.)
• Different types arise from pre-explosion stellar conditions
• Type Ia has been
shown to have a
change in brightness
over time that has a
shape related to its
total luminosity
 Implies that SNe Ia
can be used as
“standard candles”
Example supernova remnant—
Crab nebula in Taurus
Brightness 
Supernovae Ia – Standard Candles for Cosmology
Time 
The Cosmological “Distance Ladder”
Standard candles:
Type Ia
Supernovae
[SNe Ia]
Recent Discovery:
The Expansion of the Universe Seems to be Accelerating
The gravity of matter should retard the expansion. But a new distance
indicator shows that the expansion rate was slower in the past!
Taking this into account, best age estimate
of Universe is 13.8 Gyrs.
Note, 2011 Nobel Prize in Physics
was awarded for this discovery
Redshift (fractional shift in
wavelength of spectral lines)
Type I supernovae: from ones in nearby
galaxies, know luminosity. In distant galaxies,
determine apparent brightness. Thus
determine distance. Works for more
than 3000 Mpc. From redshifts, they are
not expanding as quickly from each
other as galaxies are now.
H0 was
smaller in
past (i.e.
for distant
galaxies)
Source: E. Wright, UCLA
What can explain the
acceleration?Current theory:
“Dark Energy”
Einstein in 1917 introduced a special mathematical term, Lambda (“L”)
as part of General Relativity.
He thought it was needed to balance gravitational attraction and create a
static Universe (turned out to be wrong!).
But, we can think of L as repulsive force that exists even in a vacuum.
The accelerating universe indicates there is (something akin to) a L.
More generally called "dark energy". We have little idea of its physical
nature.
The measured amount of acceleration implies that there is actually
more “dark energy” than the energy contained in matter !
Current Theories : Universe is 70% + “Dark Energy” !!
Supported by –
CMBR measurements
Supernovae Ia measurements
Statistical studies of
Galaxy Clusters
Will this change? Stay tuned!
• Astronomers and physicists are seeking advanced methods to study
the early universe to try and understand “Dark Energy”
• One leading candidate – a new space telescope, “WFIRST”
Successes of the Big Bang Theory
1) It explains the expansion of the universe.
2) It predicted the cosmic microwave background radiation, its
uniformity, its current temperature, and its black-body
spectrum.
3) It predicted the correct helium abundance (and lack of other
primordial elements).
Misconceptions about the Big Bang
1. “The universe was once small.” The observable universe, which is
finite, was once small. The nature of the entire universe at early times
is not yet understood. It is consistent with being infinite now (or has
enormous radius of curvature).
2. “The Big Bang happened at some point in space.” The CMBR
showed that it happened everywhere in the universe.
3. “The universe must be expanding into something.”
It is not expanding into “empty space”. That would imply the Big Bang
happened at some location in space.
It is a stretching of space itself.
4. “There must have been something before the Big Bang.”
The Big Bang was a singularity in space and time (like the center of a
black hole). Our laws of physics say the observable universe had
infinitesimally small size, and infinite temperature and density. Such
“infinities” indicate a breakdown of our theories.
In these conditions, we don’t have a physics theory to describe
the nature of space and time. At the Big Bang, time took on the
meaning that we know it to have.
"Before" is only a relevant concept given our everyday
understanding of time. We must await a better understanding of
the nature of space and time. Such theories are in their infancy.
Why did Big Bang occur? We don’t know.
Shouldn’t be surprising that these concepts are hard to grasp.
So was the heliocentric Solar System 400 years ago.