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Astronomy 1000
Introduction To The Universe
Lecture 23: The Big Bang
Final Exam Schedule
Astro 1000 A
10th Dec. (Thur) 10:00 a.m. to 12:00 noon
Astro 1000 C
8th Dec. (Tues) 3:00 p.m to 5:00 pm
• final covers final 6-lectures plus
• two topics already covered in class
to be announced during last week.
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The Origin of the Universe
The “Big Bang”
- Relativity & the Big Bang
- Evidence for the Big Bang
* Hubble’s Law
* Cosmic Microwave Background
* Hydrogen & Helium abundance
- The Formation of Large Scale Structure
The Cosmological Principle
In speaking about the entire Universe we have to establish a few reasonable assumptions.
1) The Laws of Physics (Relativity, Quantum Mechanics, Quantum Electrodynamics)
are the same throughout the Universe and do not change with time.
! This assumption is actually testable. So far, the “constants” of physics do not seem
to have changed to “parts in a million” since the observable Universe was ~1/4 of its
current age.
2) The Universe is Isotropic on large scales.
That is, it looks the same in every direction.
This must be true everywhere in the Universe.
! the number of galaxies, galaxy clusters,
etc. you observe per square degree is the
same in any direction, provided you look
far enough away (i.e., > 300 Mpc).
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The Cosmological Principle
In speaking about the entire Universe we have to establish a few reasonable assumptions.
3) On sufficiently large scales (~300 Mpc, say) the Universe should look the same
everywhere. That is, the Universe is Homogeneous on large scales.
This assumption is consistent with best studies of structure on the largest scales: there are no
structures larger than ~300 Mpc (as far as we can tell!). Take a cube 300-Mpc on a side and set
it anywhere in the Universe. The contents of this big box should be approximately the same.
The Cosmological Principle
1) The Laws of Physics are the same everywhere and do not change.
2) The Universe is Isotropic (i.e., looks the same in any direction).
3) The Universe is Homogeneous (i.e., is the same everywhere).
We don’t know for sure that these assumptions are 100% correct everywhere. However, they
are consistent with all current observations.
If we accept the Cosmological Principle, several implications follow:
1) There can be no “edge” to the Universe.
! If you’re at the Universe’s “edge”, you will count different #’s of galaxies in
different directions. Also, a 300-Mpc wide box inside the “edge” will not look
the same as a 300-Mpc wide box outside the “edge”.
2) The Universe has no “center”.
! An observer at the “center” would see a different Universe compared with an
observer somewhere else. There is no preferred position in the Universe.
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General Relativity
General Relativity is Einstein’s theory of gravity. It helps describes the Universe on largest scales.
Special Theory of Relativity
1) Describes how different observers describe the same event when speeds approach “c”
2) Space and time are not separate things, but are welded together: “space-time”
General Theory of Relativity (GR): a new theory of Gravity
Newton: Massive objects (galaxies, stars, planets) exert gravitational forces on each other.
The resulting gravitational force causes objects to change their paths (e.g., make
a planet move in a circle around a star).
Einstein: Massive objects (star) “curve” or “warp” space-time. Nearby objects (planet)
follow curved paths in this warped space-time, giving rise to orbits (for example).
There is no Gravitational Force!
Matter tells space-time how to warp. Space-time tells matter how to move.
! Given the distribution of matter (galaxies, clusters of galaxies, etc.) in the Universe,
General Relativity will give the structure of space-time and its evolution.
General Relativity
Mass distorts space-time. Objects try to move in straight lines, but in a curved space-time
these “straight lines” are actually curved: Matter tells space-time how to bend/ Space-time
tells matter how to move.
The Earth’s mass causes surrounding space-time to “warp”. Objects moving near the Earth
(moon, Hubble Space Telescope, satellites, etc.) move in this “warped” space-time and follow
curved paths. There is no force of gravity according to General Relativity.
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Einstein’s Field Equations
“You think you have math problems…” Einstein in a letter to a girl
complaining about Algebra.
Newton’s Version of Gravity: FGrav = -G M1 M2/R2
F = dp/dt
Mass creates a gravitational force … … the force changes the object’s motion.
Einstein’s Version of Gravity: Rµ! = 8" Tµ!
(ten coupled equations … yikes!)
Mass & energy tells
space how to curve…
…curved space tells
mass how to move.
A Static or Evolving Universe?
Einstein found solutions of the equations of General Relativity that were consistent with the then
standard view among scientists: the Universe is unchanging, eternal, & static.
In mid-1920’s, George Henri Lemaitre, a Catholic priest, independently
finds solutions to Einstein’s equations of GR in which the Universe is
dynamic - i.e., it changes over time.
In particular, Lemaitre’s solution has the Universe expanding outward
from a “singularity” - a state of infinite density and zero-size! He likens it
to a “cosmic egg exploding at the moment of creation”.
Lemaitre also predicts what will become known as “Hubble’s Law”.
Most scientists (including Einstein initially) hate the idea, finding it too
reminiscent of the Judaeo-Christian idea of creation.
They derisively refer to it as the “Big Bang”.
Einstein eventually comes around and agrees with Lemaitre, calling his
earlier (non-expanding) solution “the biggest mistake of my career”.
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Hubble’s Law and the Big Bang
Hubble found - and Lemaitre predicted - that the further away a galaxy is, the faster it
appears to be moving away from us. What does this tell us about the Big Bang???
Recall:
Recessional Velocity = distance x Ho
Where Ho = 72 km/s/Mpc
= Hubble’s constant
Q: How long has it taken a given galaxy to
reach its observed distance?
A:Time = distance/velocity
= distance/(distance x Ho)
= 1/Ho
Note: this is true for any galaxy we could = ~14-billion years
have chosen.
Hubble’s Law implies that ~14-billion years ago all galaxies were in the same place!
Where Was the Big Bang?
It is incorrect to think of the Big Bang as having taken place at some point in the Universe,
Rather, the entire Universe - matter, energy, space-time - was created in the Big Bang!
The Balloon analogy:
Stick a bunch of coins on a balloon and inflate it more.
! The coins represent galaxies
! The balloon represents space-time.
! Matter + Space-time are the Universe.
• As you inflate the balloon the Universe expands, and
the galaxies move away from each other.
• An observer on any coin would see all the other coins
Time
moving away from him/her (Cosmological Principle).
• More distant galaxies (coins) appear to recede faster
than nearby galaxies (Hubble’s Law).
• There is no center in this Universe (Cosmological Prin.)
• Now deflate the balloon (run the Universe backwards!):
all the galaxies (coins) arrive at the same point at the
same time. The Big Bang didn’t happen at any one point.
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Recovering Hubble’s Law
Consider one of the coins (galaxies) on the inflating balloon (Universe), and the distances to
two other coins: one very close and one very distant.
B
Compare the distances to galaxies A & B as
A the “Universe” expands from times T1 to T2 :
T1 A: B:
B Velocity = Distance/Time
A
The more distant galaxy “B” has moved
a larger distance in the same time as
galaxy “A” has. This is Hubble’s Law!
T2 !This will be true for any galaxy/coin.
Redshift and recessional speed
Lines from a distant galaxy
#$
Hubble and others thought that this “redshift” was due a Doppler Shift, i.e.,
more distant galaxies were moving away from us at faster and faster speeds.
Vrecession ~ c z
7
Re-interpreting Redshifts
We explained the redshift of galaxies (i.e., spectral features shifting to longer wavelengths) as
a Doppler shift, due to their motion w/r to us. This is wrong! Photons traveling from distant
galaxies have their wavelengths increased by the expansion of Space-time. It has nothing to do
with velocities at all!
The redshift of a photon emitted by a distant galaxy measures the amount by which the Universe
has expanded since that photon was emitted. The further it travels, the more the Universe expands,
the more “stretched out” the photon becomes, the longer its wavelength becomes.
Evidence for the “Big Bang”
There are Three “Pillars” of evidence for the Big Bang. One is Hubble’s Law. The second
is the Cosmic Microwave Background radiation (CMB)…
The Universe soon after the Big Bang (~1 sec) was characterized by extremely high
densities and temperatures (T ~ 1010 K!). The Universe was filled with extremely
high energy photons in thermal equilibrium with matter:
! a Blackbody spectrum!
In the 1960’s it was realized by several teams of scientists that these photons would
still be present, though due to the expansion of the Universe, the photons would have
been greatly stretched out to longer wavelengths - peaking at $ ~ 1-2 mm.
A team at Princeton University started building a telescope to search for these photons!
8
Evidence for the “Big Bang”
“Boys… we’ve been scooped.”
In 1964, two engineers (Robert Wilson & Arno
Penzias) are trying to identify and eliminate sources
of radio noise/interference for US telephone service.
Using their funky “sugar-scoop” radio antenna,
they notice a persistent “hiss” coming from all
directions in space.
They tried (and eliminated) all sorts of possible
sources for this “hiss” (including fermenting
bird droppings in the antenna!).
They eventually realized that they were detecting
photons left over from the Big Bang, scooping the
team at Princeton University, & winning the 1978
Nobel Prize in physics!
But is this radiation a Blackbody as it was supposed to be?
Evidence for the “Big Bang”
Measuring the Cosmic Microwave Background’s
spectrum is extremely difficult from the Earth’s
surface due to atmospheric absorption.
People tried anyway, some claiming that the CMB
is not a Blackbody!
The issue is settled by the 1989 launch of COBE:
The Cosmic Background Explorer. COBE finds
the CMB is a Blackbody with T = 2.735 K.
The solid line is a Blackbody spectrum (T=2.735 K)
fit to the COBE data (black dots). The fit is
astonishingly good (note the error bars are smaller
than the size of the dots).
9
Evidence for the “Big Bang”
Stellar nucleo-synthesis does a marvelous job of accounting for the abundances of heavy
elements. However, there appears to be far too much Helium in the Universe.
! Most helium could not have been formed in the interiors of stars. It must have
another origin.
In the 1940’s two physicists - Charles Alpher & George Gamow - realized that shortly after
the Big Bang the conditions were right for the formation of helium nuclei - for about 200-sec.
neutron
deuteron
100-seconds after Big Bang, T ~109 K, and
Universe filled with photons, electrons,
neutrons and protons. Protons outnumber
neutrons 5-to-1.
proton (a)
(a) At these temperatures/densities protons
neutron
& neutrons can fuse to make a deuteron.
photon
(b) But the deuteron is promptly destroyed
by high energy photons…
(b) proton
Evidence for the “Big Bang”
After 200-seconds, the Universe has expanded and cooled enough to allow deuterons to survive.
neutron Step 1 - proton & neutron fuse together resulting
deuteron in a deuteron (“heavy” hydrogen nuclei)
proton
deuteron Step 2 - deuterons can now live long
Helium-3
enough to fuse together, leaving a
helium-3 nucleus (“light” helium).
Helium-4 Step 3 - for the next 100-seconds, the helium-3
nuclei can capture a neutron, forming
a nucleus of helium.
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Evidence for the “Big Bang”
Helium production takes place for only a brief window in the early Universe: from
200-sec to 300-sec after the Big Bang. Afterwards, the Universe has expanded
enough to make it reduce the temperature and density below the levels needed to
sustain these reactions: Helium production abruptly stops after 300-sec!
deuteron
Helium-3 Detailed calculations by Alpher & Gamow
showed that during this time one helium
nucleus forms for each 16 protons:
1 helium nucleus
12 protons + 1 helium nucleus
Helium-4 = 4 = 1/4 = 25% by mass
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This is precisely the abundance of helium we
observe. The remaining 75% of matter in the
Early Universe was hydrogen.
Indirect Evidence for the Big Bang
Quasars are currently extremely rare in the “local” universe. But once they were very common.
Quasar abundance changes greatly
with redshift - peaking at z ~ 2.5,
when universe was about 1/3 of its
current age.
This completely contradicts the
Steady State cosmology, which
predicts no change ever in universe.
This plot is taken to mean that z > 2.5
the universe wasn’t old enough to
form massive galaxies and SMBH.
This implies that the universe had
a definite beginning - the Big Bang.
11
The Formation of Structure
The Early Universe was extremely uniform and homogeneous. How did walls, voids,
clusters, and galaxies ever form out of this? Clues came from an orbiting radio telescope:
Cosmic Microwave Background Explorer (COBE) from the 1990s.
COBE measured the CMB temperature over the entire sky.
The map at left shows the resulting temperature map.
Blue is slightly hotter/red is slightly cooler. The pattern is
due to the Earth’s motion in space (Doppler Shift)
The map at left shows the resulting map of CMB temperature
after the Earth’s motion through space has been removed.
What’s left is the Milky Way (red band in middle) and some
Interesting “splotches”.
This map shows a map of small temperature variations
In the sky after removing the contribution from the Milky
Way. These temperature variations are small but very
Important!
The Formation of Structure
This map from COBE shows pattern of small temperature variations in the CMB radiation.
The CMB emission is actually remarkably uniform. The variations visible above as blue & red
Splotches represent variations of ~5 parts in 100,000, or about 0.0001 K around the 2.7 K CMB.
These very small temperature fluctuations represent (and arise from) fluctuations
in the matter distribution in the Early Universe (z ~ 1000).
12
The Formation of Structure
COBE was followed by another orbiting mission with higher angular resolution: the
Wilkinson Microwave Anisotropy Probe (WMAP) to look more closely at the CMB.
This map from WMAP shows the CMB after
removing emission from the Milky Way galaxy
and the Earth’s motion.
The CMB emission is still remarkably uniform.
Again, very small temperature fluctuations are
evident, indicating fluctuations in matter
distribution.
Temperature fluctuations visible in WMAP: !T/T=10-5 ! !"/" ~ 10-4
Structures visible today have much higher density contrasts:
!"/" ~ 103 (rich galaxy clusters)
!"/" ~ 106 (massive galaxy)
The Formation of Structure
The big question: how do we get from a
Z~ 1000
nearly perfectly homogenous early Universe
to the very clumpy one we see all around us?
The answer: extremely small over-dense regions
grew progressively denser under their own
self-gravitation. Eventually, these regions
became dense enough to form the filaments,
walls (and voids), and clusters of galaxies.
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The Formation of Structure
The Universe appears to have started as a mixture of (mostly) dark matter and ordinary matter.
A few-thousand years after the Big Bang the dark matter started to clump due to its own gravity.
The dark matter clumps grew into large scale structures (filaments, walls, clusters, etc.) and
“ordinary” matter flowed into it, eventually forming galaxies.
! Dark matter formed the structures. Ordinary matter followed its overall distribution.
The Formation of Structure
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The Formation of Structure
Here’s another numerical simulation showing the development of structure in Dark Matter
starting from ~1000-years after the Big Bang to the present. The region in the simulation
expands with the Universe so you can watch the same structure form.
The Universe is very “smooth” at first.
Again, random density fluctuations in
the Dark Matter distribution grow both
in size and mass as they attract more &
more Dark Matter via gravity.
Ordinary matter (hydrogen & helium
clouds) will also flow into these dense
regions and start collecting at the
centers, eventually forming primeval
galaxies.
Summary
1. Cosmological Principle: The Universe is Isotropic & Homogeneous. The Laws of Physics are
the same everywhere.
2. Lemaitre found solutions of Einstein’s GR equations that allowed for an expanding Universe,
originating in a singularity (derisively called the Big Bang).
3. Hubble’s Law implies all galaxies were at same place ~14-billion years ago.
4. The Big Bang did not occur “in” space. Spacetime + matter + energy were created in BB.
5. Redshifts do not arise from Doppler Shifts, but from photons travelling through an expanding
Universe.
6. Three Pillars of the BB: Hubble’s Law, the Microwave Background radiation, & Cosmic
Nucleo-synthesis.
7. Large scale structure forms as random density perturbations in the Dark Matter grow over
time. Ordinary Matter (hydrogen & helium gas) follows this distribution.
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