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Cosmology
Cosmology
The Study of the Creation and Evolution of
the Universe as an entity
• Did the Universe have a beginning?
– If so, how did it begin?
– When did it begin?
• Has the Universe changed over time?
– Is it changing/evolving now?
• What will the Universe become?
– If there is a final state, what will it be like?
– How much time will it take?
Cosmology
Let's begin by considering an old and
very simple question:
Why is the sky dark at night?
Olbers' Paradox
It is this seemingly stupid question
that leads us to Olbers' Paradox.
Obviously, at night the Sun is
illuminating the opposite hemisphere
of the Earth, but what about the
stars?
Olbers' Paradox
Suppose that we consider a shell about the Earth at some distance away.
Confined within the bounds of this shell are a number of stars:
R
Let's say that
on the average
there are N
stars in this
shell
Olbers' Paradox
If we add additional shells, the
total light from a shell decreases as
1/r2
But the number of stars in a shell
increases as the area of the shells
(we assume they are thin enough
that we don't have to worry about
the thickness of any shell,
therefore the number of stars
increases by r2
Total Light per Shell = Light/star X Number of Stars in the shell
r2
Olbers' Paradox
Total Light per Shell = Light/star X Number of Stars in the shell
=
Light/star x N x r2
r2
=
Light/Star x N
Total Light is the sum of the light/shell times the
total number of shells
This sums to INFINITY
The dimming of the light by distance is balanced
by the increasing number of stars
Olbers' Paradox
An infinite amount of light is not as bright as daylight --- It
would incinerate the Earth!
The paradox?
We are not incinerated; the night sky is dark.
What's wrong? Well, the stars are not that close together --But the galaxies are!
Hubble Deep Sky North
Olbers' Paradox
Perhaps there are clouds of gas and dust blocking
the starlight? So what, the gas and dust would
eventually heat up and re-radiate the starlight.
For a static, infinite Universe, we've got a problem,
not only should the sky be as bright as the sun at
night, but much, much brighter. And, of course, it
isn't.
This problem remained unsolved for over 100 years
The Cosmological Constant
• In 1915, Einstein produced his General
Theory of Relativity which amongst many
other thing predicted that the Universe
was either collapsing or expanding. As this
was contrary to 'known fact', Einstein
reluctantly introduced a constant into his
equations, , which forced the universe to
remain static.
• He later referred to this as 'the greatest
blunder of his career' for reasons we shall
see in a moment.
Hubble's Law
•
In the 1920's, Edwin Hubble began to measure the spectra of the
galaxies – remember, at this time it still wasn't completely clear
just what the galaxies were. He found that the spectra was, in
general redshifted, and there was a relationship between the
distance and the radial recessional speed. Leading to the
realization that the Universe is not static but expanding.
•
The dominant motion in the universe is the smooth expansion known
as Hubble's Law.
• Recessional Velocity = Hubble's constant times distance
V = Ho D
where, V is the observed velocity of the galaxy away from us, usually in
•
km/sec; H is Hubble's "constant", in km/sec/Mpc and D is the distance to
the galaxy in Mpc
In 1929, Hubble estimated the value of the expansion factor, now
called the Hubble constant, to be about 500 km/sec/Mpc. Today
the value is still rather uncertain, but is generally believed to be in
the range of 45-90 km/sec/Mpc.
Hubble’s Law
•
•
•
While in general galaxies follow the
smooth expansion, the more distant
ones moving faster away from us,
other motions cause slight deviations
from the line predicted by Hubble's
Law.
Few of the points fall exactly on the
line. This is because all galaxies have
some additional residual motion in
addition to the pure expansion.
– This is referred to as the
"cosmic velocity dispersion" or
"cosmic scatter" and is probably
due to the fact that the gas
clouds that formed the galaxies
all had some small additional
motion of their own.
The recessional velocity of a galaxy
at a particular distance inferred
from Hubble's law is called the
"Hubble velocity".
This diagram shows a typical plot of
distance versus recessional velocity,
with each point showing the relationship
for an individual galaxy.
Models of the Universe
• While Hubble discovered the Expanding Universe,
unfortunately his data was flawed. He mistook – largely due to
the available equipment of his time – H II regions for galaxies,
and used a different type of Cepheid variable (only one type
was known then) in determining distances. This resulted in a
Hubble Constant of about 500 km/sec/Mpc. Since H0 can be
inverted to give the age of the universe, this results in the
universe being created about 2 billion years ago.
• This is a bit of a problem, the geological records here on Earth
are older that 2 billion years. Hmmmm
• One solution to this quandary is to devise a model of the
Universe which, while expanding, doesn't depend on a starting
time.
–
This was proposed by Bondi, Gold and Hoyle in the 1950’s
Choices
• The Cosmological Principle
– The Universe looks the same from any
location in any direction
• Applies to large scale
• Homogeneous and Isotropic
• embodies the “there is no preferred place”
• The Perfect Cosmological Principle
– The Universe looks the same from any
location in any direction and any time
The Steady State Model
This model of the Universe states that it has neither a beginning or an
end. The Universe is the same now as it always was and always will
be.
This, of course, evades the question of the geological record since the
expansion rate is independent of a beginning point in time.
We still have to account for the expansion. This is done by the idea of
"continuous creation of matter." If matter is allowed to be
spontaneously created "out of nothing" then the additional matter
will cause the universe to expand appropriately.
How much matter? What about conservation of mass and energy?
The creation rate is about 1 hydrogen atom/cubic meter/10 billion
years
This is much to small for us to test the conservation law – we don't
know if it holds at this level.
The Big Bang Model
• Somewhat later, Hubble's Constant was
revised (using new data) and reduced to a
value of between 55 and 75 km/sec/Mpc.
Leading to an age of between 10 and 15
billion years.
• George Gamow proposed a model in which
there was a definite beginning point. At a
given point in the past, the primordial
universe exploded. The expansion is a
result of this cosmic explosion. This was
termed the "Big Bang"
The Big Bang
The term, Big Bang, is somewhat unfortunate
because it gives the impression that the
stars and galaxies are flying apart like the
shards from an exploding bomb.
This is not what is happening!
What is expanding is space-time itself – the
galaxies are simply embedded in an everenlarging framework.
Big Bang Expansion
The galaxies (raisins) are not expanding, the space-time
framework (bread dough) supporting them is.
Olbers' Paradox Revisited
Now we finally have an answer to Olbers' Paradox.
• The universe is not infinitely old nor infinitely large
• The light is redshifted, losing energy, due to the
expansion of the universe
• There is a point where the rate of expansion nears
the speed of light beyond which the light cannot get
reach us in the amount of time since the big bang.
Models
• The debate raged until 1964, when Arno Penzias and Robert
Wilson of Bell Labs constructed a new type of microwave radio
antenna.
• They kept getting a static signal, no matter how they tuned and
oriented the antenna. At one point they even constructed a
pigeon trap thinking that the guano being deposited in the horn of
the antenna by the nesting pigeons was the source of the static.
• Finally someone mentioned to them to talk to Robert Dicke at
Princeton --- It seems that Dicke had predicted that the cooling
of the expanding universe from its original hot, dense state would
be detectable as a 3º K blackbody background radiation.
CMB
•Penzias and Wilson then
looked at the signal and
fitted it to the blackbody
curve -- It was a match at
2.7 º K
•The remnants of the Big
Bang had been found.
Models
• Finding the 2.7 º K Cosmic Microwave
Background radiation was the first
nail in the coffin for the Steady
State theory.
• Other nails were added with quasars,
distribution of peculiar galaxies and
other things found at distances
corresponding to high-redshift
values.
Cosmic Microwave Background
Here is a map of the CMB corrected for our motion
through the Universe and removing the noise
generated by our galaxy. The difference between
the red and blue levels (the fluctuations) is 1 in
100,000 or about ±30 micro-Kelvin
Geometry Anyone?
Before we continue, let’s take a brief look at something
you all learned long ago.
Remember that the circumference of a circle is 2∏ times
the radius?
How about the sum of the interior angles of a triangle
add up to 180 degrees?
How about the statement that parallel lines never meet?
These rules provide what we call “Flat” space
Flat Space
Positively-curved Space
Negatively-curved Space
Parallel lines diverge
Geometries
How does this relate to the Universe?
Wait and See…
What Next?
• If the Universe had a beginning, will it have an end?
• This will be determined by the total amount of mass in the
Universe
– If there is enough mass, then the force of gravity will slowly
stop the expansion and pull it back together again
– If there is not enough then it will keep expanding
– The boundary between these two extremes is the critical mass
• Since we don’t know the exact values, it’s more useful to talk in
terms of the ratio of the total mass of the Universe to this
critical mass.
– It is given the symbol

= (actual mass)/(critical mass)
The Nature of the Universe
• There are 4 possibilities
– An ever-expanding universe expanding faster and faster
• The Open Universe
( < 1)
– A universe expanding at the same rate as it is now
• The Critical Universe ( = 1)
– A universe that will eventually slow, and then collapse in a ‘Big
Crunch’
• The Closed Universe ( > 1)
– A (theoretical) universe with no matter (and no gravity)
• The 'Coasting' Universe
( = 0)
• Only useful to theorists – the real universe has matter
Ω0 = 1
In a Ω = 1 Universe, the two factors are perfectly balanced.
The Universe will expand forever, but at a slower and slower
rate.
After an infinite amount of time, the Universe will stop
expanding and “coast to a halt.”
o
Ω0 > 1
If Ω > 1, there is more mass than necessary, and
gravity wins. The expanding Universe eventually slows,
stops, and then contracts faster and faster until the Big
Crunch.
o
Ω0 = 0
If Ω = 0, there is no matter in the Universe and no gravity
to slow down the contraction. The Universe expands at
a constant rate forever. Of course, this Coasting Universe is
purely theoretical – since we know there is mass and gravity!
o
Ω0 ≤ 1 and Λ > 0
If Ω0 ≤ 1 (not enough mass) and we add a cosmological
constant Λ > 0 creating a repulsive force, the Universe
will continue to expand, but an accelerated rate.
Which is correct?
The recent observations from WMAP suggest we are living
in the perfectly balanced Ωo = 1 Universe. The Universe
will continue to expand forever.
Evidence, from Type Ia Supernovas, is also suggesting we
are living in an accelerating Λ > 0 Universe being driven
apart by strange “dark energy.”
The Shape of the Universe
Problems?
The Big Bang model (now the standard)
has some problems which are difficult
to resolve:
–
–
–
–
The Horizon Problem
The Flatness Problem
The Structure Problem
The Relic Problem
The Horizon Problem
• Why is the CMB so uniform?
– Looking at one part of the sky and looking in the opposite direction, radio
telescopes measuring the CMB see the temperature to 1 part in 10,000.
• Suppose the universe is 14 billion years old, then the two directions
are separated by 28 billion lightyears.
– Thus they should not be "causally connected"
• That is, they should not know about each other
• The two regions should not have the same temperature
– In the past the situation was even worse
• 100,000 years after the Big Bang, the separation would be 10 million
lightyears
The Flatness Problem
Why are we so close to a flat universe?
The Universe is nearly flat today, this implies that it had to be
nearly flat in the beginning.
However both the average density and the critical density
change with time
In the past, right after the Big Bang, if the average
density were slightly larger or smaller we have and open
or closed universe.
At the beginning the density would have to be very close
to the critical value (1 part in 1015); Otherwise a Big
Crunch or Big Chill would have occurred long ago.
Other Problems?
• The Structure Problem
– What formed the perturbations we see around us. Why is the
Universe structurally the same everywhere if it was not in causal
contact in the beginning.
• The Relic Problem
– The GUTs (Grand Unification Theories) predict massive particles
that are not observed in reality. What happened to these
particles?
The Inflationary Universe
These problems are resolved in the Inflationary
model of the Big Bang.
This states that what we call the Observable
Universe was really only a small region of the
initial universe. This region was small enough to be
in causal contact. The region then underwent
exponential expansion. The exponential growth
caused the flattening out of any curvature;
diluted the massive GUTs particles and small
quantum fluctuations were preserved and ‘blown
up’ providing the seeds for structure formation.
Inflation
• Modern particle theories predict that, at very high
energies, there exists a form of matter that creates a
gravitational repulsion!
• Inflation proposes that a patch of this form of matter
existed in the early universe
– it was probably more than a billion times smaller than
a single proton!
• The gravitational repulsion created by this material was
the driving force behind the big bang.
• The repulsion drove it into exponential expansion,
doubling in size every 10-37seconds or so!
• The density of the repulsive gravity material was not
lowered as it expanded!
Inflation
• Although more and more mass/energy appeared as the repulsivegravity material expanded, total energy was conserved!
• The energy of a gravitational field is negative!
• The positive energy of the material was compensated by the
negative energy of gravity.
• The repulsive-gravity material is unstable, so it decayed like a
radioactive substance, ending inflation.
• The decay released energy which produced ordinary particles,
forming a hot, dense “primordial soup.”
• Inflation lasted maybe 10-35 seconds. At the end, the region
destined to become the presently observed universe was about
the size of a marble.
• The “primordial soup” matches the assumed starting point of the
standard big bang— the standard big bang description takes
over. The region continues to expand and cool to the present day.
Evidence for Inflation
•
•
Large scale uniformity. The cosmic background radiation is uniform in
temperature to one part in 100,000. It was released when the universe was
about 300,000 years old. In standard cosmology without inflation, a
mechanism to establish this uniformity would need to transmit energy and
information at about 100 times the speed of light.
“Flatness problem:” Why was the mass density of the early universe so
close to the critical density?
Ω=
,where
•
𝐴𝑐𝑡𝑢𝑎𝑙 𝑀𝑎𝑠𝑠 𝐷𝑒𝑛𝑠𝑖𝑡𝑦
𝐶𝑟𝑖𝑡𝑖𝑐𝑎𝑙 𝑀𝑎𝑠𝑠 𝐷𝑒𝑛𝑠𝑖𝑡𝑦
the “critical density” is that density which gives a geometrically
flat universe. At one second after the big bang, Ω must have been equal to
one to 15 decimal places! Extrapolating back to the Planck time, 10-43
seconds, Ω must have been one to 58 decimal places! Inflation explains
why.
Since the mechanism by which inflation explains the flatness of the early
universe almost always overshoots, it predicts that even today the universe
should have a critical density.
Evidence for Inflation
•
•
Small scale non-uniformity of the cosmic background radiation.
Although only at the level of 1 part in 100,000, these nonuniformities can now be measured!
The properties measured so far agree beautifully with inflation.
ΩΛ = 0.7
ΩCDM = 0.257
Inflation!
• About 10-35 seconds after the Big Bang, the Universe cooled to
1027 K
• This caused a "phase transition" (Like water changing into ice)
• This phase transition released a lot of energy
• The strong force split from the other forces releasing
tremendous amounts of energy
• The universe expanded by a factor of 1050 in 10-33 seconds!
• Inflation solves the Horizon and Flatness problems The parts
of the Universe we see now were causally connected before
inflation Thus the CMB will be the same in all directions
afterward
• The Universe becomes flat because of the stretching of space
Experimental Evidence!
Inflation predicts that the quantization of the gravitational field
coupled to exponential expansion produces a unique pattern in the
CMB.
BICEP2 Detector
BICEP2 (Background Imaging of
Cosmic Extragalactic Polarization)
released its results in March 2014
South Pole Telescope
This pattern, basically a curling
in the polarization, or
orientation, of the light, can be
created only by gravitational
waves produced by inflation.
Epochs of the Universe
• From the Big Bang until now, the universe can be viewed as
proceeding through different "epochs" (time periods).
• Distinguishing characteristics:
– Each succeeding epoch is cooler and thinner.
– Different "forces" and/or "particles" may dominate!
Dark Matter
• There is not enough visible mass in the
universe to have  > 1
• Even if we add estimates of the unseen
dark matter – it isn’t enough
Dark Energy
• Recently it has been suggested that
Einstein’s blunder was in fact more
insight than most of us possess.
• His Cosmological Constant, , is being
associated with a ‘Dark Energy’ which
is repulsive at large distances.
Accelerating Universe?
• Today there is strong evidence coming from the
observation of distant Type Ia Supernova, by two
different teams of astronomers, indicating that the
cosmic expansion is not slowing down, but is speeding up!
• This observation strongly supports inflationary theory:
– It confirms the theoretical conclusion that gravity can act
repulsively.
– Acceleration requires “dark energy” permeating space, the
amount needed is just right (about ±10%) to bring the total
mass density up to the critical density predicted by inflation.
(The makeup is about 1% visible matter, 29% dark matter, and
70% “dark energy”.)
A Newer View
In March 2013, the Planck spacecraft’s
first 15.5 months of data revealed that
the Universe was older than previously
thought, 13.8 Billion years
Planck Full-Sky Map
This full-sky map from the Planck mission shows matter between Earth and the edge of the observable universe. Regions
with less mass show up as lighter areas while regions with more mass are darker. The grayed-out areas are where light
from our own galaxy was too bright, blocking Planck's ability to map the more distant matter.
Normal matter, which is made up of atoms, is only a small percent of the total mass in our universe. Most of the matter in
the universe is dark -- that is, it does not emit or absorb any light -- so creating a map of its distribution is challenging.
To make the full-sky map, the Planck team took advantage of the fact that all matter, even dark matter, has gravity that
will affect light traveling to us from near the very edge of the observable universe. Planck mapped this light, called
the cosmic microwave background, with exquisite precision over the whole sky, enabling scientists to create this matter
map.
Curiouser and Curiouser
The Planck mission has
imaged the oldest light in our
universe. The results fit well
with what we know about the
universe and its basic traits,
but some unexplained
features are observed.
One of the anomalies
observed by Planck is an
asymmetry in the
temperature fluctuations of
the ancient light across two
halves of our sky.
Temperature variations are
represented by the different
colors, with red being warmer
and blue, cooler. The extent
of these variations is greater
on the hemisphere shown at
right than the one at left.
This goes against the
accepted simple model of our
universe, which holds that
the sky is the same in all
directions.
Preliminary Planck Results
This relic radiation provides scientists with a snapshot of the universe 370,000
years after the Big Bang. Light existed before this time, but it was locked in a
hot plasma similar to a candle flame, which later cooled and set the light free.
The cosmic microwave background is remarkably uniform over the entire sky,
but tiny variations reveal the imprints of sound waves triggered by quantum
fluctuations in the universe just moments after it was born. These imprints,
appearing as splotches in the Planck map, are the seeds from which matter
grew, forming stars and galaxies.
The newly estimated expansion rate of the universe, known as Hubble's
constant, is 67.15 ± 1.2 Km/Sec/Mpc.
The new estimate of dark matter content in the universe is 26.8 percent, up
from 24 percent, while dark energy falls to 68.3 percent, down from 71.4
percent.
Normal matter now is 4.9 percent, up from 4.6 percent.
Current Models
Models using  = mass + energy are now being
researched.
One such model, predicts the CMB to look like:
Where mass = 0.3 and energy = 0.7
The Fate of the Universe
The past history of the Universe is one of an
early, energetic time. As the Universe
expanded and cooled, phenomenon became less
violent and more stable.
This ruling law of Nature during the evolution of
the Universe has been entropy, the fact that
objects go from order to disorder. There are
local regions of high order, such as our planet,
but only at the cost of greater disorder
somewhere nearby.
The Fate of the Universe
If the Universe is open or flat (as our current
measurements and theories suggest) then the march
of entropy will continue and the fate of our Universe is
confined to
the principle of heat death,
the flow of energy from
high regions to low regions.
With this principle in mind,
we predict the future of
the Universe will pass
through four stages as it
continues to expand.
Stellar Era
The Stellar Era is the time we currently
live in, where most of the energy of the
Universe comes from thermonuclear
fusion in the cores of stars.
The lifetime of the era is set by the time
it takes for the smallest, lowest mass
stars to use up their hydrogen fuel.
Stellar Era
The lower mass a star is, the
cooler its core and the
slower it burns its hydrogen
fuel (also the dimmer the
star is). The slower it burns
its fuel, the longer it lives
(where `live' is defined as
still shining).
The longest lifetime of stars
less than 1/10 a solar mass
(the mass of our Sun) is 1014
years.
Stellar Era
New stars are produced from gas clouds in
galaxies. However, 1014 years is more than
a sufficiently long enough time for all the
gas to be used up in the Universe.
Once the gas clouds are gone, all the
matter in the Universe is within stars.
Degenerate Era
• Once all the matter has been converted into
stars, and the hydrogen fuel in the center of
those stars has been exhausted, the Universe
enters its second era, the Degenerate Era.
• The use of the word degenerate here is not a
comment on the moral values of the Universe,
rather degenerate is a physical word to
describe the state of matter that has cooled
to densities where all the electron shell orbits
are filled and in their lowest states.
Degenerate Era
During this phase all stars are in the form of white or
brown dwarfs, or neutron stars and black holes from
previous explosions.
White and brown dwarfs are degenerate in their matter,
slowly cooling and turning into black dwarfs.
Degenerate Era
During this era, galaxies dissolve as stars go through two-body
relaxation. Two-body relaxation is when two stars pass close to
one another, one is kicked to high velocity and leaves the galaxy,
the other is slowed down and merges with the Galactic black hole
in the center of the galaxy's core. In the end, the Universe
becomes filled with free stars and giant black holes, leftover from
the galaxy cores.
Degenerate Era
The Universe would evolve towards a vast soup of
black dwarf stars except for process known as
proton decay.
The proton is one of the most stable elementary
particles, yet even the proton decays into a
positron and a meson on the order of once per
1032 years.
Thus, the very protons that make up black dwarf
stars and planets will decay and the stars and
planets will dissolve into free leptons. This all
takes about 1037 years.
Black Hole Era
Once all the protons in the
Universe have decayed
into leptons, the only
organized units are black
holes.
From Hawking radiation, we
know that even black holes
are unstable and
evaporate into electrons
and positrons.
Black Hole Era
• This process is extremely slow, varying
inversely as the mass of the black hole.
• For Galactic mass black holes, the time
to dissolve can last up to 10100 years.
• The result is a bunch of photons, slowly
cooling in the expanding Universe.
Dark Era
After all the black holes have evaporated,
the Universe consists of an expanding sea
of very long wavelength photons and
neutrinos.
This is a system of maximum disorder, no
coherent structures or objects. No
sources of energy, and no sinks as well.
The rest of time is simply a continual
lowering of energy until the state of
quantum vacuum is reached.
Finally
In about a 100 trillion years, its going
to be a cold, dark empty universe
Unless ....
The Superstring Theory
Each fundamental particle (quark, electron, neutrino)
is a different vibration mode of a tiny, elongated,
one-dimensional energy packet called a “string”
“Strings” are so small (10-33 cm), they are almost
point-like
Universe is 11-dimensional, but 7 of the dimensions
are too small to see
Leads to M-Brane theory where two M-branes collide
causing a Universe to be born – giving rise to a Multiverse.