Download Option D Lesson 6 Cosmology and Further - Physics

OPTION D: LESSON 5
Cosmology (Including the Big Bang)
Newton’s model of Universe
 Newton Believed that the universe is infinite in
both space and time.
 It is uniform and static.
 This means that there are an infinite number of
stars heading out in all directions
to infinity.
 If this were not the case, then the
universe would collapse under its own
gravitational force.
Oblers’ Paradox
 If the universe extends infinitely,
then eventually if we look out into
the night sky, we should be able to
see a star in any direction, even if the
star is really far away.
 Since the universe was infinitely old,
the light from stars at extremely far
distances would have already reached us,
even if they were 40 billion light years
away.
 If there are infinite stars, then you should
be able to see a star anywhere in the night sky, and so the sky
should have the same brightness everywhere.


But (at night) the sky is dark! (Ok, dark but speckled with bright points of
light called stars!)
How can this be explained? Something is not right with Newton’s
model of the Universe.
Oblers’ paradox
Why is the night sky dark?
or
Why isn't the night sky as uniformly bright
as the surface of the Sun?
If the Universe has infinitely many stars, then it should be.
Oblers’ Paradox in tree form
With a big enough forest, you will see a trees no matter
where you look…
Solution to Oblers’
 http://www.youtube.com/watch?v=gxJ4M7tyLRE
 Newton’s Model of the Universe is wrong.
 The Universe is expanding, so distant stars are red-
shifted out of the visible spectrum. (Doppler effect) .
 The Universe is young (and not infinite in time). Light
from really really distant light hasn't had time to reach us
yet. We are looking back in time to see the Universe
before the stars were created!
THE BIG BANG
MODEL
Doppler effect
• In astronomy, the Doppler effect was originally studied in the visible part
of the electromagnetic spectrum. Today, the Doppler shift, as it is also
known, applies to electromagnetic waves in all portions of the spectrum.
• Also, because of the inverse
relationship between frequency and
wavelength, we can describe the
Doppler shift in terms of
wavelength. Radiation is
redshifted when its wavelength
increases, and is blueshifted when
its wavelength decreases.
Doppler effect
•
In astronomy, the Doppler effect was originally studied in the visible part of the electromagnetic
spectrum. Today, the Doppler shift, as it is also known, applies to electromagnetic waves in all
portions of the spectrum.
•
Astronomers use Doppler shifts to calculate precisely how fast stars and other astronomical objects
move toward or away from Earth.
•
Notice how the absorption
spectra of the sun (at the top)
and the supercluster BAS11
(on the bottom) compare.
•
Both have the same
pattern of absorption
lines, indicating they are
from the same
elements, but the lines
on the lower picture are
shifted towards the
right of the spectrum
(shifted towards the
red!). This indicates
that BAS11 is moving
away from us.
Doppler Shift

The change in wavelength due to the Doppler shift is related to the
“speed” of the object moving by:
λ − λ0 ∆λ 𝑣
=
≈
λ0
λ0 𝑐
Where: λ is the observed wavelength.
λ0 is the wavelength emitted.
Δ λ is the change in wavelength.
v is the speed of the object.
c is the speed of light.
Note: This equation relies on the v<<c.
In Astrophysics, we assign this ratio the letter z to indicate the redshift of a
galaxy.
∆λ 𝑣
𝑧=
≈
λ0 𝑐
Hubble’s law




Edwin Hubble (and a guy called
Milton Humanson) noticed that all
observed galaxies displayed a red
shift.
Hubble then used observed (type
Ia) supernovae in distant galaxies
as a “standard candle” to measure
the distance to these galaxies.
Hubble compared the distance to
these galaxies with the speed they
were receding.
When a graph is plotted of speed of galaxies vs distance, we end up with a direct
relationship.
 So the speed of recession of galaxies is related to their distance from Earth by:
𝑣 = 𝐻0 𝑑
Where:
v is the speed of recession.
d is the distance to the galaxy.
H0 is the “Hubble Constant”.
The current best estimate of the Hubble constant is 70 kms-1Mpc-1.
Implication of Hubble Law
and Hubble Constant.
 The fact that all there is a direct relationship
between speed of galaxies and their distance from
us implies that at an earlier point in time, everything
in the Universe was much closer together.
 In fact, we can trace the universe backwards to a
point in time (~13.7 billion years ago) when the
Universe was compressed into a space smaller than
the size of 1 atom.
 From this point in time, the Universe expanded in
the “Big Bang” creating time and space.
 The Hubble constant gives us an estimate of the
current rate of expansion of the universe.
Background radiation
• In 1960 two physicists, Dicke and Peebles, realising that there was
more Helium in the universe than could be produced by stars.
• They proposed that in the beginning of the Universe it was at a
sufficiently high temperature to produce Helium through fusion.
• In this process a great amount of highly energetic radiation would
have been produced. However, as the Universe expanded and
cooled, the energy of that radiation decreased as well (wavelength
increased).
• It was predicted that the actual photons would have an maximum λ
corresponding to a black body spectrum of 3K.
• Weins law tells us that the radiation from a black body of
temperature 3 K would be in the microwave region of the spectrum.
• So, we should be looking for microwave radiation.
Background radiation
• Shortly after this
prediction, two other
physicists Penzias and
Wilson were working
with a microwave
aerial. They found that
no matter in what
direction they pointed
the aerial it picked up a
steady, continuous
background radiation.
Background radiation
• In every direction, there is a very low energy and very
uniform radiation that we see filling the Universe. This is
called the 3 Degree Kelvin Background Radiation, or the
Cosmic Background Radiation, or the Cosmic Microwave
Background (CMB).
• These names come about
because this radiation is
essentially a black body
with temperature slightly
less than 3 degrees
Kelvin (about 2.76 K),
which peaks in the
microwave portion of the
spectrum.
Age of the Universe

We can also use the Hubble constant to estimate the age of the universe.
Since we can assume that all matter started out at the same location in space and travelled outwards.
The speed of objects in the universe is related to their distance from us and the time since the start of
the universe.
𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
𝑠𝑝𝑒𝑒𝑑 =
𝑡𝑖𝑚𝑒 𝑠𝑖𝑛𝑐𝑒 𝑡ℎ𝑒 𝑢𝑛𝑖𝑣𝑒𝑟𝑠𝑒 𝑏𝑒𝑔𝑎𝑛
So:
𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
𝑠𝑝𝑒𝑒𝑑
But Hubble's law tells us that the speed of an object in the universe is directly related to its distance:
𝑣 = 𝐻0 𝑑
𝑑
𝑡=
𝐻0 𝑑
So:
1
𝑡=
𝐻0
𝑡𝑖𝑚𝑒 𝑠𝑖𝑛𝑐𝑒 𝑡ℎ𝑒 𝑢𝑛𝑖𝑣𝑒𝑟𝑠𝑒 𝑏𝑒𝑔𝑎𝑛 =
This gives us an upper estimate for the age of the universe. In fact the universe is likely younger since
gravitational attraction will slow the rate of expansion of the universe over time.
Background radiation
Why is the background radiation an
evidence for the Big Bang?
• The cosmic background radiation (sometimes called the
CBR), is the afterglow of the big bang, cooled to a faint
whisper in the microwave spectrum by the expansion of
the Universe for 15 billion years (which causes the
radiation originally produced in the big bang to redshift to
longer wavelengths).
Big Bang
The Big Bang Model is a broadly accepted theory for the
origin and evolution of our universe.
It postulates that 12 to 14 billion years ago, the portion of
the universe we can see today was only a few millimetres
across.
It has since expanded from this hot dense state into the
vast and much cooler cosmos we currently inhabit.
We can see remnants of this hot dense matter as the now
very cold cosmic microwave background radiation which still
pervades the universe and is visible to microwave detectors as
a uniform glow across the entire sky.
Big Bang
The singular point at which space, time, matter
and energy were created. The Universe has been
expanding ever since.
Main evidence:
Expansion of the Universe – the Universe is expanding
(redshift)  it was once smaller  it must have started
expanding sometime  “explosion”
Background radiation  evidence of an hot Universe that
cooled as it expanded
He abundance  He produced by stars is little  there is
no other explanation for the abundance of He in the Universe
than the Big Bang model.
The Big Bang
 If we mathematically trace the position of all the galaxies
in the universe backwards in time, we get to a point
approximately 13.8 billion years ago, when all matter is in
the same location. To do this, we had to use general
relativity.
 This implies a that there is a point when all matter was in
a region that was infinitely dense. (Really it means that
our ability to understand physics breaks down, or “the
laws of physics cannot model the exact state of the
universe at that point in time”).
The Big Bang: Inflation and
history of the universe.
I don’t think you need to memorize this, but it is worth
being familiar with the stages and the different
processes. HL should be much more familiar than SL

In the early stages of the universe (the first 10-45~10-36 seconds or so which was about 13.8 Billion years ago) , it was
incredible hot and dense. This period is referred to as “Unification of Forces”, and is considered the start of the
Universe.

The next step, (between 10-36 to 10-32 seconds of the Universe’s age) there was a period of rapid expansion, where it
grew exponentially. This is called Inflation. After inflation, the Universe was about 10-29 times its current size.

The next period was between 10-32 and 10-5 seconds of Universe age. During this period the Universe continues to
expand and cool, but at a slower rate. During this time Matter and Anti-Matter (in the form of quarks and leptons)
interact. There appears to be more Anti-Matter than Matter. This period is called the Quark-Lepton Era.

After the first 10-5 seconds it the Universe has cooled to a point protons and neutrons (Hadrons) could be formed.
This is called the Hadron Era.

The next stage 10-2s to 103 s Nucleosynthesis starts to occur. Protons and neutrons combine, forming deuterium
and helium. The amount of matter left is a relatively small amount compared to what started, and it is what is left
over after matter and anti-matter interacted during Quark-Lepton Era.

By this stage the formation of light nuclei has generally finished, and the Universe exists as a plasma of electrons,
protons, neutrons, and helium. At this stage photons are interact with matter. This stage is called the Plasma era.

After approximately 3x105 years, it had cooled (3000K) enough to the point at which helium and hydrogen nuclei
could join with electrons to form stable nuclei. At this point photons no longer interact with matter, and matter
becomes “transparent to radiation”. What we observe as the CMB is radiation from this point onwards.

109 years to present…Finally gravitation can start to bring matter together, this leads to the formation of stars,
galaxies etc…
Cosmic Background Radiation
The image on the right shows the CMB as seen from
Earth. The variation in colours represents slight
changes in temperature as measured by the CMB.


Although there are slight differences (we’ll talk more
about these later), on average, whatever direction we
look, the CMB is pretty much the same.


The image is this shape b/c it is a projection of the entire
sky “wrapping around the Earth”.
We say it is “Isotropic”, meaning equal in all directions.
The fact the CMB is isotropic is very important. It
implies that there is no “centre of the Universe”.

This means that the Universe is not expanding in the same
way as-say an exploding watermelon would expand into a
room.



If you were living on a chunk of exploding watermelon and
you look in one direction (towards where the centre of the
watermelon was) you would see remnants of the heat of
the explosion (and you would see all the other chunks of
watermelon moving away from you).
If you look away from the centre of the watermelon in the
direction you were moving, it would be colder (and you
would see many fewer chunks of watermelon!)
The CMB courtesy of NASA and ESA
Slowmo guys!

The Universe is not like that. Every direction you look, it is
pretty much the same. There is no area of extra hot, nor is
there an area of extra cold. The CMB is the pretty much
the same temperature everywhere (Isotropic!) Indicating
that there is no “centre” that we are expanding away
Follow link to see exploding watermelon
from.
https://www.youtube.com/watch?v=hMjL76obRLI
Big Bang and Expansion of
the Universe.
 It is very important to realize that even
though we say the Universe is expanding, it is
not expanding “into anything”.
 Time and space are getting larger. The Universe is
getting larger and larger, but there is nothing that
exists “outside” the universe for it to grow into.
And therefore whatever direction you look, you
see the same amount of universe!
 In fact, time and space were created during
the big bang!
Cosmological Red-Shift
 The idea that the Universe isn’t expanding into
anything, it is just getting bigger changes the
way that we have to think about the motion of
the galaxies.
 Other galaxies are not actually moving away
from us, it is simply that space in-between us
and them is getting bigger.
 Remember, we used the redshift of light from
the Galaxies to determine the expansion of the
Universe.
 Well, if the Galaxies are not moving away from us,
then how is it that radiation from them is redshifted?
Cosmological Red-Shift
 Since space is constantly
growing, it is like the Universe is
being “re-scaled”.
 This means that the space
between distant galaxies and us
is bigger, but it also means that
over time, the space within a
wavelength of a wave has also
grown.

This means that when we receive
radiation from distant galaxies
(that was sent a long time ago), the
waves have effectively grown
(since space within it has grown),
meaning that we measure a longer
wavelength when we receive the
wave than we would have done
when it was sent.
Cosmological Redshift: Scale factor.


The “cosmological redshift” is very similar to the “Doppler redshift”.
Previously we saw the redshift was:
∆λ λ − λ0 𝑣
𝑍=
=
≈
Only true if c>>v.
λ0
λ0
𝑐

Where:
λ is the wavelength of radiation measured.
λ0 is the wavelength of radiation emitted.
v is the velocity of the motion of the object emitting radiation.
c is the speed of light.
We can rearrange this.
∆λ λ − λ0
λ
=
= −1
λ0
λ0
λ0
Well, now instead of it being a “receding” star that is emitting light. It is actually
a “rescaling” of the universe.
𝑍=



So if the redshift “Z” is 2, then this means that the measured wavelength is 3 times the size it
was when it was emitted. This can be interpreted to means that the universe is 3 times larger
than it was when the radiation was emitted.
So now:

Where:
∆λ
λ
𝑅
𝑍=
= −1=
−1
λ0 λ0
𝑅0
True irrespective of
the “speed” of growth
of the universe.
R is the size of the observable universe.
R0 is the radius of the observable universe when the light was emitted.
Cosmological Redshift: Scale factor.
 So now:
λ
𝑅
𝑍 = −1=
−1
λ0
𝑅0
 We call “R” the “cosmic scale factor”.
HL Only
The fate of the Universe.
 So what will happen to the universe?
 Three different possibilities:
 It will keep expanding forever.
 “Open Universe”
 Expansion will gradually slow down until at a point
infinitely far into the future, it will stop expanding and
start to contract (at infinity, ie never).
 “Flat Universe”
 It will start contracting due to its own gravitational pull .
 “Closed Universe”
HL Only
Fate of the Universe


The three different theories are shown in a graph of “radius (or size) of the
universe” vs. “Time”
Notice each different model has the start (Big Bang) at a slightly different point
in time in the past. With the “open universe” starting the furthest back.
Fate of the Universe
HL Only
Universe
Closed
Enough matter 
density is high enough
to stop expansion 
gravity will stop the
Universe expansion and
cause it to contract (Big
Crunch)
Flat
Critical density 
Universe will only
start to contract
after an infinite
amount of time
Open
Not Enough matter
 density is such
that gravity is too
weak to stop the
Universe expanding
forever
HL Only
Fate of the Universe
 It is the “mass density” of the Universe that will control
which of the three fates will occur.
 Mass density is the amount of matter per unit volume.
 “Critical Density” (ρc) is the value for mass density that is
the dividing line between an open universe and a closed
universe.
 If the density of the universe is less than critical density,
 If ρ<ρc the universe will be “Open” expanding forever.
 If the density of the universe is greater than critical,
 If ρ>ρc the universe will be “Closed”, ultimately stopping its
expansion and then contracting.
 If the density of the universe is the same as the critical density
 If ρ=ρc the universe will be “Flat”, it will expand forever at a rate
that approaches zero.
 Critical density is approximately ρc≈10-26 kgm-3
HL Only
Density of the Universe.
 It is difficult to estimate the density of the
Universe by determining the mass of all the
objects we can see within a large volume of
space and dividing by that volume, because
when this was tried, the density of Galaxies
wasn’t even enough to keep a galaxies moving
around a “cluster centre” (the way we see that
they actually are!)
 We now know that we can see only about 10% of
the Universe.
 The rest of the matter in the Universe is “Dark Matter”
(dark b/c we cannot see it!)
Dark Matter.
 There are two proposed forms of dark matter to
explain the discrepancy between the density
calculated by observation, and the density necessary
to bind the universe together as we observe it.
MACHO’s
WIMP’s
Massive compact halo objects – brown and
black dwarfs or similar cold objects and
even black holes.
Non-barionic weakly interacting massive
particles (neutrinos among other particles
predicted by physics of elementary
particles)
MACHOs
 Massive Compact Halo Objects.
 Really big astronomical things that we can’t see.
 Include Brown Dwarfs, Black Holes, even Neutron
Stars and Planets that drift through space
unassociated from any objects.
Wimps
 Weakly Interacting Massive Particles.
 Tiny elementary particle that do not interact
with other elements. Examples of these are
Neutrinos and other elementary particles.
So?
 Turns out that distance objects are moving away from us much
faster than predicted by the big bang.
 Based on Gravitation, we would expect them to be slowing down,
but they are not. In fact observational data suggests that the rate
that they are moving away from us is INCREASING.
 This suggests that the Universe is more OPEN than expected.
 This must explained by the existence of some energy that we
can’t measure (or observe).

We call this energy “Dark Energy”
 “Dark Energy” is the name of the energy that creates a repulsive
force that explains the acceleration of the universe.
 So although there is evidence that the Universe is at “Critical
Density”, it is not expanding as suggested by any of the graphs.
HL Only
http://upload.wikimedia.org/wikipedia/commons/thumb/6/6f/CMB_Timeline300_no_W
MAP.jpg/440px-CMB_Timeline300_no_WMAP.jpg
Astrophysics is
International…
 For example the Atacama Large Millimeter Array is a large
radio telescope in Chile. It is an international partnership
between Europe, the United States, Canada, East Asia and
the Republic of Chile.
 Costing more than a billion US dollars, it is the most
expensive ground-based telescope in operation.
 ALMA began scientific observations in the second half of
2011 and the first images were released to the press on 3
October 2011.
 By the summer of 2011 sufficient telescopes were
operational during the extensive program of testing prior to
the Early Science phase for the first images to be captured.
These early images give a first glimpse of the potential of
the new array that will produce much better quality images
in the future as the scale of the array continues to increase.
Atacama Large
Millimeter array.
 An early observation of the array was a pair of
colliding galaxies with dramatically distorted
shapes, known as the Antennae Galaxies.
Although ALMA did not observe the entire
galaxy merger, the result is the
best submillimeter-wavelength
image ever made of the
Antennae Galaxies, showing
the clouds of dense cold gas
from which new stars form,
which cannot be seen using
visible light