Cosmology
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The Olbers Paradox
Why is the sky
dark at night?
If the Universe is
infinite, every line of
sight should end on
the surface of a star.
 The night sky
should be as bright as
the surface of stars!
Solution to the Olbers Paradox:
If the Universe
had a beginning,
then we can only
see light from
galaxies that has
had time to travel
to us since the
beginning of the
Universe.
Which other evidence to we have that
the Universe had a beginning?
1.
2.
3.
4.
5.
The finite ages of stars.
The finite ages of galaxies.
Hubble’s Law.
The evolution galaxies.
All of the above.
Hubble’s Law
Distant galaxies are
receding from us with a
speed proportional to
distance
The Expanding Universe
On large scales, galaxies are moving apart,
with velocity proportional to distance.
It’s not galaxies moving through space.
Space is expanding, carrying the galaxies along!
The galaxies themselves are not expanding!
If all galaxies are receding
from us, does that mean that
we must be in the center of
the Universe?
1.
2.
3.
Yes.
No, you would have the same impression
from any other galaxy as well.
No, we must rather be near the edge of
the universe.
The Expanding Universe
If recession speed is proportional to
distance, every galaxy is receding from
every other galaxy in the Universe.
Finite, but without Edge?
2-dimensional analogy:
Surface of a sphere:
Surface is finite, but has no edge.
For a creature living on the sphere,
having no sense of the third
dimension, there’s no center (on the
sphere!): All points are equal.
Alternative: Any point on the
surface can be defined as the
center of a coordinate system.
“Athens, OH: It’s not the end of the world. – But
you can see it from here!”
“In an appropriately chosen coordinate system,
Athens, OH, is the center of the Universe!”
The Cosmological Principle
1) Homogeneity: On the largest scales, the local Universe has
the same physical properties throughout the Universe.
2) Isotropy: On the largest scales, the local Universe looks the
same in any direction that one observes.
3) Universality: The laws of physics are the same everywhere in the Universe.
What is the logical connection
between homogeneity and isotropy?
1.
2.
3.
4.
If the Universe is homogeneous, it must
be isotropic.
If the Universe is isotropic, it must be
homogeneous.
Both 1. and 2. (i.e., homogeneity and
isotropy are equivalent)
None of the above.
If the Universe is homogeneous,
it must be isotropic.
If the Universe is homogeneous, then it can’t
make a difference which way you observe; you
should always see the same structure.
However, it can be isotropic, but not homogeneous:
Shape and Geometry
of the Universe
Back to our 2-dimensional analogy:
How can a 2-D creature investigate
the geometry of the sphere?
Measure curvature of its space!
Closed surface
(positive curvature)
Flat surface
(zero curvature)
Open surface
(negative curvature)
According to the theory of General
Relativity, gravity is caused by …
1. The equivalence principle.
2. The increasing mass of a relativistically
moving object.
3. The curvature of space-time.
4. The mass-energy equivalence.
5. The constant speed of light.
Cosmology and
General Relativity
According to the theory of general
relativity, gravity is caused by
the curvature of space-time.
The effects of gravity on the largest cosmological
scales should be related to the curvature of space-time!
The curvature of space-time, in turn, is determined by
the distribution of mass and energy in the Universe.
Space-time tells matter how to move;
matter tells space-time how to curve.
The Big Bang
Tracing back the expansion of the Universe
 There must have been a beginning with extremely
high density and temperature: the Big Bang!
This must have happened ~ 14 billion years ago
The age of the Universe
The Early History of the Universe
Electron
Positron
Gamma-ray photon
Electrons, positrons, and gammarays in equilibrium between pair
production and annihilation
The Early History of the Universe
Protons and neutrons form a few
helium nuclei; the rest of protons
remains as hydrogen nuclei
Almost no elements heavier
than Helium are produced.
25 % of mass in Helium
75 % in Hydrogen
The Early History of the Universe
Photons are incessantly scattered
by free electrons; photons are in
equilibrium with matter
Radiation dominated era
Photons have a blackbody
spectrum at the same
temperature as matter.
The Early History of the Universe
Protons and electrons recombine
to form atoms => Universe
becomes transparent for photons
Transition to matter dominated era
z = 1000
The Cosmic Microwave Background
After recombination, photons can travel freely through space.
Their wavelength is only stretched (red shifted)
by cosmic expansion.
Today, this “cosmic background radiation”
can still be observed!
Recombination: z = 1000; T = 3000 K
At a time corresponding to z = 1000, the
background radiation had a blackbody
temperature of 3000 K. At what wavelength
does that spectrum peak?
1.
2.
3.
4.
5.
3 mm
1 mm
3 mm
1 mm
3 nm
Wien’s Displacement Law:
lmax = 3,000,000 nm / T[K]
= 1,000 nm = 1 mm
For T = 3000 K.
If this background radiation with lmax = 1 mm
has been redshifted by z = 1000 until today,
at which wavelength does it peak today?
1.
2.
3.
4.
5.
3 mm
1 mm
3 mm
1 mm
3 nm
The wavelength has been stretched
by a factor of z = 1000:
lmax = 1 mm → 1 mm
This corresponds to a blackbody
of temperature T = 3 K.
(More precisely, it’s actually 2.735 K).
The Cosmic Microwave Background
If the Universe was perfectly homogeneous on all scales
at the time of reionization (z = 1000), then the CMB
should be perfectly isotropic over the sky.
Instead, it shows small-scale fluctuations:
The Cosmic Microwave Background
Angular size
of the CMB
fluctuations
allows us to
probe the
geometry of
space-time!
CMB fluctuations have a characteristic size of 1 degree.
Universe
has a flat
geometry
Knowing the basic principles of general
relativity, the curvature of space-time
reveals information about …
1.
2.
3.
4.
5.
the total content of mass (and energy) in the Universe.
the number of stars in the Universe.
the age of the Universe.
the abundance of heavy elements in the Universe.
the number of dimensions of the multi-dimensional
space-time.
The Future of the Universe
Will the expansion continue forever?
Or will it come to a halt and be
reversed towards a “Big Crunch”
Assume you have a catapult that can shoot a ball
up into the air so that it would just-so escape
Earth’s gravity. Now, if you use that same catapult
with the same ball on a planet that has twice the
mass, but the same radius as our Earth. What will
happen to the ball?
1.
2.
3.
4.
The ball will also escape that planet’s gravity and
actually have excess velocity at the end.
The ball will also just-so escape that planet’s gravity.
The ball will fall back onto the planet’s surface.
The ball will go into an orbit around the planet.
Deceleration of the Universe
Cosmic expansion should be slowed down by the
mutual gravitational attraction of the galaxies.
Fate of the Universe depends on the
matter density in the Universe.
Define “critical density”, rc, which is just-so enough
to slow the cosmic acceleration to a halt at infinity.
Size scale of the Universe
The Future of the Universe
r < rc => Universe
will expand forever
Maximum
age of the
Universe:
~ 1/H0
r > rc => Universe
will collapse back
Time
If the density of matter equaled the critical density, then
the curvature of space-time by the matter would be justso sufficient to make the geometry of the Universe flat!
What causes a Type Ia Supernova?
1.
2.
3.
4.
5.
The collapse of the iron core of a very massive star into
a neutron star at the end of its life.
The collapse of the iron core of a very massive star into
a black hole at the end of its life.
The collapse of a white dwarf that has accreted too
much material in a binary system.
The explosive onset of hydrogen fusion on the surface of
a white dwarf in a binary system.
The collapse of the Carbon/Oxygen core of a sun-like
star into a white dwarf at the end of its life.
Measuring the “Deceleration”
of the Universe …
By observing type Ia
supernovae,
astronomers can
measure Hubble’s
Law at large
distances
Distance ↔
recession speed
Size scale of the
universe ↔ rate
of expansion
It was expected that this would measure the
deceleration of the universe, but …
Measuring the Deceration (?)
of the Universe
Measured Brightness
of Type Ia Supernovae
Hubble’s Law
Accelerating Universe
Redshift z (→ Expansion speed)
Distance → Look-back time
Decelerating Universe
Apparent Magnitude of
Type Ia Supernovae
The Accelerating Universe
Flat decelerating Universe
Flat accelerating Universe
Red Shift z
In fact, SN Ia measurements showed that the
Universe is accelerating!
If the Universe is currently accelerating and
expanding at the measured rate, how should
the cosmic size scale evolve with time?
B)
C)
D)
A)
E)
The Cosmological Constant
Cosmic acceleration can be
explained with the
“Cosmological Constant”, L
(“Lambda”)
L is a free parameter in
Einstein’s fundamental
equation of General Relativity;
previously believed to be 0.
Energy corresponding to L
can account for the missing
mass/energy (E = m*c2)
needed to produce a flat
space-time.
Science Mag. 1998
→ “Dark Energy”
The Stuff the Universe
is Made of
Dark Energy: 70 %
Dark Matter: 26 %
"Visible" Matter: 4 %
• We only “see” about 4 % of all the mass
and energy in the Universe!
• The nature of about 96 % of our Universe
is yet mysterious and unknown!