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?

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1. The finite ages of stars.

2. The finite ages of galaxies.

3. Hubble’s Law.

4. The evolution galaxies.

5. All of the above.

Hubble’s Law

Distant galaxies are receding from us with a speed proportional to

distance

The Expanding UniverseOn 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. Yes.

2. No, you would have the same impression from any other galaxy as well.

3. No, we must rather be near the edge of the universe.1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

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If recession speed is proportional to distance, every galaxy is receding from

every other galaxy in the Universe.

The Expanding 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 Principle1) 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?

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1. If the Universe is homogeneous, it must be isotropic.

2. If the Universe is isotropic, it must be homogeneous.

3. Both 1. and 2. (i.e., homogeneity and isotropy are equivalent)

4. 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:

Measure curvature of its space!

Closed surface Flat surface Open surface

(positive curvature) (zero curvature) (negative curvature)

How can a 2-D creature investigate the geometry of the sphere?

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 RelativityAccording 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 BangTracing back the expansion of the Universe

There must have been a beginning with extremely

high density and temperature: the Big Bang!

Universe expands as time passes

Universe cools down as time passes

This must have happened ~ 14 billion years ago

The age of the Universe

The Early History of the UniverseElectron

Positron

Gamma-ray photon

Electrons, positrons, and gamma-rays 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 BackgroundAfter recombination, photons can travel freely through space.

Their wavelength is only stretched (red shifted) by cosmic expansion.

Recombination: z = 1000; T = 3000 K

Today, this “cosmic background radiation” can still be observed!

At a time corresponding to z = 1000, the background radiation had a blackbody

temperature of 3000 K. At what wavelength does that spectrum peak?

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1. 3 mm

2. 1 mm

3. 3 m

4. 1 m

5. 3 nm

Wien’s Displacement Law:

max = 3,000,000 nm / T[K]

= 1,000 nm = 1 m

For T = 3000 K.

If this background radiation with max = 1 m has been redshifted by z = 1000 until today,

at which wavelength does it peak today?

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1. 3 mm

2. 1 mm

3. 3 m

4. 1 m

5. 3 nm

The wavelength has been stretched by a factor of z = 1000:

max = 1 m → 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 …

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1. the total content of mass (and energy) in the Universe.

2. the number of stars in the Universe.

3. the age of the Universe.

4. the abundance of heavy elements in the Universe.

5. 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?

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1. The ball will also escape that planet’s gravity and actually have excess velocity at the end.

2. The ball will also just-so escape that planet’s gravity.

3. The ball will fall back onto the planet’s surface.

4. The ball will go into an orbit around the planet.

Deceleration of the Universe

Fate of the Universe depends on the matter density in the Universe.

Cosmic expansion should be slowed down by the mutual gravitational attraction of the galaxies.

Define “critical density”, c, which is just-so enough to slow the cosmic acceleration to a halt at infinity.

The Future of the Universe

Siz

e s

cale

of t

he

Un

iver

se

Time

< c => Universe will expand forever

> c => Universe will collapse back

If the density of matter equaled the critical density, then the curvature of space-time by the matter would be just-so sufficient to make the geometry of the Universe flat!

= c => Flat UniverseMaximum age of the Universe:

~ 1/H0

What causes a Type Ia Supernova?

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1. The collapse of the iron core of a very massive star into a neutron star at the end of its life.

2. The collapse of the iron core of a very massive star into a black hole at the end of its life.

3. The collapse of a white dwarf that has accreted too much material in a binary system.

4. The explosive onset of hydrogen fusion on the surface of a white dwarf in a binary system.

5. 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

Redshift z (→ Expansion speed)

Me

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red

Bri

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nes

s o

f Typ

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Sup

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e

Decelerating Universe

Hubble’s Law

Dista

nce

→ Lo

ok-b

ack tim

eAccelerating Universe

The Accelerating Universe

Red Shift z

Ap

pare

nt M

ag

nitu

de o

f T

ype

Ia S

upe

rno

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Flat decelerating Universe

Flat accelerating Universe

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?

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A)

B)C)

D)E)

The Cosmological ConstantCosmic acceleration can be

explained with the “Cosmological Constant”,

(“Lambda”)

is a free parameter in Einstein’s fundamental

equation of General Relativity; previously believed to be 0.

Energy corresponding to can account for the missing

mass/energy (E = m*c2) needed to produce a flat

space-time. → “Dark Energy”

Science Mag. 1998

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!