cosmology iii geometry and the cmb - cornell...

Lec. 29: Geometry and CMB

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APOD: The Microwave Milky Way

Cosmology III:Geometry and the CMB

Lecture 29

Lec 29: Geometry and CMB 2

Announcements Prelim #3 on Wednesday, Nov. 14

In class: 11:15am - 12:05pm (Uris Auditorium) Will emphasize lectures 22-31 Closed notes and closed book


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Lecture Topics

The Geometry of Space (k)

The Fate of the Universe

The Cosmic Microwave Background (CMB)

The Early Universe

Problems with the Big Bang?


The Geometry of Space

General Relativity predicts space will be “curved”. [ is not 3.1415926... ]

The curvature (geometry) of the universe depends on the value of k. Closed k < 0 positive curvature

Flat k = 0 Euclidean space

Open k > 0 negative curvature


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The Closed Universe (k < 0)

For k < 0, we have a closed universe, because space bends back on itself and makes the universe finite in size.

Space has positive curvature like a sphere

The volume is finite but there is no boundary!

Light shown in one direction would eventually return in the opposite direction.


Sphere analogy w/ close universe

Finite volume, but no boundary..

Light could return from the opposite direction.

Parallel straight lines cross!

Start parallel at equator


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The Open Universe (k > 0)

For k > 0, we have an open universe. Space curves “outward”.

Universe infinite in size.

Space has negative curvature like a saddle

Infinite volume


Saddle analogy w/ open universe

Infinite volume.

Parallel straight lines diverge!

Start parallel


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Spatial Curvature A flat plane has zero curvature, a sphere has positive

curvature, and a hyperboloid has negative curvature.

Flat (k = 0)C = 2r

Positive (k < 0)C < 2r

Negative (k > 0)C > 2r


The Fate of the Universe The best estimates now yield

Ho = 71 km/sec/Mpc M = 0.27, = 0.73 k = 0 Age of universe is 13.67 Gyr

This implies The Universe is flat It will go on expanding forever Because > 0, it will expand ever faster!

The Universe will be slowing cooling down. All stars and star formation will die out.

The Big Chill


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Fire and Ice

Some say the world will end in fire,Some say in ice.From what I've tasted of desireI hold with those who favor fire.But if it had to perish twice,I think I know enough of hateTo say that for destruction iceIs also greatAnd would suffice.

Robert Frost


The Great Space-time Rip? Because we don’t know the nature of the dark

energy, we don’t really know the fate of the Universe. If dark energy density remains constant

Then the acceleration continues and in ~100 Gyr, all but a few hundred galaxies will be too redshifted to see.

If dark energy density decreases More of the Universe will be visible to us

If dark energy density increases further Then galaxies, planetary systems, planets, and atoms will be

torn apart in that order.

See February 2004, Scientific American article by Riess and Turner


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The Beginning of the Universe What about the origin of the universe? If we extrapolate backwards in time, galaxies

will be arbitrarily close together. What happened back then?

Galaxy formation Before that ?

How far back can we see? The answer to this came in 1964 with the discovery

of the Cosmic Microwave Background (CMB)


The Cosmic Microwave Background Arno Penzias and Bob Wilson (Bell Labs)

In 1964, they were carrying out a study of radio emission from the Milky Way

To identify and eliminate interference to improve the telephone system!

Found a bothersome background “hiss”coming from everywhere.

This “hiss” turns out to be a “remnant” of the Big Bang, the CMB.


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Penzias and Wilson


CMB Nobel Prize Paper

Penzias and Wilson were awarded the Nobel Prize for their discovery.


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The CMB The Cosmic Microwave Background

(CMB) has a blackbody spectral shape. T = 2.73 K (As measured by COBE) We use radio telescopes to observe it

Universe is filled with “very cool”radiation!

Presently: Matter density ~ 10-30 g/cm3

Radiation density ~ 5x10-34 g/cm3


Origin of CMB Where does the CMB originate? As we extrapolate back in time, galaxies are

closer together. And things get hotter

We eventually get to a time when galaxies (and stars) did not exist.

The Universe at the time the CMB originated was a hot plasma (a mix of ions, mostly protons, and electrons)


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The CMB originated about 300,000 years after the Big Bang Before the first galaxies and stars!

We cannot “see” beyond this period We must rely on extrapolation based on our understanding of

physics to go further back in time.

Back to the CMB


COBE (Cosmic Background Explorer) Images of CMB

Original

Subtracting dipole shows the Galactic plane and fluctuations in the CMB.

Subtracting average gives “dipole” due to motion of Earth through CMB (Doppler effect)

1992


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COBE (1992) image of fluctuation in CMB. The average, dipole, and Galactic Plane have been subtracted

WMAP (2004) image of fluctuation in CMB. The average, dipole, and Galactic Plane have been subtracted

Fluctuations in the CMB tell us about The geometry of the universe The amount of matter in the universe Whether the universe will expand forever or

collapse The expansion rate and age of the universe The primordial seeds of galaxies and clusters

Fluctuations in the CMB


Nobel Prize #2

Another Nobel prize for CMB work – awarded in 2006.


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Cosmic Ultrasound The temperature fluctuations at different size scales tell us about properties of the universe.


In-Class Question1) The CMB is important because it tells us about

a) the amount of matter in the Universeb) the primordial seeds of galaxies and clustersc) the geometry of the Universed) the fate of the Universee) all of the above


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In-Class Question1) The CMB is important because it tells us about

a) the amount of matter in the Universeb) the primordial seeds of galaxies and clustersc) the geometry of the Universed) the fate of the Universee) all of the above

2) To our best understanding, the geometry of the universe is

a) open b) flat c) closed d) can’t tell


Radiation and Matter

Presently in the universe: Matter density ~ 10-30 g/cm3 (w/ dark

matter!)

Radiation density ~ 5x10-34 g/cm3 (CMB)

The matter density of the universe dominates at present.

But this wasn’t always the case.


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The Early Universe

We now extrapolate back beyond where we can directly observe.

As the universe evolved, both the matter and radiation densities decreased (to what we see today).

The radiation density changed faster! So in the past the radiation density was

much larger relative to the matter density.


Matter Era

RadiationEra

Evolution of the universe

10 102 103 104 105 106 107 108 10910-35

10-25

10-15

10-5

Time (Years)

De

nsity

(g/

cm3 ) Matter

Density

RadiationDensity

CrossoverPoint

CM

B L

imit


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High ’s and T’s in the past.

Not only was the density higher in the past, so was the temperature.

At that time radiation begins to dominate Universe ~ 20,000 times smaller The temperature of the CMB radiation was

~ 60,000 K.

The universe was extremely hot and dense at early times.


About 13-14 billion years ago the Universe started We don’t know what triggered the Big Bang We can extrapolate back to about ~10-43 sec after the

Big Bang Beyond this the physics is not known (not understood)

The Picture So Far

BIG BANG

Universe expanding and cooling as time passes


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A Journey Back in Time


Problems with Big Bang

The Big Bang described thus far is very successful in may aspects.

However, there are two major problems that need to be addressed

The Horizon problem Why is the CMB so uniform?

The Flatness problem Why are we so close to k = 0 (a flat universe)?

cosmology iii geometry and the cmb - cornell...

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