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Cosmology Dr. Bill Pezzaglia

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2007Jun 06

Cosmology 3

A. Ancient Cosmology ModelsB. Greek ModelsC. Copernicus and NewtonD. Einstein & Curved SpaceE. Spectra and redshiftF. Expanding UniverseG. Models of the Universe

Cosmology: What is it? 4

Cosmos vs Chaos

Meaning of Cosmology

A.1 Egyptian Cosmology 5

Nut is often portrayed as a naked female stretched across the sky. The Sun (Ra) is shown entering her mouth, passing through her star speckled body and emerging from her birth canal nine months later (from the spring equinox to the winter solstice). Thus, Ra becomes a self-creating god, i.e. the Universe is self-creating and eternal.

The sky goddess Nut gives birth to Ra once a year, catalyzing both calendar development and the concept of divine royalty plus the matrilineal inheritance of the throne.

A.2 Babylonian Cosmology 6

The Earth was created by the god Marduk as a raft floating on the Apsu. The gods were divided into two pantheons, one occupying the heavens and the other in the underworld.

Babylonians believed in a six-level universe with three heavens and three earths: two heavens above the sky, the heaven of the stars, the earth, the underground of the Apsu, and the underworld of the dead.

A.3 Hindu Cosmology 7

World supported by 4 elephants atop a turtle

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A.4 Turtles 8

Stephen Hawking in A Brief History Of Time starts with the anecdote:

A well-known scientist (some say it was Bertrand Russell) once gave a public lecture on astronomy. He described how the earth orbits around the sun and how the sun, in turn, orbits around the centre of a vast collection of stars called our galaxy.

At the end of the lecture, a little old lady at the back of the room got up and said: "What you have told us is rubbish. The world is really a flat plate supported on the back of a giant turtle."

The scientists asks “what supports the turtle”?

The lady replies: “its standing on a bigger turtle!”

Scientist: “And what would that turtle rest upon?”

Lady: “its no use young man, its turtles all the way down!”

B.1 Anaximander (612-545 BC) 9

Student of Thales, the first “map maker”

Anaximander imagined the Sun to be an enormous wheel filled with fire, its rim pierced by a single hole the size of the Earth. (?)

B.2 Pythagoras (540 BC) 10

• The earth is a sphere, humans can live on all of its surface (without falling off).

• Named the 5 planets

B.3 Empedocles (490-420 BC) 11

• Air is primarily moist and secondarily warm.

• Fire is primarily warm and secondarily dry.• Earth is primarily dry and secondarily cool.• Water is primarily cool and secondarily

moist.

Origin of the list of 4 basic elements from which all things are composed

B.4 Plato (426-347 BC) 12

• Student of Socrates• Proposed objects in the heavens are composed of a “5th

element” (later called “ether” by Aristotle).

B.5 Platonic Solids 13

• Pythagorus attributed as having discovered, however may have been known since antiquity.

• Theaetetus (417-369 BC) provides proof that there are only 5 possible regular solids

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B.6 Elements of the Cosmos 14

Plato associates the 5 solids with the 5 elements of the universe.

• Earth Cube

• Fire Tetrahedron

• Air Octahedron

• Water Icosahedron

• Ether Dodecahedron

B.7 Aristotle (350 BC) 15

• Model had 55 spheres to explain the universe

B.8 Claudius Ptolemy (90-168 AD) 16

• Geocentric (Earth-Centered) model of universe

• Planets orbit earth on epicycles to explain retrograde motion

• Theory lasts till time of Copernicus

C.1 Nicolaus Copernicus (1473-1543 AD) 17Heliocentric (Sun-Centered) model of universe

C.2 Static Cosmology 18

Copernicus Cosmological Principle:• Universe is isotropic & Homogeneous• No Preferred Center

(leads to conservation of momentum)• Verified by Hubble’s Galaxy Survey

C.3 Newtonian Cosmology

Newton proposed that the universe must be infinite to be balanced; a finite universe would collapse due to gravity

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But:• 1823 Olber shows universe is not infinite

• 1920 Eddington shows Newton’s Universeis Unstable and would collapse

• 1929 Inconsistent with Hubble’s Law (expanding universe)

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C.4 Olber’s Paradox (1823?)Heinrich Olber 1758-1840discoverer of the minor planets Pallas and Vesta

If the universe is infinite in extent, and filled with stars, Why is the sky dark at night?

For example, in this cactus forest, if youlook between two cacti, you just seeanother cactus further away. In someplaces you see blue sky because theforest is not infinite, but if it was, you’djust see cacti everywhere, and so theuniverse would be “green”.

20 C.5 Olber’s ParadoxIt’s the same with stars. If you look between two stars, you will just see another.

Aren’t more distant stars fainter due to the inverse square law?

Yes, but, at a greater distance, the number of stars per angle will increase by the distance squared!

The two effects cancel out! Everywhere the sky should be as bright as the sun!

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D.1 Curved Finite Universe 22

1917 Einstein proposes universe:•Is finite, curved like a ball(this fixes Olber’s Paradox)

•But gravity would still collapse it

•Proposes negative pressure(cosmological constant) prevents collapse

•Later calls this his “biggest blunder”

D.2 Curved Space 23

If we live in a (positively) curved space, then no matter what direction we look, we might see that back of our head!

Its like living on the surface of a big ball.

This would explain why sky is dark at night.

D.3 Lookback Time 24

Speed of light is a constant: c=186,282 miles/second

The further away we look, the further into the past we are seeing!

If the universe is unchanging, then there will be just as many galaxies far away (in the past) as nearby (in the present) [if we correct for the curve of space]

E.1 Review: Spectral lines• 1802 Wollastan sees lines in solar spectra

• 1814 Fraunhofer Labelsthem A, B, C, D

• Later measures over 500 lines!

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E.2 Kirchhoff’s Laws 26 E.3 Gustav R Kirchhoff (1860)27

His three laws:1. A hot dense body will emit a

continuous spectrum2. A hot transparent gas will emit

emission line spectrum3. A cool transparent gas in front of a

source of continuous spectrum will produce absorption spectra.

E.4 Niels Bohr (Nobel Prize 1922)28

• 1913 Bohr proposes“quantized orbits” to atom.

E.5 Emission and Absorption 29

E.6 Emission & Absorption 30 E.7 Spectral Series 31

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F.1 Galactic Recession 32

•1912 Vesto Melvin Slipher first measures “doppler redshifts” of galaxies

•1917 Willem de Sitter interpreted Slipher’s red shifts as a Doppler effect, meaning that the galaxies are moving away from us (known for a time as the “de-Sitter effect). [He perhaps is the first to propose that the universe is expanding]

•1923 Carl Wirtz combined Slipher’s red shift measurements with rough estimates of the distances to galaxies based on their apparent size, and proposed a velocity-distance law, i.e. that redshift is proportional to distance. [This result has been historically ignored, and Hubble got most of the credit]

F.2 Big Bang Theory 33

•1922 Friedmann, and 1927 Father Lemaitre show that another solution to Einstein’s equation would be that the universe is expanding from kinetic energy leftover from a “big bang” creation. No need for negative pressure.

•This would also explain the observed “redshifts”

F.3 Hubble’s LawTo visualize the expansion of our three-dimensional universe, imagine a two-dimensional universe crisscrossed by a grid of parallel lines (like on a piece of graph paper). The animation shows five galaxies that happen to lie where gridlines cross. As the universe expands in all directions, the gridlines and the attached galaxies spread apart. From the viewpoint of any one of the galaxies, all the other galaxies appear to be moving away. The more distant a galaxy is, the more rapidly it appears to be receding.

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•1929 Hubble’s Law

F.4 Hubble’s Law (1929) 35

(recessional speed) =(const)x(Distance)

Or: v = H d

H=Hubble’s Constant, which will be the “slope” of the line. The approximate value is 75 km/(sec-MPC)

MPC=megaparsec (a million parsecs).

•The velocity is measured using the Doppler redshift (Z)•Redshift Defined: Z = Δλ/λ

– Example: if wavelength is 520 nm, but you measure it to be 572 nm, then Δλ=52 nm, and Z=52/520=0.1

•Doppler Formula relates velocity to redshift– v/c = Z (approximately, valid for v<<c)– c=speed of light

•Example: Z=0.1 means the speed is 10% the speed of light.

F.5 Doppler Formula 36

If we have: Z=v/c, then what about distant quasars that have Z=3. Does this mean its traveling 3 times the speed of light?

No

The true “relativistic” doppler formula:(Z+1)2 = (c+v)/(c-v)

As you approach the speed of light, the redshift goes to infinity.

Redshift of Z=3 is speed of 88.25% speed of light.

Relativistic Doppler Formula

0

0.5

1

1.5

2

2.5

3

3.5

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0 0.2 0.4 0.6 0.8 1

speed (v/c)

Reds

hift

Z

G.1 Steady State Model 37

•1948 Sir Fred Hoyle (and others) propose that the universe may appear to be expanding, but its actually not changing. Matter is constantly created to keep the “flow” going.

•“Every cluster of galaxies, every star, every atom had a beginning, but the universe itself did not."

•He ridiculed LeMaitre’s theory by calling it the “big bang” theory.

•1960 Discovery of cosmic radiation (left over from big bang) torpedoed Hoyle.

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G.2 Hubble Time: 13 billion years 38

If the universe has been expanding at a constant rate, then by “playing the movie backwards”, 13 billion years ago the universe was a single point (big bang!)

G.3 Decelerating Universe 39

We expect the universe is decelerating due to all the gravitational attraction between galaxies. Hence the age of the universe is somewhat less than the Hubble Time (13 billion years)

G.4 Open vs Closed Universe 40

CLOSED UNIVERSE: Just like a ball thrown upward will fall back to earth due to gravity, we might expect the universe will slow down, and collapse.

OPEN UNIVERSE: If you throw a ball upward fast enough, it won’t fall back, but it certainly will slow down due to gravity

We expect that the universe must be decelerating due to gravity. Whether the universe is open or closed is only a question of how fast it is slowing down.

G.5 Measuring Deceleration 41

Redshift is proportional to expansion rate

Brightness of cluster is a measure of distance, which is a measure of lookbacktime into the past.

Expect to see deviations from Hubble’s law in the past, when universe was expanding faster.

G.6 The Universe is Accelerating? 42

1998 Measurements of distant supernova (i.e. in the distant past) were 20% fainter than expected.

Interpretation: universe WAS slowing down for first half of lifetime

BUT, since then, it has been ACCELERATING

This is a big surprise

Notes• http://www.phys.unsw.edu.au/astro/cosmo/jkw_lecture/sld034.htm

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