how do you make a universe?

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How Do You Make a Universe?

Geary AlbrightSaturday Morning Physics

March 3, 2012

• The history of the Universe can be summed up like this: Hydrogen is a light, odorless, colorless gas, that if given enough time, turns into people.

• In this lecture, I am going to try to fill in some of the gaps in this statement….

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Whence the Universe?

Ripple in still waterWhen there is no pebble tossedNor wind to blow

lyric/haiku, R. Hunter

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The Great Nebula Debate

• Starting with Charles Messier in 1781, astronomers began cataloging faint nebulae (nebula is Latin for cloud) in the sky.

• Initially, they were assumed to be part of the Milky Way (sipral nebulae). However, as better telescopes came along, it was clear that they were composed of stars. Therefore, they might be other distant systems of stars.

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M-31 The Andromeda Galaxy

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The Shapely-Curtis Debate

– In 1920, a debate was held at the National Academy of Sciences in Washington, D.C. to settle the question. • Harlow Shapley argued that they must be

part of our Galaxy. • Heber Curtis, who was a graduate of the

University of Virginia, argued that they are separate “island universes.”

• Shapley won the debate, Curtis was correct.

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The Shapely-Curtis Debate

Harlow Shapely

Heber Curtis

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Distances to Galaxies

• In 1924, Edwin Hubble used the 100-inch Hooker Telescope on Mt. Wilson to resolve individual stars in the Andromeda Galaxy.– Among these stars were some Cepheid

variables.– Using the method pioneered by Henrietta

Leavitt, Hubble was able to calculate the distance to these nebulae.

– This proved once and for all that the spiral nebulae were outside the Milky Way and were galaxies just like the Milky Way.

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The Local Group

• The Milky Way is a member of the Local Group of galaxies.– The local group is spread over 3

million LY and contains about 40 members.

– There are three large spirals (The Milky Way, M-31 the Andromeda Galaxy, M-33).

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M-31 Andromeda Galaxy

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Local Group

Spiral Galaxy M-33

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M-87 Giant Elliptical Galaxy in the Virgo Cluster

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Hubble Ultra Deep Field Area is about 1/100 the size of the full Moon and10,000 Galaxies!

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The Expanding Universe

• In 1912, the American astronomer Vesto Slipher measured the spectra of about 40 faint spiral nebulae.– He found that almost all the galaxies

showed a redshift. That is, the absorption lines in the spectrum were shifted to longer (redder) wavelengths.

– This indicated that all the galaxies were moving away from our Galaxy.

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If almost all the galaxies that we see are moving away from the Milky Way, what does that tell us about our location in the Universe?

1. We are at the exact center.

2. We are near the center, but not necessarily at the exact center.

3. We are near the edge of the universe.

4. It tells us nothing about our location in the universe.

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Edwin Hubble (1889-1953)

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The Expanding Universe

• In the late 1920’s, Edwin Hubble and Milton Humason, began a systematic survey of the distances to nearby spiral galaxies and their recession velocity.– In 1929, they published a paper

showing that the recession velocities of the galaxies are directly proportional to their distances.

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The Hubble Law

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Velocity-Distance Relation 1929

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The Hubble Law

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The Expanding Universe

• The relationship between velocity and distance is:

– Where v is the recession velocity, H0 is the Hubble constant (equals the slope of the line), and D is the distance to the object.

– This equation is called the Hubble Law.

DHv 0

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The Hubble Law• The most widely accepted value for the

Hubble constant is:

• An accurate value of the Hubble constant is difficult to obtain.– It requires accurately measuring the

recession velocity (easy) and distance (difficult) to a number of galaxies.

– Mpc = Mega-parsec ~ 3 million light years

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The Hubble Law

• The Hubble Law simply says that a galaxy moves away from us at a speed of 71 km/s for every million pc of its distance.– A galaxy at 1 Mpc is receding at 71 km/s.– A galaxy at 2 Mpc is receding at 142

km/s.– A galaxy at 5 Mpc is receding at 355 km/s

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The Expansion of the Universe• The Hubble Law implies that the

universe is expanding.• At first, the idea that all galaxies are

moving away from us seems to indicate that we are at the center of the universe. However, in a uniformly expanding space, every galaxy is moving away from every other galaxy.

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The Expansion of the Universe• Imagine a rubber ruler with four ants on it.• Assume that this ruler is expanding so

that it uniformly doubles it length every minute.

• Consider the distances from the ant at 2 cm to the other ants after 1 minute (when the ruler has doubled in length). Note that ant 2 is not at the center of the ruler.

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The Hubble Law

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As the ruler stretches, do all of the ants see all of the other ants moving away from them?

1. Yes

2. No

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The Expansion of the Universe• Ants that are farther apart move away

from each other with a greater velocity.• The speed at which the distant ants

recede is proportional to their distance, just like the Hubble Law!

• On this ruler, all the ants will see all the other ants moving away from them. Just like galaxies in our universe!

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The Expansion of the Universe• For a three dimensional analogy, consider

raisins in a loaf of rising bread.• Regardless of which raisin you pick, all the

other raisins are moving away from it.• The reason they are receding from each

other is the bread between them is expanding. The same is true for the universe, the space between the galaxies is expanding.

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The Hubble Law

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The Birth of the Universe

• The Hubble Law expansion of the universe increases the distance between any two points as time moves forward.

• This implies that at some time in the distant past the distance between any two points was zero and that the density of the universe was infinite.

• The expansion of the universe from this beginning is called the Big Bang.

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The Birth of the Universe

• Where, then, is the center of the expansion? How far are we from the Big Bang that created the universe?

• The universe has no center! All points in space are expanding away from all other points in space. They are NOT expanding away from a single central point.

• To picture this, imagine living on the surface of a balloon as it was being inflated.

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The Hubble Law

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The Birth of the Universe

• It is incorrect to think of the Big Bang as an explosion from a single point.

• Since the entire universe was created in the Big Bang, including all of space and time, the explosion occurred everywhere at once.

• The universe is not expanding into some “empty space” beyond the galaxies, since the space in which the galaxies exist was created in the Big Bang.

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The Birth of the Universe

• What came before the Big Bang?– Since all of our laws of physics were created

in the Big Bang, we cannot use them to probe back to a time before the Big Bang occurred.

• Are there parallel universes where, for example, my parallel identity is getting an A+ in all my high school classes?– Again, our laws of physics apply only to our

universe and are contained within it. We may not be able to use them to probe the existence of other universes outside our own.

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The Birth of the Universe

• In fact, the expansion of the universe is the expansion of space itself. – A better way to think about the expansion of the

universe is not that the distant galaxies are moving away from us, but that they are stationary and the space between the galaxies is expanding.

– As the space between the galaxies expands, distant galaxies appear farther away.

– In addition, this expansion of space stretches the waves of light as they travel. This expansion of the wavelength creates the redshift.

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Expansion Redshift

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The Fate of the Universe

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Some say the world will end in fire,

Some say in ice.

From what I’ve tasted of desire

I hold with those who favor fire.

But if I had to perish twice,

I think I know enough of hate

To say that for destruction ice

Is also great

And would suffice.

Robert Frost

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Olber’s Paradox

• Consider this question “Why is the night sky dark?” – The answer has profound cosmological

implications.– It was believed that the universe was

infinite in size and infinitely old. Everywhere you look your line of sight will eventually end on the surface of a star. Therefore, the night sky would be as bright as the surface of a star!

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Olber’s Paradox

• Edmund Halley thought the darkness was due to the distance of stars, making them appear dim. However, as feeble as the light may be, the combined light from an infinite number of stars would still light the sky.

• Dust in the universe cannot solve the problem either, since the dust would eventually heat up and be as bright as a star.

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Olber’s Paradox

• The modern answer to Olber’s paradox is that the universe has a finite age (about 13.7 billion years old).

– We can only see the light from objects that are less than 13.7 billion LY away, only those objects are close enough so their light has had the time to get here since the origin of the universe

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Olber’s Paradox

– This solution was first proposed by Edgar Allen Poe in 1848.

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The Age of the Universe

• Since all galaxies are receding from us, and their velocity is proportional to their distance, indicates that the Universe is expanding.– If we could somehow make time run

backward, we would see the Universe contracting, that is, the galaxies would be getting closer together.

– We can use this fact to calculate the age of the Universe by determining when the distances between the galaxies goes to zero.

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The Age of the Universe

• To calculate the age of the Universe use:

00

0

H

1

dH

dT

dHvv

dT

Hubble’s Law

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The Age of the Univserse

• That is, the age of the Universe is simply 1/H0 if the universe expanded at a constant rate since the beginning.– Note: you must convert the Mpc to

kilometers and the seconds to years to get an age expressed in years.

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The Age of the Universe

• For H0=71 km/s per megaparsec we have

years billion 13.8years1013.8T

m 1000km 1

pc 1m 103.086

Mpc 1pc 10

s103.158yr 1

km 71Mpc s 1

T

km/s/Mpc 711

H1

T

10

166

7

0

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The Age of the Universe

• The only assumption made above is that the Universe has been expanding at a constant rate since the beginning. – However, the gravity of objects will tend to

slow the expansion over time (deceleration).– On the other hand, Einstein’s cosmological

constant, if it exists, could cause the expansion to speed up (acceleration).

– Observations of the expansion rate of distant galaxies can tell us which is the case.

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The Expanding Universe

• Immediately after developing his General Theory of Relativity in 1915, Einstein realized it could be applied to Universe as a whole.– The matter and energy in the Universe

would warp the geomety of space.– At the time, it was believed that the

Universe was infinite in extent and that it was static (neither expanding nor contracting).

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The Expanding Universe

• Einstein’s calculations showed that an infinite static universe was unstable. – The gravity of all the bodies would

cause it to collapse. – Therefore, there must be some

repulsive force, called the cosmological constant, that balances gravity.

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The Expanding Universe

– When Edwin Hubble showed that the Universe was expanding, Einstein realized his equations showed an expanding Universe was stable.

– He could have predicted the expansion of the Universe well before it was discovered observationally.

– He later referred to the introduction of the cosmological constant as “the biggest blunder of my life.”

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The Geometry of the Universe• General relativity describes how

matter (and energy, since E=mc2) curve the space around them.

• These ideas can be applied to the universe as a whole. Indeed, the geometry of space depends on the mass and energy conained in the Universe.

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The Geometry of the Universe• The equations of general relativity show

that there are two possible states for the universe, closed and open.– In a closed universe there is enough matter

and energy and their combined gravitational pull will stop the expansion and cause it to contract again.

– In an open universe the combined gravitational pull of all the matter and energy is insufficient to stop the expansion and the universe will expand forever.

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The Geometry of the Universe

Bound

Unbound

Marginally bound

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The Geometry of the Universe

– The parameter that determines the fate of the universe is the combined density of matter and energy.

– The dividing line between these two states is a universe which has exactly the critical density of material needed to stop the expansion after an infinite amount of time.

G 8π3H

ρ 0c

2

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The Geometry of the Universe

– The critical density depends on the Hubble Constant (a faster expansion would require more gravitational attraction to stop it).

– For H0=71 km/s, the critical density is about 1026 kg/m3. That’s about 5 hydrogen atoms per cubic meter.

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A Closed Universe

• The geometry of spacetime is spherical.• A closed universe is finite in size and

spacetime curves so that a beam of light would come back to where it started.

– Some have speculated that closed universes could give rise to another Big Bang. These “oscillating theories” cannot be tested and are therefore more philosophical than scientific.

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A Closed Universe

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An Open Universe

• In an open universe the current expansion will continue forever.

• The geometry of an open universe is hyperbolic (saddle shaped).– An open universe is infinite in extent.

Although space and time began with the Big Bang, they have no limit. The gravitational attraction of the material in the universe can slow the expansion, but cannot stop it.

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A Critical Universe

• In a critical, or flat, universe the expansion can just barely continue forever.

• The velocity of expansion will asymptotically go to zero.

• The geometry is flat.

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Which Universe do we have?• If we total up all the normal matter

in the Universe, we get a density about 4% of the critical density.

• Dark Matter seems to make up about 23% of the critical density.

• So matter is only 27% of the critical density, and if there is no other contribution, then the universe is open.

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Flatness Problem

• Astronomers and physicists have noted that the universe is suspiciously close to the “special” critical density.– The universe could have had any

density; one thousands, millions, or billions of times smaller or larger than the critical density.

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Acceleration of the Universe?• In 1998, publications began to

appear showing that the expansion rate of the universe appears to be accelerating.– This new work is based on using Type

I supernovae as standard candles to find their distance.

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Supernova in the News

• On Monday April 1, 2001, astronomers using the Hubble Space Telescope reported the most distant supernova ever discovered.

• The supernova occurred in a faint elliptical galaxy 10 billion light years away in the Hubble Deep Field.

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SN 1997ff in the HDF

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Supernova in the News• The supernova was found to be closer

than it would be if the universe expanded at a constant rate.

• The Hubble Constant was therefore found to be smaller at this great distance, i.e. earlier in the Universe

• This supernova is the best evidence that the expansion is accelerating.

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The Geometry of the Universe• The current best fit model of our

universe looks like:– The universe is flat (at the critical density).– The density of normal matter is 4% of the critical

density.– The density of dark matter is 23% of the critical

density.– The energy that is causing the acceleration of the

universe (called Dark Energy) is about 73% of the critical density.

– When this energy is combined with the normal and dark matter, we get a flat universe.

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Ultimate Fate of the Universe• As time goes on, galaxies will recede

from one another with ever increasing speed.

• Eventually, even the nearby galaxies will be receding from us at a speed greater than the speed of light.

• The Universe will grow cold and dark.

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Evidence for the Big Bang• There are two major observational

facts that strongly support the Big Bang:

1) The Universe is expanding according to Hubble’s Law.

2) The Universe is filled with electromagnetic radiation with a blackbody temperature of about 2.7 K.

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Cosmic Background Radiation• In 1965, Arno Penzias and Robert Wilson were

using a very sensitive radio telescope to study radio emission from the sky.– They found a background source of noise with a

temperature of 3 K that they could not explain.– After discussing the observations with other

astronomers, Penzias and Wison realized they had discovered the radiation from the Big Bang.

– Nobel Prize in physics in 1978 for the discovery.

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Bell Lab’s Horn Antenna, Holmdel, NJ

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Source of the Cosmic Radiation

• After nucleosynthesis, the temperature of the universe is high enough that the atoms are all ionized

• The electrons have too much energy and are not bound to the atoms.

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End of the Radiation Era

• The free electrons can scatter photons.

• Light does not travel far before being scattered by an electron, so the universe is opaque.

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The End of the Radiation Era• When the universe cools to ~3000 K

(~380,000 years), electrons are captured by the protons to form hydrogen atoms.

• This process is called recombination. – After recombination, the matter no longer

scatters the radiation and they decouple.– The universe becomes transparent.

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Cosmic Background Radiation• At this time, the photons had a

blackbody spectrum with a temperature 3000 K.

• Since then, the expansion of the universe has stretched the wavelength of these photons.

• The expansion of the universe causes a decrease in the temperature of the blackbody radiation.

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COBE• In 1989, NASA launched the Cosmic

Background Explorer satellite to study the Cosmic Background Radiation.– COBE showed that the microwave background is

a perfect black body with a temperature of 2.725 K.

– A slight temperature (Doppler) shift shows that the Sun and Earth are moving through space at 500 km/s toward the constellation Hydra.

– COBE also found small clumps in the background radiation, which indicate the formation of structures even at this early stage.

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Wilkinson Microwave Anisotropy Probe• On June 30, 2001 NASA launched

the Wilkinson Microwave Anisotropy Probe to study the fluctuations in the cosmic microwave background.

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Wilkinson Microwave Anisotropy Probe

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Wilkinson Microwave Anisotropy Probe• Universe is 13.7 billion years old with a

margin of error of close to 1%.• First stars ignited 200 million years after

the Big Bang.• Light in WMAP picture from 380,000

years after the Big Bang.• Content of the Universe:

– 4% Atoms, 23% Cold Dark Matter, 73% Dark energy.

• This is the way the world ends

• This is the way the world ends

• This is the way the world ends

• Not with a bang but a whimper

• From The Hollow Men by T.S. Elliot

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