Class web site:

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Astronomy 305/Frontiers in Astronomy

• Class web site
• http//glast.sonoma.edu/lynnc/courses/a305
• Office Darwin 329A
• [phone]
• Best way to reach me lynnc_at_charmian.sonoma.edu

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Group 12
Way to go, Group 12!
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Golden Age of Cosmology

• Standard Big Bang Cosmology
• Big Bang Nucleosynthesis
• Cosmic Microwave Background
• Did the Universe have a bout of Inflation?
• Horizon Problem
• Flatness Problem
• Multiverses
• Geometry and Curvature of Space

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Big Bang?
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Big Bang Timeline
Big Bang Nucleosynthesis
We are here
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Standard Big Bang Cosmology

• Sometime in the distant past there was nothing
  space and time did not exist
• Vacuum fluctuations created a singularity that
  was very hot and dense
• The Universe expanded from this singularity
• As it expanded, it cooled
• Photons became quarks
• Quarks became neutrons and protons
• Neutrons and protons made atoms
• Atoms clumped together to make stars and galaxies

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Standard Big Bang Cosmology

• Top three reasons to believe big bang cosmology
• Big Bang Nucleosynthesis
• Cosmic Microwave Background
• Hubble Expansion

Big Bang by Physics Chanteuse Lynda Williams
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Big Bang Nucleosynthesis

• Light elements (namely deuterium, helium, and
  lithium) were produced in the first few minutes
  of the Big Bang

The predicted abundance of light elements heavier
than hydrogen, as a function of the density of
baryons in the universe (where 1 is
critical) Note the steep dependence of deuterium
on critical density. Goal is to find a critical
density that explains all the abundances that are
measured
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Big Bang Nucleosynthesis

• Heavier elements than 4He are produced in the
  stars and through supernovae
• However, enough helium and deuterium cannot be
  produced in stars to match what is observed in
  fact, stars destroy deuterium in their cores,
  which are too hot for deuterium to survive.
• So all the deuterium we see must have been made
  around three minutes after the big bang, when
  T109 K
• BBN predicts that 25 of the matter in the
  Universe should be helium, and about 0.001
  should be deterium, which is what we see.
• BBN also predicts the correct amounts of 3He and
  7Li

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Big Bang Timeline
Cosmic Microwave Background
We are here
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Cosmic Microwave Background

• Discovered in 1965 by Arno Penzias and Robert
  Wilson who were working at Bell Labs
• Clinched the hot big bang theory

Excess noise in horned antennae was not due to
pigeon dung!
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Where is the CMBR?

• Map of redshift vs. time after Big Bang

Universe has expanded and cooled down by 1z
(about 1000) since the photons last scattered off
the CMBR
CMBR Z1000
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CMBR

• Photons in CMBR come from surface of last
  scattering where they stop interacting with
  matter and travel freely through space
• CMBR photons emanate from a cosmic photosphere
  like the surface of the Sun except that we
  inside it looking out
• The cosmic photosphere has a temperature which
  characterizes the radiation that is emitted
• It has cooled since it was formed by more than
  1000 to 2.73 degrees K

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Big Bang Timeline
We are here
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What is inflation?

• Inflation refers to a class of cosmological
  models in which the Universe exponentially
  increased in size by about 1043 between about
  10-35 and 10-32 s after the Big Bang (It has
  since expanded by another 1026)
• Inflation is a modification of standard Big Bang
  cosmology
• It was originated by Alan Guth in 1979 and since
  modified by Andreas Albrecht, Paul Steinhardt and
  Andre Linde (among others)

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Why believe in inflation?

• Inflation is a prediction of grand unified
  theories in particle physics that was applied to
  cosmology it was not just invented to solve
  problems in cosmology
• It provides the solution to two long standing
  problems with standard Big Bang theory
• Horizon problem
• Flatness problem

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Horizon Problem

• The Universe looks the same everywhere in the sky
  that we look, yet there has not been enough time
  since the Big Bang for light to travel between
  two points on opposite horizons
• This remains true even if we extrapolate the
  traditional big bang expansion back to the very
  beginning
• So, how did the opposite horizons turn out the
  same (e.g., the CMBR temperature)?

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Horizon problem

• The Universe at t 300,000 y after the Big Bang
  (when the CMBR was formed)

A and B are sources of photons that are now
arriving on Earth Horizon distance is 1/100 of
the distance between A and B
Horizon distance is 3 x 300,000 y because the
Universe is expanding tells you how far light
could travel
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Horizon Problem

• Inflation allows the early Universe to be small
  enough so that light can easily cross it at early
  times

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No inflation

• At t10-35 s, the Universe expands from about 1
  cm to what we see today
• 1 cm is much larger than the horizon, which at
  that time was 3 x 10-25 cm

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With inflation

• Space expands from 3 x 10-25 cm to much bigger
  than the Universe we see today

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CMBR vs. Inflation

• Inflation also predicts a distinct spectrum of
  fluctuations for the CMBR which arise from the
  original quantum fluctuations in the
  pre-inflation bubble

Everything we see in the Universe started out as
a quantum fluctuation!
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Flatness Problem

• Why does the Universe today appear to have W
  between 0.1 and 1 the critical dividing line
  between an open and closed Universe?
• Density today will differ greatly from density of
  early Universe, due to expansion if W starts
  out lt1, it will get much lower and vice versa ?
  only values of W very near 1 can persist
• A value for W 1 also implies the existence of
  dark matter as well as the cosmological constant

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Flatness Problem

• Density of early Universe must be correct to 1
  part in 1060 in order to achieve the balance that
  we see

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Flatness Problem

• Inflation flattens out spacetime the same way
  that blowing up a balloon flattens the surface
• Since the Universe is far bigger than we can see,
  the part of it that we can see looks flat

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Big Bang Revisited

• Extrapolating back in time, we conclude that the
  Universe must have begun as a singularity a
  place where the laws of physics and even space
  and time break down
• However, our theories of space and time break
  down before the singularity, at a time of 10-43
  s, a length of 10-33 cm, and a density of 1094
  cm3
• This is known as the Planck scale

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Planck scale activity

• The goal of this activity is to calculate the
  Planck mass, length, time and energy.
• Remember

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Vacuum fluctuations

• Virtual particle pairs continually emerge and
  disappear into the quantum vacuum
• If you observe the particles, you give them
  enough energy to become real
• The particles can also get energy from any nearby
  force field

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Quantum Universe

• Edward Tryon (1970) suggested that the Universe
  has a total E0 because in a flat Universe, the
  negative energy of gravity is exactly balanced by
  the positive energy of matter
• With E0, there is no time limit on the
  Universes existence from the Uncertainty
  Principle
• The quantum fluctuation Universe will collapse
  again due to the gravity of the singularity,
  unless it is given a sudden surge of energy
• Spontaneous symmetry breaking of the previously
  unified forces provides this energy

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Unified Forces

• The 4 forces are all unified (and therefore
  symmetric) at the Planck scale energy

inflation
Planck scale
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Symmetry Breaking

• Here is an example it is unclear which glass
  goes with which place setting until the first one
  is chosen

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Broken Symmetry

• At high T, the Universe is in a symmetrical
  state, with a unique point of minimum energy
• As the Universe cools, there are many possible
  final states but only one is chosen when the
  symmetry breaks

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False Vacuum

• The unified (symmetric) state of the very early
  Universe is a state of negative energy called the
  false vacuum
• A phase transition turns the false vacuum into
  the true vacuum and provides the surge of energy
  that drives inflation similar to the energy
  released when water freezes into ice
• During inflation, spacetime itself expands faster
  than the speed of light

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False Vacuum

• The Universe is now stuck in a state of false
  vacuum which decays very slowly
• When it reaches the true vacuum state, inflation
  will stop and particles will form

The shallow slope near the false vacuum allows
the Universe to keep the energy density almost
constant as it expands
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Pocket Universes

• As the false vacuum decays, particles are created
  in pocket universes

In each time slice, the original pocket universe
expands by a factor of 3 while new ones are
created out of the false vacuum in a fractal
pattern
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Formation of child Universe

• As false vacuum expands, space distorts to form a
  wormhole

True vacuum
False vacuum
This entire region is 10-25 cm
wormhole
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Child Universe

• The child universe disconnects from the original
  space

Observers in the parent universe see a black hole
form!
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Multiverses

• Universe was originally defined to include
  everything
• However, with inflation, the possibility exists
  that our bubble universe is only one of many
  such regions that could have formed
• The other universes could have very different
  physical conditions as a result of different ways
  that the unified symmetry was broken
• New universes may be forming with each gamma-ray
  burst that makes a black hole!

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A Humbling Thought

• Not only do we not occupy a preferred place in
  our Universe, we dont occupy any preferred
  universe in the Multiverse!

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Cosmological curvature parameters

• W density of the universe / critical density

• lt 1 hyperbolic geometry
• W 1 flat or Euclidean
• W gt 1 spherical geometry

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Flatland by Edwin A. Abbott

• The characters in Flatland

Rank in Flatland is a function of increasing
symmetry A woman, soldier, workman,merchant,
professional man, gentleman, nobleman, high priest
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Flatland

• What do they see when a 3D being (Lord Sphere)
  comes to visit?

3D cross-sections of Lord Sphere float through
the 2D world of Flatland
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Troubles in Flatland

• Its hard to eat in a 2D world!
• It is also impossible to tie your shoes! Why?

A digestive tract cuts a 2D being in half!
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Troubles in Flatland

• A Square and his wife alone in their 2D house,
  when Lord Sphere drops in from the third dimension

There is no privacy in 2D from a 3D being!
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Troubles in Flatland

• A 3D being would be able to change the symmetry
  of a 2D resident or help him escape from jail!

The 3D being can lift the 2D resident up out of
Flatland!
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Troubles in Flatland
movie

• How do Flatlanders know the shape of their
  Universe?
• A flat plane (with edges) is an open 2D Universe
• Is there a closed 2D Universe?

A Moebius strip is a 2D closed universe
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Exploring Geometries

• Take the newspaper
• Cut a long skinny strip
• Twist one end of the strip once and tape together
• Congratulations you have just made a Moebius
  strip!
• How many sides does this have? Try drawing on it
  to see.
• What happens to it when you cut it all around the
  strip direction?

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Troubles in Flatland

• What would happen if Flatlanders walked all the
  way around a closed 2D world?
• They would be mirror-reversed!
• Flat torus another example of a closed 2D world

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Infinite Universe?

• Is the Universe infinite or just really, really,
  really big?
• Some scientists (like Janna Levin) prefer to
  think of the Universe as finite but unbounded. An
  example of such a space is a 3D torus.
• With such a topology, we could see the backs of
  our heads, if we could see far enough in one
  direction

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Curved Space

• This is not an infinite series of reflections,
  but is caused by light traveling all the way
  around the hyperdonut
• A hyperdonut is one example of a curved space in
  3D

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3D Torus games

• Play game here

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The 4D Universe

• Many cosmologists believe that our Universe is a
  4D hypersphere
• This is a 3D movie projection of a 4D hypersurface

movie
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Geometry in the 4th dimension

• A 2D square is created by moving a line in a
  perpendicular direction
• A 3D cube is created by moving a square in a
  perpendicular direction

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Geometry in the 4th dimension

• A Flatlander can only visualize a cube, if it is
  unfolded in 2D
• If you move a 3D cube in a fourth perpendicular
  direction, you get a hypercube
• A 3D being can only visualize a hypercube by
  unfolding it in 3D into a tesseract

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Geometry in the 4th dimension

• Christus Hypercubus was painted by Salvador Dali
  in 1955 it features a tesseract
• A 4D hypercube is bounded by 8 3D cubes, has 16
  corners and a volume L4

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Geometry in the 4th dimension

• Here is another 2D projection of a 4D hypercube
• At each face, you can see a cube in different
  directions as you change your perspective

d2 x2 y2 z2 w2
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Troubles in Spaceland

• Thieves from the fourth dimension could steal
  things from locked safes (or operate without
  cutting you open!)

There is no privacy in 3D from a 4D being!
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Visitors from the 4th dimension

• Try the digustoscope to see yourself as a 4D
  being in a 3D world!

Do powerful beings such as a Cosmic Creator (or
the Devil) live in the Fourth Dimension?
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Angels and Devils

• This 2D exercise from U Wash helps you to
  visualize the effects of different geometries
• But first, lets see how 2D beings would see a 3D
  object passing through their world (e.g. Flatland
  by Abbott)
• Cube movies
• Sphere movies

60
Resources

• Inflationary Universe by Alan Guth (Perseus)
• A Short History of the Universe by Joseph Silk
  (Scientific American Library)
• Before the Beginning by Martin Rees (Perseus)
• Inflation for Beginners (John Gribbin)
  http//www.biols.susx.ac.uk/Home/John_Gribbin/cosm
  o.htm
• Ned Wrights Cosmology Tutorial
  http//www.astro.ucla.edu/wright/cosmolog.htm
• James Schombert Lectures http//zebu.uoregon.edu/
  js/21st_century_science/lectures/lec24.html

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Resources

• Hyperspace by Michio Kaku (Anchor Books)
• Fourth dimension web site http//www.math.union.e
  du/dpvc/math/4D/welcome.html
• Michio Kakus web site http//www.mkaku.org
• Exploring the Shape of Space http//www.geometryga
  mes.org/ESoS/index.html
• Fourth Dimension by Rudy Rucker (Houghton
  Mifflin)

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Web Resources

• Cosmic Background Explorer http//space.gsfc.nasa.
  gov/astro/cobe/cobe_home.html
• University of Washington Curvature of Space
  http//www.astro.washington.edu/labs/clearinghouse
  /labs/Curvature/curvature.html
• Surfing through Hyperspace by Clifford A.
  Pickover (Oxford)
• VROOM visualization of 4 dimensions
  http//www.evl.uic.edu/EVL/VROOM/HTML/PROJECTS/02S
  andin.html

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Web Resources

• Bell Labs Cosmology Archives
• http//www.bell-labs.com/project/feature/archives/
  cosmology/
• Davide P. Cervones Flatland cubes
  http//www.math.union.edu/dpvc/courses/2000-01/MT
  H053-SP01/notes/
• Big Bang Cosmology Primer http//cosmology.berkele
  y.edu/Education/IUP/Big_Bang_Primer.html
• Martin Whites Cosmology Pages http//astron.berke
  ley.edu/mwhite/darkmatter/bbn.html