Observational Cosmology:

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Observational Cosmology An Introduction
Wolfgang Hillebrandt MPI für Astrophysik
Garching
Heraeus-Workshop, Bremen, September 25 - 29, 2006
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Acknowledgement To a large extend, these
lectures are based on a lecture series given by
Matthias Steinmetz at the University of Arizona,
Tucson, in 2001.
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The new Cosmos.
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The Scientific Method
specific instances
? Science is a history of corrected mistakes
(Popper)
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Outline of the lectures

• Historical overview
• The standard model of cosmology
• Classical tests and predictions
• The cosmic expansion rate
• The cosmic microwave background
• Primordial nucleosynthesis
• Formation of large-scale structure and galaxies

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Historical Overview
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Aristotle (350 B.C.) First coherent physical
model

• Everything on Earth composed of four elements
  earth, water, air and fire
• Each of these elements moves differently earth
  toward the center of the Universe, fire away from
  the center, water and air occupy the space
  between.
• Earth at the center of the Universe
• Objects of different composition fall differently
• Concept of force Motions that deviate from the
  natural motion of the element must be sustained
  by a force.

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Aristotles cosmology

• In contrast to Earthly motions, celestial motions
  do continue indefinitely ? two types of motion
  limited, straight towards/away from the center
  (Earthly realm) and continuing on circles in the
  heavens
• Celestial bodies cannot be composed of Earthly
  elements ? ether as a fifth element
• Limited motion on Earth/indefinite motion in the
  heavens reflect imperfect Earth/perfect heavens
• Eternal and unchanging heavens ? Universe without
  beginning or end
• Universe has a finite size

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Aristarchus (250 B.C.) the Sun
at the center

• He knew the size of the Earth (roughly)
• He knew the size of the Moon and the distance
  between the Moon and the Earth (from lunar
  eclipses)
• Using basic geometry, he was able to determine
  the size and distance of the Sun
• Result The Sun is 19 times todays value 390
  times more distant than the Moon and (because it
  has the same apparent size on the sky) is 19
  times larger than the Moon (and also much larger
  than Earth)
• Conclusion the Sun (i.e. the largest object) is
  at the center of the universe

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Aristarchus Measuring the distance of the Sun
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Aristarchus Why was his model never accepted by
his contemporaries?

• He was considered a mathematician, not an
  astronomer
• He stood against the two main authorities of his
  time, Aristotle and Hipparchus
• His model was in conflict with the physics of his
  time, in particular Aristotles physics
• no evidence for the Earth rotating
• no evidence for the Earth moving

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Ptolemy (100 A.D.) defines the cosmology for
the next 1500 years

• Assembled the astronomical knowledge (basically
  Aristotles cosmology and Hipparchus
  observations) ? Almagest (The Great System)
• Expanded and improved the models
• Patched up inconsistencies ? Epicycle theory
• but at the expense of giving up simplicity

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Retrograde motion
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Epicycle model
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Ptolemy (100 A.D.) defines the cosmology for
the next 1500 years

• Assembled the astronomical knowledge (basically
  Aristotles cosmology and Hipparchus
  observations) ? Almagest (The Great System)
• Expanded and improved the models
• Patched up inconsistencies ? Epicycle theory
• But at the expense of giving up simplicity
• Thomas Aquinas ? cornerstone of Christian
  doctrine
• Believe that all that could be discovered had
  already been discovered

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Problems of Ptolemys model

• Model couldnt fit observations
• put the Earth off center
• epicycles upon epicycles
• total of more than 100 epicycles
• Nevertheless errors in the predicted positions of
  planets accumulated to several degrees by 1400
  A.D.

King Alfonso X If the Lord Almighty had
consulted me before embarking upon Creation, I
should have recommended something simpler
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The Copernican Revolution (1500)

• 15th century rediscovery of Greek scientific
  thought
• Shape and size of the Earth were well known among
  educated people (Columbus myth)
• Nicholas Copernicus De revolutionibus orbium
  coelestrium On the Revolution of Heavenly
  Spheres put the Sun at the center ?
  heliocentric world model inspired by the work of
  Aristarchus ?

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Why is the heliocentric model so attractive ?

• Its simple
• It naturally explains why the inner
  planets Mercury and Venus never travel far
  from the Sun
• Reproduces much better the observed change in
  brightness of planets
• It provides a natural explanation for the seasons
• It provides a natural explanation of retrograde
  motions without relying on epicycles

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Heliocentric model
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Problems of the heliocentric model (at that time)

• Against Christian Scriptures
• New discovery
• Predicts parallaxes ?observation
• Problem rotating Earth ?Aristotles physics
• Less accurate than the Ptolemaic model ? working
  model required even more epicycles
• Question Why did he published his work only near
  the end of his life ? Was he afraid of the
  authority of the Church or was he embarrassed
  because of the failure of his model ?

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Just being smart is not enough ...

• Better data
• Final touch-up of the model
• Promotion of the new model

• Tycho Brahe
• Johannes Kepler
• Galileo Galilei

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Tycho Brahe (1546-1601)

• Last of the great naked-eye observers
• exceptionally careful and systematic observer ?
  first modern scientist
• Earth at center, planets orbit the Sun
• detailed measurement of Mars orbit over 30 years
• Observed comets and parallax of comets ? Comet
  behind the orbit of the Moon
• Observed a supernova new star in Cassiopeia,
  no parallax measurable ? supernova must be on
  celestial sphere

? Challenge of the Aristotelian idea of the
perfect, eternal, unchanging heavens
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Johannes Kepler (1571-1630)

• Tychos successor in Prague
• He realized that neither the Ptolemaic nor
  Tychos nor the heliocentric model can fit
  Tychos data within the stated accuracy
• Proposal planets move on ellipses, not circles

Circle distance to the center is constant
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Galileo Galilei (1564-1642)

• Has not invented the telescope !
• But was the first to point the
  telescope at the night sky
• Designed tests for Aristotles physics and
  finally rejected it
• Famous for his trial for heresy 1633
• Exonerated in 1980 !

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Galileos astronomical discoveries

• Mountains on the Moon similar to Earth? not
  perfect spherical bodies
• Stars point like planets spheres
• Phases of Venus ? Ptolemaic world system
• Moons of Jupiter ? miniature system
• Interpretation of Sun spots ? unchanging heavens
• Milky Way Zillions of Stars

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Galileos physics

• Concept of inertia and momentum
• Aristotle force is responsible for motion
• Galileo force is responsible for changes in
  motion
• ? relativity of uniform motion
• Fall experiments objects of different
  composition fall at the same rate ? Aristotle?
  basis for Einsteins equivalence principle
• Thought experiments

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• Better data
• Final touch-up of the model
• Promotion of the new model

• Tycho Brahe
• Johannes Kepler
• Galileo Galilei

Still missing someone to put the pieces together
to form a coherent physical theory in the modern
sense ? Sir Isaac Newton
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Sir Isaac Newton (1643-1727)

• Fundamental contributions in optics, physics and
  mathematics
• invented calculus (independently Leibnitz)
• invented the mirror telescope
• discovered than white light is composed of
  colored light
• theory of mechanics
• theory of gravity
• demonstrated that Keplers laws are a consequence
  of the theory of mechanics and gravity Principia

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Newtons three laws

• Newtons first law A body at rest or in the
  state of
• uniform motion will remain at rest or in uniform
  motion,
• unless acted upon by a net external force.

Newtons second law The acceleration of an
object is equal to the net force applied to it,
divided by its mass.
Newtons third law For every action, there is an
equal and opposite reaction.
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Newtons triumph discovery of Neptune

• 1781 W. Herschel discovers Uranus
• Measurements of Uranus orbit around the Sun
  slight deviations from perfect ellipse. These
  cannot be accounted for by the perturbing
  influence of the known planets ? another planet ?
• Leverrier and Adams calculated the position of a
  hypothetical planet that could be responsible for
  the observed deviations
• Galle (1846) pointed a telescope to the predicted
  position and found the new planet (Neptune)
  within 1 of the predicted position

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Next step apply Newtons laws to cosmology

• Problem 1750 universe identical with solar
  system. Stars far away, but how far ?
• We need empirical data regarding the size and age
  of the universe, so we can compare model
  predictions against data

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Determining the Size and Age of the Universe???
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How do we measure distances in daily life ?

• Parallaxes
• Travel time
• Via size of objects comparison with standard
  yard sticks
• Via brightness of objects comparison with
  standard candles

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Parallaxes

• Measure the position of an object with respect to
  its background
• Nearby objects show a larger motion than
  objects far away do
• The parallax angle q , the distance of the object
  D and the diameter of the Earths orbit d are
  connected by simple geometrical relations. For
  small angles, it is d D ? q units !!!! q
  measured in rad !

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Travel time

• If you know the speed v youre traveling with and
  the travel time ?t, the distance D can be
  obtained by simple multiplication
  D v ?t
• Astronomy Use light travel times, i.e. v 300
  000 km/sec

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Comparison with a standard ruler

• An object nearby spans a larger angle than an
  object of identical physical size far away
• The physical size l of the object, its distance D
  and the angle q under which it appears are
  connected by simple geometrical relations. For
  small angles, it is l D ? q units !!!! q
  measured in rad !
• If the physical size l of an object is known (?
  standard ruler), its distance D can be determined
  by measuring the angle q under which the object
  appears

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Comparison with a standard candle

• A nearby object appears brighter than an object
  of same luminosity far away
• The absolute luminosity Labsolute of an object,
  its distance D and its apparent luminosity
  Lapparent are connected by simple geometrical
  relations. It is Lapparent Labsolute / D2
  
• If the absolute luminosity Labsolute of an object
  is known (? standard candle), its distance D can
  be determined by measuring its apparent
  luminosity Lapparent

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Three Types of Distance Measurement

• Direct Measurements Measuring the physical
• distance to an object directly

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Direct Measurements (Important!)

• Light Travel Time Measure the time taken for a
  radar pulse to bounce off of an object or a
  signal to arrive from a spacecraft
• Parallax Stars appear to wobble
• when observed from different
• directions the nearer the star,
• the larger the motion. Good to
• 1 kpc

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Standard Rulers

• Expanding Photosphere Method (EPS or
  Baade-Wesselink)
• Type II supernova explosions
• Measure speed of expansion of debris and time
  since explosion Þ real size of nebula
• Useful to distances of 10-100 Mpc

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Standard Rulers

• Water Masers Measure the proper motions and
  accelerations of water masers in the accretion
  disks of AGN to get actual orbital radius of
  masers and mass of central object. Only one
  measurement so far.
• Gravitational lensing Time delay of fluctuations
  in lensed object gives info on geometry. Depends
  on mass of lens and theoretical lensing model.
  Good to 1 Gpc

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Standard Candles (Important!)

• Main Sequence fitting Calibrate the luminosity
  of main sequence stars in nearby clusters with
  parallax distances and fit clusters farther out.
  Good to 10-100 kpc.

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Standard Candles

• Luminosity functions
• Choose a type of object with a charcteristic
  distribution of absolute luminosities
• Measure distribution of apparent luminosities in
  a distant galaxy
• Scale to match true luminosities, get distance
• Globular clusters and planetary nebulae good to
  50-100 Mpc

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Standard Candles (Important!)

• Cepheid and RR Lyrae variables
• Pulsating stars which change in brightness with a
  characteristic period
• Period is proportional to absolute luminosity
• Common and bright (esp. Cepheids), thus visible
  in nearby galaxies
• Good to 20 Mpc

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Standard Candles

• Surface brightness fluctuations
• Distant objects appear smaller
• More stars per pixel in a galaxy far, far away
• Smoother light distrubution, less variation from
  pixel to pixel
• Amplitude of fluctuations proportional to
  distance
• Good to 100 Mpc, z0.01

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Courtesy John Tonry
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Standard Candles (Important!)

• Galaxy kinematics
• Tully-Fisher relation rotation speed of spiral
  galaxies proportional to mass of glaxy
  proportional to total luminosity
• Dn-s, Fundamental Plane, Faber-Jackson
  relations velocity dispersion and size of
  elliptical galaxies proportional to total
  luminosity
• Good to 500 Mpc, z0.1

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Standard Candles (Important!)

• Type Ia supernovae
• Exploding white dwarf star
• Shape of light curve and dimming timescale give
  absolute luminosity
• Extermely luminous so they can be observed at
  great distances
• Good to 1 Gpc, z1

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Other Methods

• Novae as standard candles not very standardized,
  good only to 20 Mpc
• Sunyaev-Zel'dovich effect good to 1 Gpc, z1
  but model dependent, not well calibrated yet.
  Measure density of x-ray emitting gas in clusters
  with CMB, measure temperature independently,
  gives absolute x-ray luminosity.

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The Distance Ladder

• Different techniques useful at different
  distances use nearby standards to calibrate more
  distant ones where they overlap
• Cepheids are a key step many in the Milky Way
  and LMC, so distances are directly measurable by
  parallax or only a step away, yet bright enough
  to overlap many secondary distance indicators
• Cepheids ? luminosity functions, SBF, galaxy
  kinematics, SNIa

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The Distance Ladder

• Gravitational lensing, Sunyaev-Zel'dovich effect,
  Expanding Photosphere Method provide independent
  checks of Cepheid based distance scale
• Lensing and SZ effect potentially useful out to
  very large distances

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Size of the Universe (I)

• Size of the Earth
• radius 6370 km
• Eratosthenes (200 B.C.)
• Size of the solar system
• several billion km
• rough idea Aristarchus (250 B.C.)
• detailed layout 1750

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Size of the Universe (II)

• Distance to the stars
• until 1838 far away
• Bessel (1838) measured the first parallax of a
  star (61 Cygni). Result 0.3
• So how far is 61 Cygni ? Recall d D ? q
• d diameter of Earths orbit (149.7 million km)
• D distance of 61 Cygni
• q parallax (0.3)

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Distance of 61 Cygni

• So lets plug in numbers ...
• But dont forget to transform angles into radians
  !!!
• 0.3 0.3/3600 8.3?10-5 º
• into radians 8.3?10-5 º ? ?/180 1.45 ?10-6
• put into formula D 149.7 ?106 km/1.45 ?10-6
  ? 1014 km
• for comparison 1 light year (Ly) 1 Ly 300
  000 km/s ? 86400 s/d ? 365 d/yr 9.5 ?1012 km

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Astronomers favorite length unit
1 parsec (1pc) is the distance that produces a
parallax shift of 1 or 1 parsec (1pc) is the
distance under which the radius of the Earths
orbit around the Sun spans an angle of 1

• Distance in pc 1/parallax in
• 1 pc 3.26 Ly

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Shape and Size of the Milky Way

• 1600 Galileo MW collection of stars
• 1750 Immanuel Kant, Thomas WrightMW is a disk
• 1780 Herschel counted stars in 700 fields
  around the sky MW is flattened 41, Sun is near
  the centerbut is it ?

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Size of the Milky Way

• Kapteyn (1920)
• measures distances to stars in the MW
• conclusion
• MW about 5 kpc across
• Sun near the center

• Shapley (1920)
• measured distances to globular clusters
• conclusion
• MW about 100 kpc across
• Sun 20 kpc off center

Solution ???
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Nature of spiral nebulae ?

• Curtis
• MW is 10 kpc across
• Sun near center
• spiral nebulae were other galaxies
• high recession speed
• apparent sizes of nebulae
• did not believe van Maanens measurement
• ? Milky Way one galaxy among many others

• Shapley
• MW is 100 kpc across
• Sun off center
• spiral nebulae part of the Galaxy
• apparent brightness of nova in the Andromeda
  galaxy
• measured rotation of spirals (via proper motion)
  by van Maanen
• ? Milky Way Universe

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Solution I

• Role of dust
• obscuration Kapteyn/Curtis could only see a
  small fraction of the Milky Way disk
• dimming stars appear to be dimmer ? Shapley,
  ignoring dust, concluded that globular clusters
  are farther away than they actually are.
• ? Milky Way is 30 kpc across, Sun is 8.5 kpc off
  center.

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Solution II

• Van Maanens observation (rotation of spiral
  nebulae) turned out to be wrong.
• There is a difference between novae and
  supernovae, supernovae are much brighter?
  Andromeda is farther away than anticipated by
  Shapley
• ? Spiral nebulae are galaxies like the Milky
  Way. Distance millions of parsec.

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Limits on the Age of the Universe (I)
Age of the Earth

• Before 1670 little attention, but common
  perception that the Earth is young
• 1669 Nicolaus Steno older rocks below, younger
  rocks above. Layering of rocks ? age sequence
• 1800 Realization that Earth may be very old
• 1858 Wallace and Darwin Evolution of species ?
  Earth must be very old (hundreds of million of
  years)

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Limits on the Age of the Universe (II)
Age of the Earth/Sun

• Problem in the 19 century, the Sun was believed
  to be only 100 million years old (it would run
  out of fuel otherwise)
• Solution nuclear fusion (Eddington-Bethe-Weizsäck
  er 1930s)
• Today radioactive dating of rocks ? Earth (and
  solar system) is 4.6 billion years old
• Later in these lectures age of the universe 14
  billion years

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Lets come back to Newtons Universe

• In order to avoid collapse
• homogeneous
• isotropic
• infinite size
• no center
• Infinite in time
• has always been
• will always be
• ? perfect cosmological principle!

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The cosmological principle

• Homogeneous the universe looks the same
  everywhere on large scales? there is no special
  place (center)
• Isotropic the universe looks the same in all
  directions on the sky
• ? there is no special direction (axis)

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The perfect cosmological principle

• Homogeneous the universe looks the same
  everywhere on large scales? there is no special
  place (center)
• Isotropic the universe looks the same in all
  directions on the sky? there is no special
  direction (axis)
• Unchanging The universe looks the same at all
  times ? there is no special epoch

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Homogeneity and Isotropy
Copernican Principle
?
Isotropy
Homogeneity

Isotropy around another point
?
Isotropy
Homogeneity

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Does the cosmological principle apply to our
universe ?
The cosmic microwave background radiation
(CMB) afterglow from the big bang. Its smooth
to 1 part in 105
? Yes, the universe appears to be
homogeneous and isotropic!
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Does the strong cosmological principle apply to
our universe ?
Galaxies 10 billion years ago
Galaxies today
? no, the universe appears to change with time
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Problems with an infinite universe

• Olbers Paradox Why is the night sky dark?

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Problems with an infinite universe

• Olbers Paradox Why is the night sky dark?

Each shell contributes L1 4? ? r12?x
l infinite number of shells ? infinite
luminosity
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How to solve Olbers paradox ?

• Universe is finite
• Universe has finite age
• The distribution of stars throughout space is not
  uniform
• The wavelength of radiation increases with time.
• Note for the big bang model, all these
  conditions are satisfied

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Break!
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Two clouds on the horizon of 19th century physics

• Michelson-Morley result
• Thermal radiation of hot bodies (so-called black
  body radiation)

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Einsteins new relativity

• Galileo
• The laws of mechanics are the same in all
  inertial frames of reference
• time and space are the same in all inertial
  frames of reference
• Einstein
• The laws of physics are the same in all inertial
  frames of reference
• the speed of light in the vacuum is the same in
  all inertial frames of reference
• ? time spans and distances are relative

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Doppler effect
The light of an approaching source is shifted to
the blue, the light of a receding source is
shifted to the red.
red shift
blue shift
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Doppler effect
redshift z0 not moving z2 v0.8c z? vc
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Some open problems of special relativity

• How to deal with accelerations ?
• How to deal with gravity ?
• Newtons gravity acts instantaneously, i.e. it is
  inconsistent with special relativitys conclusion
  that information cannot be communicated faster
  than the speed of light.
• Distance is relative, so which distance to use in
  computing the gravitational force ?

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General relativity

• Mass tells space how to curve
• Space tells mass how to move

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The entire Universe in one line
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Some effects predicted by the theory of general
relativity

• Gravity bends light
• Gravitational redshift
• Gravitational time dilation
• Gravitational length contraction

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Consequences of the equivalenceprinciple mass
bends light
Equivalence principle Accelerated frame is
equivalent to a frame subjected to gravity
Outside Observer
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Examples for light bending
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Examples for light bending
Einstein Cross - G22370305
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Examples for light bending
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How to find out that space is not flat?
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How to find out that space is not flat?
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In flat space
?
?
?
??? 180º
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In curved space
??? ? 180º
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Euclidean (flat) geometry

• Given a line and a point not on the line, only
  one line can be drawn through that point that
  will be parallel to the first line
• The circumference of a circle of radius r is 2? r
• The three angles of a triangle sum up to 180?

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Spherical geometry

• Given a line and a point not on the line, no
  line can be drawn through that point that will be
  parallel to the first line
• The circumference of a circle of radius r is
  smaller than 2? r
• The three angles of a triangle sum up to more
  than 180?

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Hyperbolic geometry

• Given a line and a point not on the line, an
  infinite number of lines can be drawn through
  that point that will be parallel to the first
  line
• The circumference of a circle of radius r is
  larger than 2? r
• The three angles of a triangle sum up to less
  than 180?

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The Standard Model of Cosmology
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Lets apply Einsteins equation to the Universe

• What is the solution of Einsteins equation for a
  homogeneous, isotropic mass distribution?
• As in Newtonian dynamics, gravity is always
  attractive
• A homogeneous, isotropic and initially static
  universe is going to collapse under its own
  gravity
• Alternative expanding universe (Friedmann)

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Einsteins proposal cosmological constant ?

• There is a repulsive force in the universe
• vacuum exerts a pressure
• empty space is curved rather than flat
• The repulsive force compensates the attractive
  gravity ? static universe is possible
• but such a universe turns out to be unstable
  one can set up a static universe, but it simply
  does not remain static
• Einstein greatest blunder of his life, but is
  it really ?

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The quantum vacuum acts like a gas of negative
pressure!
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Edwin Hubble (1889-1953)

• Four major accomplishments
• in extragalactic astronomy
• The establishment of the Hubble classification
  scheme of galaxies
• The convincing proof that galaxies are island
  universes
• The distribution of galaxies in space
• The discovery that the universe is expanding

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The Hubble tuning fork
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The Hubble tuning fork

• Elliptical galaxies (E0-E7)
• classified according to their flattening
  10?(1-b/a)
• Spiral galaxies (S0, Sa-Sd)
• classified according to their bulge-to-disk ratio
• Sa large bulge, Sd small bulge
• S0 transition spiral to elliptical
• Barred spiral galaxies (SB0, SBa-SBd)
• classified according to their bulge to disk ratio
• Irregular galaxies (Irr)

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Again The Doppler effect
redshift z0 not moving z2 v0.8c z? vc
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The redshift-distance relation
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A modern Hubble diagram
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Key results

• Most galaxies are moving away from us
• The recession speed v is larger for more distant
  galaxies. The relation between recess velocity v
  and distance d fulfills a linear relation
  v H0 ? d
• Hubbles measurement of the constant H0
  H0 500 km/s/Mpc
• Todays best fit value of the constant
  H0 72 km/s/Mpc

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Question

• If all galaxies are moving away from us,
• does this imply that we are at the center?

Answer

• Not necessarily, it also can indicate that the
• universe is expanding and that we are at no
• special place.

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So why was Hubbles original measurement so far
off ?

• Distance measurement based on the
  period-luminosity relation of Cepheid stars
• What are Cepheids? They are variable pulsating
  stars

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So why was Hubbles original measurement so far
off ?

• There exists a luminosity-period relation for
  Cepheid stars

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So why was Hubbles original measurement so far
off ?

• there are two populations of Cepheids (but Hubble
  was not aware of that)
• type I metal rich stars (disk of galaxies)
• type II metal poor stars (halo of galaxies)
• type II Cepheids (W Virginis) are less luminous
  than type I Cepheids (d Cephei)

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initial distance 1 length unit final
distance 2 length units recess velocity
1 length unit per time unit
initial distance 2 length units final
distance 4 length units recess velocity
2 length units per time unit
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Consequence

• Distance scale was calibrated based on type II
  Cepheids
• Distances to other galaxies were measured using
  type I Cepheids
• yard stick was systematically to small

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How old is the universe ? (III)

• A galaxy at distance d recedes at velocity vH0 ?
  d.
• When was the position of this galaxy identical to
  that of our galaxy? Answer

tHubble Hubble time.
For H0 72 km/s/Mpc tHubble
14 Gyr
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How big is the universe? (III)

• We cant tell. We can only see (and are affected
  by) that part of the universe that is closer than
  the distance that light can travel in a time
  corresponding to the age of the Universe
• But we can estimate, how big the observable
  universe is

dHubble Hubble radius. For H0 72
km/s/Mpc dHubble 4.2 Gpc
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The great synthesis (1930)

• Meeting by Einstein, Hubble and Lemaître
• Einstein theory of general relativity
• Friedmann and Lemaître expanding universe as a
  solution to Einsteins equation
• Hubble observational evidence that the universe
  is indeed expanding
• Consequence
• Universe started from a point? The Big Bang
  Model !

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A metric of an expanding Universe

• Recall flat space
• better using spherical coordinates (r,?,?)

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A metric of an expanding Universe

• But, this was for a static space. How does this
  expression change if we consider an expanding
  space ?
• R(t) is the so-called scale factor

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A metric of an expanding Universe

• Robertson-Walker metric
• R(t) is the scale factor
• k is the curvature constant
• k0 flat space
• kgt0 spherical geometry
• klt0 hyperbolic geometry

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A metric of an expanding Universe

• But, so far, we only considered a flat space.
  What, if there is curvature ?
• k is the curvature constant
• k0 flat space
• kgt0 spherical geometry
• klt0 hyperbolic geometry

kgt0
klt0
k0
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Cosmological redshift

• While a photon travels from a distance source to
  an observer on Earth, the Universe expands in
  size from Rthen to Rnow.
• Not only the Universe itself expands, but also
  the wavelength of the photon ?.

121
Cosmological redshift

• General definition of redshift? for
  cosmological redshift

122
Cosmological redshift

• Examples
• z1 ? Rthen/Rnow 0.5
• at z1, the universe had 50 of its present day
  size
• emitted blue light (400 nm) is shifted all the
  way through the optical spectrum and is received
  as red light (800 nm)
• z4 ? Rthen/Rnow 0.2
• at z4, the universe had 20 of its present day
  size
• emitted blue light (400 nm) is shifted deep into
  the infrared and is received at 2000 nm
• most distant astrophysical object discovered so
  far z6.4

123
(SDSS image taken in October 2003)
124
A large redshift z implies ...

• The spectrum is strongly shifted toward red or
  even infrared colors
• The object is very far away
• We see the object at an epoch when the universe
  was much younger than the present day universe
• most distant astrophysical object discovered so
  far z 6.4
• z gt 6.4 dark ages

125
Break!
126
Can we calculate R(t) ?

• Foutside 0

127
Can we calculate R(t) ?
128
What is the future of that galaxy ?

• Critical velocity escape speed
• vltvesc galaxy eventually stops and falls back
• vgtvesc galaxy will move away forever

129
Lets rewrite that a bit ...

• ??lt0 ? vltvesc galaxy eventually stops and falls
  back
• ??gt0 ? vgtvesc galaxy will move away forever

130
Lets rewrite that a bit ...

• Homogeneous sphere of density ?
• so for the velocity
• but what is ?? ?

131
Lets switch to general relativity

• Friedmann equation
• same k as in the Robertson-Walker metric

132
Lets switch to general relativity

• Friedmann equation
• k is the curvature constant
• k0 flat space, forever expanding
• kgt0 spherical geometry, eventually recollapsing
• klt0 hyperbolic geometry, forever expanding

133
Can we predict the fate of the Universe ?

• Friedmann equation

• k0

134
Can we predict the fate of the Universe ?

• If the density ? of the Universe
• ? ?crit flat space, forever expanding
• ? gt?crit spherical geometry, recollapsing
• ? lt ?crit hyperbolic geometry, forever expanding
• so what is the density of the universe?
• We dont know precisely
• ? gt?crit very unlikely
• currently favored model ? ? 0.3?crit

135
kgt0
klt0
k0
136
How big is ?crit ?

• ?crit 8?10-30 g/cm3 ? 1 atom per 200 liter
• Density parameter ?0
• ?0 1 flat space, forever expanding (open)
• ?0 gt1 spherical geometry, recollapsing (closed)
• ?0 lt1 hyperbolic geometry, forever expanding
• Currently favored model ?0 0.3

137
Observational Tests and Predictions
138
Observational cosmology The quest for three
numbers !

• The Hubble constant H0
• how fast is the universe expanding
• The density parameter ?0
• how much mass is in the universe
• The cosmological constant ??
• the vacuum energy of the universe
• (or the deceleration parameter q0 , which is a
  combination of the others)

139
1. Measuring H0
140
Distances in the local universe

• Assume a linear expansion (Hubble law)
  vczH0D
• Use the distance modulus
  m-M5log(D/10pc)-5
• Distances of a standard candle (Mconst.)
  m5log(z)b
  b M255log(c)-5log(H0)

141
Expanding Photosphere Method

• Baade (1926), Schmidt et al. (1993), Eastman et
  al. (1996), Hamuy et al. (2001)
• Assume homologous expansion R(t)R0v(t-t0)
  
• Photometric angular diameter

142
Distances from EPM
(SN 1999em, Hamuy et al. 2001)
Slope gives the distance Intercept the size of
the progenitor and/or time of explosion
143
Distances from EPM

• Note that this distance measurement is completely
  independent of any other astronomical object!
• no distance ladder
• Assumption
• massive envelope that creates a photosphere
• spherical symmetry
• not true for many core collapse supernovae
• correction factors for deviation from black body
  spectrum
• model dependent

144
EPM so far

• Limitations
• needs large and extensive data sets
• difficulties to get into the Hubble flow
• distances only to galaxies with supernovae
• difficult to build large sample
• Promise
• completely independent distance measurements
• checks on the Cepheid distance scale

145
Distances with Type Ia Supernovae

• Use the Hubble diagram (m-M vs. log z)
• m-M5log(z)255log(c)-5log(H0)
• Note that the slope is given here.
• Hubble constant can be derived when the absolute
  luminosity M is known
• logH0log(z)5log(c)-0.2(m-M)

146
Hubble constant from SNe Ia

• Calibrate the absolute luminosity
• through Cepheids
• classical distance ladder
• depends on the accuracy of the previous rungs on
  the ladder
• LMC distance, P-L(-C) relation, metallicities
• HST program (Sandage, Tammann)
• HST Key Programme (Freedman, Kennicutt, Mould,
  Madore)
• through models
• extremely difficult (but possible!)

147
Absolute Magnitudes of SNe Ia
(Saha et al. 1999)
148
Testing the SNe Ia as distance indicators

• Hubble diagram of SNe Ia in the local, linear
  expansion, Hubble flow
• Calibration through primary distance indicators
• Theoretical models

149
Nearby SNe Ia
Phillips et al. (1999)
150
Light curve shape luminosity

• ?m15 relation
• Phillips (1993), Hamuy et al. (1996), Phillips et
  al. (1999)
• MLCS
• Riess et al. (1996, 1998), Jha et al. (2003)
• stretch
• Perlmutter et al. (1997, 1999), Goldhaber et al.
  (2001)
• MAGIC
• Wang et al. (2003)

151
The principles of light-curve calibrations
(Goldhaber et al. 2001)
152
The SN Ia luminosity can be normalised Bright
slow Dim fast
(Riess et al. 1996)
153
Correlations
154
Normalisation of the peak luminosity

• Using the luminosity-decline rate relation one
  can normalise the peak luminosity of SNe Ia

Reduces the scatter!
155
The nearby SN Ia sample
Evidence for good distances
156
Hubble constant from SNe Ia

• Extremely good (relative) distance indicators
• distance accuracy better than 10
• Uncertainty in H0 mostly from the LMC and the
  Cepheid P-L relation
• Todays best value (Cepheids SNe Ia)

H0 (72 7) km/s/Mpc
157
2. Measuring O0 and q0
158
How can we measure ?0 ?

• Count all the mass we can see
• tricky, some of the mass may be hidden
• Measure the rate at which the expansion of the
  universe is slowing down
• a more massive universe will slow down faster
• Measure the geometry of the universe
• is it spherical, hyperbolic or flat ?
• (Most accurate I will come back to this later
  in connection with the CMB)

159
Lets try to measure the deceleration

• Acceleration according to Newton
• Deceleration parameter

160
So whats the meaning of q0 ?

• Deceleration parameter q0
• q0gt0.5 deceleration is so strong that
  eventually the universe stops expanding
  and starts collapsing
• 0ltq0lt0.5 deceleration is too weak to
  stop
• the expansion
• Whats the difference between q0, ?0 and k ?
• k curvature of the universe
• ?0 mass content of the universe
• q0 kinematics of the universe

161
So lets measure q0 !

• How do we do that?
• Measure the rate of expansion at different times,
  i.e. measure and compare the expansion based on
  nearby galaxies and based on high redshift
  galaxies or other objects, e.g., Type Ia
  supernovae.
• Gravity is slowing down expansion ? expansion
  rate should be higher at high redshift.

162
So lets measure q0 !
q0 0
q0 0.5
Data indicates q0 lt 0 ? Expansion is
accelerating
fainter
more distant
163
Science discovery of the year 1998

• The expansion of the universe is accelerating !!!
• But gravity is always attractive, so it only can
  decelerate
• ? Revival of the cosmological constant ?

164
Friedmanns equation for ?gt0

• k is the curvature constant
• k0 flat space, flat universe
• kgt0 spherical geometry, closed universe
• klt0 hyperbolic geometry, open universe

• k is the curvature constant
• k0 flat space
• kgt0 spherical geometry
• klt0 hyperbolic geometry
• but for sufficiently large ? a spherically curved
  universe may expand forever

165
Deceleration parameter q for ?gt0
166
The fate of the Universe for ?gt0
Mean distance between galaxies
time
167
Is the fate of the Universe well determined ?

• deceleration
• ½?0 ?? gt 0 decelerating
• ½?0 ?? lt 0 accelerating
• curvature
• ?0 ?? 1 flat
• ?0 ?? lt 1 hyperbolic
• ?0 ?? gt 1 spherical
• two equations for two variables ? well posed
  problem (for constant ?)

168
Recent supernova data
169
Very high redshift SNe Ia
170
The outcome
171
Observational cosmology the quest for three
numbers !

• The Hubble constant H0
• how fast is the universe expanding
• The density parameter ?0
• how much mass is in the universe
• The cosmological constant ??
• the vacuum energy of the universe
• Current observational situation
• H0 72 km/s/Mpc
• ?0 0.3 ?? 0.7 ? flat space

172
How old is the Universe?

• We had
• A galaxy at distance d recedes at velocity vH0 ?
  d.
• When was the position of this galaxy identical to
  that of our galaxy? Answer

• tHubble Hubble time. For H0 72 km/s/Mpc
  tHubble 13.5 Gyr

173
The age of the Universe revisited

• So far, we have assumed that the expansion
  velocity is not changing (q00, empty universe)
• How does this estimate change, if the expansion
  decelerates, i.e. q0gt0 ?

• An ?0gt0, ?0 universe is younger than 14 Gyr

174
The age of the Universe revisited

• So far, we only have considered decelerating
  universes
• How does this estimate change, if the expansion
  accelerates, i.e. q0lt0 ?

• An ?gt0 universe can be older than 14 Gyr

175
The age of the Universe revisited

• ?00, ?0 tHubble 1/H0 14 Gyr
• ?01, ?0 tHubble 2/(3H0) 10 Gyr
• Open universes with 0lt?0lt1, ?0 are between 10
  and 14 Gyr old
• Closed universes with ?0gt1, ?0 are less than 10
  Gyr old
• ?gt0 increases, ?lt0 decreases the age of the
  universe
• ?00.3, ?0.7 tHubble 0.96/H0 13.7 Gyr

176
Can we measure the age of the Universe ?

• Not directly
• But we can constrain the age of the Universe. It
  must not be younger than the oldest star in the
  Universe.
• How do we measure the age of stars?
• radioactive dating
• stellar evolution models
• Result age of the oldest star 12-14 Gyr
• In excellent agreement with ? gt 0 cosmology!

177
The life of a universe some key facts

• Unless ? is sufficiently large (which is
  inconsistent with observations) all cosmological
  models start with a big bang.
• An universe doesnt change its geometry. A flat
  universe has always been and will always be flat,
  a spherical universe is always spherical and so
  on.
• Two basic solutions
• eventual collapse for large ?0 or negative ?
• eternal expansion otherwise

178
Some common misconceptions

• The picture that the Universe expands into a
  preexisting space like an explosion
• The question what was before the big bang?
• Remember spacetime is part of the solution to
  Einsteins equation
• Space and time are created in the big bang

179
So is the big crunch the same as the big bang run
in reverse ?

• No. The Universe has meanwhile formed stars,
  black holes, galaxies etc.
• Second law of thermodynamicsThe entropy
  (disorder) of a system at best stays the same but
  usually increases with time, in any process.
  There is no perpetual motion machine.
• Second law of thermodynamics defines an arrow of
  time.

180
Friedmanns equation for ?0, ?0lt1

• At early epochs, the first term dominates
• the early universe appears to be almost flat
• At late epochs, the second term dominates
• the late universe appears to be almost empty

181
Friedmanns equation for ?gt0, ?0lt1

• At early epochs, the first term dominates
• the early universe appears to be almost flat
• At late epochs, the third term dominates
• the late universe appears to be exponentially
  expanding

182
A puzzling detail

• ?0 for most of its age, the universe looks
  either to be flat or to be empty
• ?gt0 for most of its age, the universe looks
  either to be flat or to be exponentially
  expanding
• Isnt it strange that we appear to live in that
  short period between those two extremes
• gt Flatness problem !

183
Break!
184
3. The cosmic microwave background
185
General acceptance of the big bang model

• Until mid 60ies big bang model very
  controversial, many alternative models
• After mid 60ies little doubt on validity of the
  big bang model
• Four pillars on which the big bang theory is
  resting
• Hubbles law ?
• Cosmic microwave background radiation ?
• The origin of the elements
• Structure formation in the universe

186
Georgy Gamov (1904-1968)

• If the universe is expanding, then there has
  been a big bang
• Therefore, the early universe must have been
  very dense and hot
• Optimum environment to breed the elements by
  nuclear fusion (Alpher, Bethe Gamow, 1948)
• success predicted that helium abundance is 25
• failure could not reproduce elements more
  massive than lithium and beryllium (? formed in
  stars)

187
What are the consequences ?

• In order to form hydrogen and helium at the right
  proportions, the following conditions are
  required
• density ? ? 10-5 g/cm-3
• temperature T ? 109 K
• Radiation from this epoch should be observable as
  an isotropic background radiation
• Due to the expansion of the universe to ? ?
  3?10-30 g/cm3, the temperature should have
  dropped to T ? 5 K (-268 C)
• Can we observe this radiation ?

188
The discovery of the relic radiation

• Gamovs result on the background radiation was
  not well recognized by the scientific community
• Result was rediscovered by Dicke and Peebles in
  the early sixties. They started developing an
  antenna to search for the background radiation
• T ? 5 K ? microwaves
• but

189
Penzias and Wilson 1965

• Working at Bell labs
• Used a satellite dish to measure radio emission
  of the Milky Way
• They found some extra noise in the receiver, but
  couldnt explain it? discovery of the background
  radiation
• Most significant cosmological observation since
  Hubble
• Nobel prize for physics 1978

190
A quote ...

• John Bahcall "The discovery of the cosmic
  microwave background radiation changed forever
  the nature of cosmology, from a subject that had
  many elements in common with theology to a
  fantastically exciting empirical study of the
  origins and evolution of the things that populate
  the physical universe."

191
How far can we see ?

• Naked eye 2 million Lyr (Andromeda galaxy)
• Large telescopes 13 billion Lyr (z 6.4)
• What are the limiting factors ?
• there are no bright sources at high z
• light is redshifted into the infrared
• absorption
• The universe appears to be fairly transparent out
  to z 6.4

192
When does a gas become opaque?

• A gas appears opaque (e.g. fog) if light is
  efficiently scattered by the atoms/molecules of
  the gasThe three important factors are thus
• the density of the gas (denser ? more particles
  ? more scattering)
• the efficiency with which each individual
  particle can scatter light
• wavelength of the light

193
The transition from a transparent to an opaque
universe

• At z0 the universe is fairly transparent
• At higher z, the universe becomes denser (?
  ?0?(1z)3) and hotter (TT0?(1z))
• At z1100, the universe is so dense that its
  temperature exceeds 3000K. In a fairly sharp
  transition, the universe becomes completely
  ionized and opaque to visible light. (last
  scattering surface)
• At z1100, the universe is 300 000 yrs old

194
Before recombination The Universe is
opaque After recombination The Universe is
transparent Transition 300 000 years after
the Big Bang
195
Last scattering surface
transparent
opaque
196
Black body radiation

• A hot body is brighter than a cool one (L?T4,
  Stefan-Boltzmanns law)
• A hot bodys spectrum is bluer than that of a
  cool one (?max?1/T, Wiens law)

197
The cosmic microwave background radiation (CMB)

• Temperature of 2.7280.004 K
• Isotropic to 1 part in 100 000
• Perfect black body
• 1990ies CMB is one of the major tools to study
  cosmology
• Note 1 of the noise in your TV is from the big
  bang

198
Nobel Price in Physics 2006 for COBE
John Mather
George Smoot
199
Should the CMB be perfectly smooth ?

• No. Todays Universe is homogeneous and isotropic
  on the largest scales, but there is a fair amount
  of structure on small scales, such as galaxies,
  clusters of galaxies etc.

200
Should the CMB be perfectly smooth ?

• We expect some wriggles in the CMB radiation,
  corresponding to the seeds from which later on
  galaxies grow

201
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202
The Cosmic Background Explorer (COBE) (1989 -
1993)

• Main objectives
• To accurately measure the temperature of the CMB
• To find the expected fluctuations in the CMB

203
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204
Main results from COBE
205
Interpretation of the results from the COBE)

• The Earth is moving with respect to the CMB ?
  Doppler shift
• The emission of the Galaxy
• Fluctuations in the CMB

206
The BOOMERANG mission

• COBE was a satellite mission, why ?
• Measure at mm and sub-mm wavelengths
• Earth atmosphere almost opaque at those
  wave-lengths due to water vapor
• satellite missions take a long time and are
  expensive
• What can be done from the ground ?
• Balloon experiment
• Desert ? South Pole

207
The BOOMERANG mission (2000)
208
The BOOMERANG mission
209
Where do the CMB fluctuations come from ?

• Wrinkles some regions have a slightly higher
  gravity, some a slightly lower (potential
  wells)
• Matter falls into potential wells

210
How can we measure the geometry of the universe ?

• We need a yard stick on the CMB
• For different curvatures, a yard stick of given
  length appears under different angles

211
Measuring the Curvature of the Universe Using the
CMB
Result from Boomerang The Universe is flat to
within 10!
212
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213
Measuring the Curvature of the Universe Using the
CMB

• Recall with supernovae, one measures q0 ½?0
  ??
• CMB fluctuations measure curvature? ?0 ??
• two equations for two variables? problem solved

214
Present and future missions
Planck
WMAP
215
Results from WMAP
216
Can we see the sound of the universe ?

• Compressed gas heats up? temperature
  fluctuations

217
Interpretation of the data
Geometry of the Universe flat
(Euklidian) Dark Energy 70 Dark Matter
26 Baryons 4 Age of the Universe 14 Billion
years (Uncertainties lt 5)
218
4. Primordial nucleosynthesis
219
General acceptance of the big bang model

• Until mid 60ies big bang model very
  controversial, many alternative models
• After mid 60ies little doubt on validity of the
  big bang model
• Four pillars on which the big bang theory is
  resting
• Hubbles law ?
• Cosmic microwave background radiation
• The origin of the elements
• Structure formation in the universe

• Until mid 60ies big bang model very
  controversial, many alternative models
• After mid 60ies little doubt on validity of the
  big bang model
• Four pillars on which the big bang theory is
  resting
• Hubbles law ?
• Cosmic microwave background radiation ?
• The origin of the elements ?
• Structure formation in the universe

220
Georgy Gamov (1904-1968)

• If the universe is expanding, then there has
  been a big bang
• Therefore, the early universe must have been
  very dense and hot
• Optimum environment to breed the elements by
  nuclear fusion (Alpher, Bethe Gamow, 1948)
• success predicted that helium abundance is 25
• failure could not reproduce elements more
  massive than lithium and beryllium (? formed in
  stars)

221
The structure of matter
222
Nomenclature
or

• Z number of protons
• A number of nucleons (protons and neutrons)
• N number of neutrons (A-Z)
• X name of the element

223
Abundances of elements

• Hydrogen and helium most abundant
• gap around Li, Be, B

224
Thermal history of the universe

• When the universe was younger than 300 000 yrs,
  it was so hot that neutral atoms separated into
  nuclei and electrons. It was too hot to bind
  atomic nuclei and electrons to atoms by the
  electromagnetic force
• When the universe was younger than 1 sec, it
  was so hot that atom nuclei separated into
  neutrons and protons. It was too hot to bind
  protons and neutrons to atomic nuclei by the
  strong nuclear force

225
Formation of helium in the big bang

• Hydrogen 1 nucleon (proton)
• Helium 4 nucleons (2 protons, 2 neutrons)
• In order to from helium from hydrogen one has to
• bring 2 protons and 2 neutrons close together, so
  the strong nuclear force can act and hold them
  together
• close together Coulomb repulsion has to be
  overcome ? high velocities ? high temperatures
• but 4 body collisions are highly unlikely

226
Transforming hydrogen into helium

• Hot big bang neutrons and protons
• Use a multi step procedure
• p n ? 2H
• p 2H ? 3He
• n 2H ? 3H
• 3He 3He ? 4He 2 p
• some side reactions
• 4He 3H ? 7Li
• 4He 3He ? 7Be

227
Mass gap/stability gap at A5 and 8