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Observational Cosmology An Introduction

Wolfgang Hillebrandt MPI für Astrophysik

Garching

Heraeus-Workshop, Bremen, September 25 - 29, 2006

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.

The Scientific Method

specific instances

? Science is a history of corrected mistakes

(Popper)

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

Historical Overview

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.

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

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

Aristarchus Measuring the distance of the Sun

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

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

Retrograde motion

Epicycle model

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

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

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 ?

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

Heliocentric model

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 ?

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

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

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

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 !

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

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

- 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

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

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.

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

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

Determining the Size and Age of the Universe???

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

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

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

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

Three Types of Distance Measurement

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

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

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

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

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.

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

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

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

Courtesy John Tonry

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

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

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.

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

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

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

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)

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

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

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 ?

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 ???

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

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.

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)

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

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!

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)

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

Homogeneity and Isotropy

Copernican Principle

?

Isotropy

Homogeneity

Isotropy around another point

?

Isotropy

Homogeneity

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!

Does the strong cosmological principle apply to

our universe ?

Galaxies 10 billion years ago

Galaxies today

? no, the universe appears to change with time

Problems with an infinite universe

- Olbers Paradox Why is the night sky dark?

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

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

Break!

Two clouds on the horizon of 19th century physics

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

body radiation)

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

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

Doppler effect

redshift z0 not moving z2 v0.8c z? vc

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 ?

General relativity

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

The entire Universe in one line

Some effects predicted by the theory of general

relativity

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

Consequences of the equivalenceprinciple mass

bends light

Equivalence principle Accelerated frame is

equivalent to a frame subjected to gravity

Outside Observer

Examples for light bending

Examples for light bending

Einstein Cross - G22370305

Examples for light bending

How to find out that space is not flat?

How to find out that space is not flat?

In flat space

?

?

?

??? 180º

In curved space

??? ? 180º

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?

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?

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

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)

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 ?

The quantum vacuum acts like a gas of negative

pressure!

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

The Hubble tuning fork

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)

Again The Doppler effect

redshift z0 not moving z2 v0.8c z? vc

The redshift-distance relation

A modern Hubble diagram

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

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.

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

So why was Hubbles original measurement so far

off ?

- There exists a luminosity-period relation for

Cepheid stars

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)

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

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

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

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

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 !

A metric of an expanding Universe

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

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

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

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

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 ?.

Cosmological redshift

- General definition of redshift? for

cosmological redshift

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

(SDSS image taken in October 2003)

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

Break!

Can we calculate R(t) ?

- Foutside 0

Can we calculate R(t) ?

What is the future of that galaxy ?

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

Lets rewrite that a bit ...

- ??lt0 ? vltvesc galaxy eventually stops and falls

back - ??gt0 ? vgtvesc galaxy will move away forever

Lets rewrite that a bit ...

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

Lets switch to general relativity

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

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

Can we predict the fate of the Universe ?

- Friedmann equation

- k0

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

kgt0

klt0

k0

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

Observational Tests and Predictions

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)

1. Measuring H0

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)

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

Distances from EPM

(SN 1999em, Hamuy et al. 2001)

Slope gives the distance Intercept the size of

the progenitor and/or time of explosion

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

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

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)

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!)

Absolute Magnitudes of SNe Ia

(Saha et al. 1999)

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

Nearby SNe Ia

Phillips et al. (1999)

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)

The principles of light-curve calibrations

(Goldhaber et al. 2001)

The SN Ia luminosity can be normalised Bright

slow Dim fast

(Riess et al. 1996)

Correlations

Normalisation of the peak luminosity

- Using the luminosity-decline rate relation one

can normalise the peak luminosity of SNe Ia

Reduces the scatter!

The nearby SN Ia sample

Evidence for good distances

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

2. Measuring O0 and q0

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)

Lets try to measure the deceleration

- Acceleration according to Newton
- Deceleration parameter

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

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.

So lets measure q0 !

q0 0

q0 0.5

Data indicates q0 lt 0 ? Expansion is

accelerating

fainter

more distant

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 ?

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

Deceleration parameter q for ?gt0

The fate of the Universe for ?gt0

Mean distance between galaxies

time

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 ?)

Recent supernova data

Very high redshift SNe Ia

The outcome

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

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

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

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

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

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!

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

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

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.

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

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

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 !

Break!

3. The cosmic microwave background

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

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)

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 ?

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

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

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."

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

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

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

Before recombination The Universe is

opaque After recombination The Universe is

transparent Transition 300 000 years after

the Big Bang

Last scattering surface

transparent

opaque

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)

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

Nobel Price in Physics 2006 for COBE

John Mather

George Smoot

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.

Should the CMB be perfectly smooth ?

- We expect some wriggles in the CMB radiation,

corresponding to the seeds from which later on

galaxies grow

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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

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Main results from COBE

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

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

The BOOMERANG mission (2000)

The BOOMERANG mission

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

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

Measuring the Curvature of the Universe Using the

CMB

Result from Boomerang The Universe is flat to

within 10!

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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

Present and future missions

Planck

WMAP

Results from WMAP

Can we see the sound of the universe ?

- Compressed gas heats up? temperature

fluctuations

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)

4. Primordial nucleosynthesis

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

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)

The structure of matter

Nomenclature

or

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

Abundances of elements

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

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

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

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

Mass gap/stability gap at A5 and 8