Observational Cosmology:

Observational Cosmology:
An Introduction Wolfgang Hillebrandt MPI für Astrophysik Garching NOVICOSMO 2009 Rabac, Croatia September , 2009

Acknowledgement: To some extend, these lectures are based on a lecture series given by Matthias Steinmetz at the University of Arizona, Tucson.

The “new” Cosmos….

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.

Aristotle’s cosmology
In contrast to Earthly motions, celestial motions 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 [today’s 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 Aristotle’s 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 Aristotle’s 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

Problems of Ptolemy’s model
Model couldn’t 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 ?
It’s 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 Aristotle’s 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) Tycho’s successor in Prague
He realized that neither the Ptolemaic nor Tycho’s nor the heliocentric model can fit Tycho’s data within the stated accuracy Proposal: planets move on ellipses, not circles

Galileo Galilei (1564-1642) Has not invented the telescope !
But: was the first to point the telescope at the night sky Designed tests for Aristotle’s physics and finally rejected it Famous for his trial for heresy 1633 Exonerated only in 1979 !

Galileo’s 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

Galileo’s 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 Einstein’s 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 ( ) Fundamental contributions in optics, physics and mathematics: invented calculus (independently: Leibnitz) invented the mirror telescope discovered that white light is composed of colored light theory of mechanics theory of gravity demonstrated that Kepler’s laws are a consequence of the theory of mechanics and gravity: Principia

Newton’s 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 Newton’s 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 Earth’s orbit d are connected by simple geometrical relations. For small angles, it is d = D  q [units !!!! q measured in rad !]

Travel time If you know the speed v you’re 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 = 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 Standard Rulers: Size = Distance x q(angle on sky) Need to know the real size of the object Standard Candles: Lapparent = Labsolute / D2 Need to know the true luminosity of an object

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: solar system Parallax: good to ~1 kpc (astrometry from space!)

Expanding Photosphere Method (EPS or Baade-Wesselink)
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 Mpc (Most recent paper: Jones et al., ApJ 696 (2009) 1176)

(Strong) Gravitational lensing:
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 very few measurements so far. (Strong) 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 Rulers (Important!)
Baryon acoustic oscillations (BAO): Arise from the competition between gravitational attraction and gas pressure in the primordial plasma. Imprint on scales ~ 100Mpc/h. Weak lensing: Images of source galaxies can be stretched (shear) and magnified (convergence). Relies on statistics of the lensed population. CMB: Horizon size at the time of hydrogen recombination.

Standard Candles Main Sequence fitting: Calibrate the luminosity of main sequence stars in nearby clusters with parallax distances and fit clusters farther out. Good to kpc.

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

Surface brightness fluctuations Distant objects appear smaller More stars per pixel in a galaxy far, far away Smoother light distribution, less variation from pixel to pixel Amplitude of fluctuations proportional to distance Good to ~100 Mpc, z~0.01

Courtesy John Tonry

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 ~ Mpc

Galaxy kinematics Tully-Fisher relation: rotation speed of spiral galaxies proportional to mass of glaxy proportional to total luminosity Dn-σ, “Fundamental Plane”, Faber-Jackson relations: velocity dispersion and size of elliptical galaxies proportional to total luminosity Good to ~500 Mpc, z~0.1

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, z~1

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, SZ, BAO, WL, CMB

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 = 106 km/1.45 10-6  1014 km  10Ly

Shape and Size of the Milky Way
~1600 Galileo: MW = collection of stars ~1750 Immanuel Kant, Thomas Wright: MW is a disk ~1780 Herschel: counted stars in ~700 fields around the sky: MW is flattened 4:1, Sun is near the center but is it ?

Solution ??? 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 Maanen’s 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.

Solution II Van Maanen’s 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 millions of years)

Limits on the Age of the Universe (II): Age of the Earth/Sun
Problem: in the 19th century, the Sun was believed to be only 100 million years old (it would run out of fuel otherwise) Solution: nuclear fusion (Eddington-Bethe-Weizsäcker 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

Let’s come back to Newton’s 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)

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. It’s smooth to 1 part in 105  Yes, the universe appears to be homogeneous and isotropic!

Problems with an infinite universe
Olber’s Paradox: Why is the night sky dark? Each shell contributes L1 = 4  r12x l* infinite number of shells  infinite luminosity

How to solve Olber’s 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

Two clouds on the horizon of 19th century physics
Michelson-Morley result Thermal radiation of hot bodies (so-called black body radiation) Two hurricanes result Theory of relativity Quantum mechanics

Einstein’s 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 redshift: z=0: not moving z=2: v=0.8c z=: v=c

Some open problems of special relativity
How to deal with accelerations ? How to deal with gravity ? Newton’s gravity acts instantaneously, i.e. it is inconsistent with special relativity’s 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
Geometry of spacetime (Einstein tensor) Distribution of mass and energy in the universe (stress-energy tensor)

Some effects predicted by the theory of general relativity
Gravity bends light Gravitational redshift Gravitational time dilation Gravitational length contraction

Examples for light bending

“Einstein Cross” - G

How to find out that space is not flat?

In flat space    ++ = 180º

In curved space ++  180º

Newton’s Law of Gravity History of Cosmology
Newton’s Laws Newton’s Law of Gravity History of Cosmology Cosmic Distance Ladder Special Relativity General Relativity ?? Size and Age of the Universe

Break!

The Scientific Method general principle deduction induction prediction revision observations individual events specific instances  Science is a history of corrected mistakes (Popper)

Karl Popper also: “Good tests kill flawed theories; we remain alive to guess again.”

The “Standard Model” of Cosmology

The entire Universe in one line
Geometry of spacetime (Einstein tensor) Distribution of mass and energy in the universe (stress-energy tensor)

Let’s apply Einstein’s equation to the Universe
What is the solution of Einstein’s 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)

Einstein’s 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

Again: the Doppler effect
redshift: z=0: not moving z=2: v=0.8c z=: v=c

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 Hubble’s measurement of the constant H0: H0 = 500 km/s/Mpc Today’s best fit value of the constant: H0 = 72 km/s/Mpc

So why was Hubble’s original measurement so far off ?
Distance measurement based on the period-luminosity relation of Cepheid stars What are Cepheids? They are variable pulsating stars

There exists a luminosity-period relation for Cepheid stars

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 (“δ Cephei”)

Consequence Distance scale was calibrated based on type II Cepheids
Distances to other galaxies were measured using type I Cepheids “yard stick” was systematically too small H0 too large!

How old is the universe ? (III)
A galaxy at distance d recedes at velocity v=H0  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 can’t 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 Einstein’s 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,,)

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

Robertson-Walker metric a(t) is the scale factor k is the curvature constant k=0: flat space k>0: spherical geometry k<0: hyperbolic geometry

But, so far, we only considered a flat space. What, if there is curvature ? k is the curvature constant k=0: flat space k>0: spherical geometry k<0: hyperbolic geometry k>0 k=0 k<0

Cosmological redshift
While a photon travels from a distance source to an observer on Earth, the Universe expands in size from athen to anow. Not only the Universe itself expands, but also the wavelength of the photon .

General definition of redshift:  for cosmological redshift:

Examples: z=1  athen/anow = 0.5 at z=1, 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) z=4  athen/anow = 0.2 at z=4, 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 objects discovered so far: quasars at (z≈6.4) and GRBs (z≈8.2)

(SDSS image; taken in October 2003)

(Swift image; GRB A)

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 = 8.2 z ≳ 9: “dark ages”

Can we calculate a(t) ? Hubble Radius distant galaxy Foutside= 0

Can we calculate a(t) ?

What is the future of that galaxy ?
Critical velocity: escape speed v<vesc: galaxy eventually stops and falls back v>vesc: galaxy will move away forever

Let’s rewrite that a bit ...
<0  v<vesc: galaxy eventually stops and falls back >0  v>vesc: galaxy will move away forever

Let’s rewrite that a bit ...
Homogeneous sphere of density  : so for the velocity: but what is  ?

Let’s switch to general relativity
Friedmann equation same k as in the Robertson-Walker metric

Let’s switch to general relativity
Friedmann equation k is the curvature constant k=0: flat space, forever expanding k>0: spherical geometry, eventually recollapsing k<0: hyperbolic geometry, forever expanding

Can we predict the fate of the Universe ?
Friedmann equation: k=0:

Can we predict the fate of the Universe ?
If the density  of the Universe  =crit: flat space, forever expanding  >crit: spherical geometry, recollapsing  < crit: hyperbolic geometry, forever expanding so what is the density of the universe? We don’t know precisely  >crit very unlikely currently favored model:   0.3crit

k>0 k=0 k<0

How big is crit ? Currently favored model: 0 = 0.3
crit = 810-30 g/cm3  1 atom per 200 liter Density parameter 0 : 0 =1: flat space, forever expanding (open) 0 >1: spherical geometry, recollapsing (closed) 0 <1: hyperbolic geometry, forever expanding Currently favored model: 0 = 0.3

“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)

Observational Tests and Predictions

1. Measuring H0

Distances in the local universe
Assume a linear expansion (Hubble law): v=cz=H0·D Use the distance modulus m-M=5log(D/10pc)-5 Distances of a ‘standard candle’ (M=const.) or calibrated ‘standard candle’ m=5log(z)+b b = M+25+5log(c)-5log(H0)

Distances with δ Cephei stars
Direct measurement of the change in angular diameter plus spectroscopic radial velocity (Kervella et al. 2004)

LMC Cepheids

NGC 300 Cepheids (~ 6MLy) (Gieren et al )

(Freedman et al. 1994)

Distances with Type Ia Supernovae
Use the Hubble diagram (m-M vs. log z) m-M=5log(z)+25+5log(c)-5log(H0) Note that the slope is given here. Hubble constant can be derived when the absolute luminosity M is known logH0=log(z)+5+log(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)

Nearby SNe Ia Phillips et al. (1999)

Light curve shape – luminosity
(B-band light curves; Calan/Tololo sample, Kim et al. 1997) After calibration: SNe Ia look like good “standard candles”!

Normalisation of the peak luminosity
Phillips et al. 1999 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
The data have a nice gaussian error distribution of 0.16 mag (8%)

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 Today’s best value (Cepheids + SNe Ia): H0 = (72 ± 7) km/s/Mpc Note: This enters as an uncertainty in many other places!

2. Measuring Ω0 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: CMB !)

Let’s try to measure the deceleration
Acceleration according to Newton: Deceleration parameter (Note: This is without a Λ-term!)

So what’s the meaning of q0 ?
Deceleration parameter q0 q0>0.5: deceleration is so strong that eventually the universe stops expanding and starts collapsing 0<q0<0.5: deceleration is too weak to stop the expansion What’s the difference between q0, 0 and k ? k: curvature of the universe 0: mass content of the universe q0: kinematics of the universe

So let’s 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 the expansion  expansion rate should be higher at high redshift.

Very distant supernovae
Supernovae are very rare, ~ 1 SN per years and galaxy. One has to observe very many galaxies!

Search strategy: 1. Repeated scanning of a certain field.
2. Electronic readout of the data. 3. Follow-up observations, e.g., HST, VLT, …

Supernovae are routinely detected at redshifts Z > 0.1:
What is the intrinsic scatter in luminosities? Are they different from the local sample? Do we understand the differences?

So let’s measure q0 ! q0 = 0 q0 = 0.5 Data indicates: q0 < 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 

Friedmann’s equation for >0
k is the curvature constant k=0: flat space k>0: spherical geometry k<0: hyperbolic geometry but for sufficiently large  a spherically curved universe may expand forever k is the curvature constant k=0: flat space, flat universe k>0: spherical geometry, closed universe k<0: hyperbolic geometry, open universe

Deceleration parameter q for >0
Acceleration according to Newton: deceleration parameter with

Mean distance between galaxies
The fate of the Universe for >0 0 = 0 Mean distance between galaxies open 0 < 1 0 = 1 closed 0 > 1 fainter today Redshift - 14 - 9 - 7 Billion years time

Recent supernova data Tonry et al. 2003

Very high redshift SNe Ia
Riess et al. 2004

SNLS, plus BAO (Astier et al., Eisenstein 2005)
The “equation of state” of the Universe: p = wρ ä ~ (ρ + 3p) , w ‹ -1/3 : acceleration!

(Kowalski 2009) Best determinations today: SNe + BAO + CMB
... and allowing for curvature: (Kowalski 2009)

The “constitution” data set (M. Kowalski)
© S.Benitez

… and fits to the data © S.Benitez

Is the fate of the Universe well determined ?
deceleration: ½0 –  > 0: decelerating ½0 –  < 0: accelerating curvature 0 +  = 1: flat 0 +  < 1: hyperbolic 0 +  > 1: spherical two equations for two variables  well posed problem (for constant Λ)

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!

The age of the Universe revisited
So far, we have assumed that the expansion velocity is not changing (q0=0, empty universe) How does this estimate change, if the expansion decelerates, i.e. q0>0 ? now An 0>0, =0 universe is younger than 14 Gyr

So far, we only have considered decelerating universes How does this estimate change, if the expansion accelerates, i.e. q0<0 ? now An >0 universe can be older than 14 Gyr

0=0, =0: tHubble =1/H0 ≈ 14 Gyr 0=1, =0: tHubble =2/(3H0) ≈ 10 Gyr Open universes with 0<0<1, =0 are between 10 and 14 Gyr old Closed universes with 0>1, =0 are less than 10 Gyr old >0 increases, <0 decreases the age of the universe 0=0.3, =0.7: tHubble =0.96/H0 ≈ 13.7 Gyr

Friedmann’s equation for =0, 0<1
Falls off like the square of R Falls off like the cube of R Expansion rate of the Universe 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

Friedmann’s equation for >0, 0<1
Falls off like the cube of R Falls off like the square of R constant Expansion rate of the Universe 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 >0: for most of its age, the universe looks either to be flat or to be exponentially expanding Isn’t it strange that we appear to live in that short period between those two extremes => Flatness problem !

3. The cosmic microwave background

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."

The cosmic microwave background radiation (CMB)
Temperature of ±0.004 K Isotropic to 1 part in 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

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

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

Measuring the Curvature of the Universe Using the CMB
Result from Boomerang (1998): The Universe is flat to within 10%!

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

Interpretation of the data (CMB + BAO + SNe) :
Geometry : “flat” (Euklidian) Ω0 = ± “Dark Energy”: ΩΛ = ± 0.015 “Dark Matter”: ΩD = ± 0.013 Baryons: ΩB = ± Age of the Universe: 13.73 ± Gyrs That’s precision cosmology!

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: Hubble’s 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: Hubble’s law  Cosmic microwave background radiation The origin of the elements Structure formation in the universe

Georgy Gamov ( ) 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)

Abundances of elements
Hydrogen and helium most abundant gap around Li, Be, B

Thermal history of the universe
When the universe was younger than 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

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 A=5 and 8
There is no stable atomic nucleus with 5 or with 8 nucleons Reaction chain stops at 7Li So how to form the more massive elements? There exist a meta-stable nucleus (8B*). If this nucleus is hit by another 4He during its lifetime, 12C and other elements can be formed

Mass gap/stability gap at A=5 and 8
Reaction chain: 4He + 4He  8B* 8B* + 4He  12C so-called 3-body reaction in order to have 3-body reactions, high particle densities are required densities are not high enough in the big-bang but they are in the center of evolved stars Conclusion: big bang synthesizes elements up to 7Li. Higher elements are formed in stars

Primordial nucleosynthesis

Consistent with abundance of H, He and Li Result: abundances of H, He and Li are consistent but: b ~0.04

But: The Li problem! CMB: Ωb h2 = ± Perfect agreement!

Can we understand why 25% He?
Before the universe cooled sufficiently to allow nucleons to assemble into helium, the neutron to proton ratio was ~1:7 4He: equal number of protons and neutrons Assume that all neutrons grab a proton to form a 4He. The left over protons form hydrogen.

Can we understand why 25% He?
Abundance of hydrogen Abundance of hydrogen Abundance of helium: = 0.25 but why is nn/np ≈ 1/7 ?

The four forces of nature
Gravity weak, long ranged electromagnetism intermediate, long ranged strong nuclear force strong, short ranged weak nuclear force weak, short ranged

} n  p+ + e- + ν  + n ↔ p+ + e- The weak nuclear force
Free neutrons decay into protons n : neutron p+ : proton e- : electron  : neutrino neutron half life: 10 min n  p+ + e- + ν  + n ↔ p+ + e- Baryons  Hadrons Leptons }

“Freeze out” of weak equilibrium
Neutron/proton ratio Freeze-out temperature: kT ~ keV Mass difference: Δmc2 = MeV nn/np ≈ 1/6 20% of the neutrons decay after 200 s nn/np ≈ 1/7

Break!

Formation of large-scale structure (and galaxies)

Web address for movies:

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: Hubble’s law  Cosmic microwave background radiation  The origin of the elements  Structure formation in the universe ←

Structure formation in the Big-Bang model

A galaxy census

How good is the assumption of isotropy?
CMB: almost perfect But what about the closer neighborhood ?

How good is the assumption of isotropy?
CMB: almost perfect But what about the closer neighborhood ? The “great wall”

The spatial distribution of galaxies
Galaxies are not randomly distributed but correlated Network of structures (filaments, sheets, walls)  “cosmic web”

The spatial distribution of galaxies
Data from the most recent survey: SDSS

How does structure form ?
Wrinkles in the CMB: regions of higher and lower temperature Those regions correspond to density fluctuations, regions of slightly higher/lower density than average Gravitational instability higher density  more mass in a given volume more mass  stronger gravitational attraction stronger gravitational attraction  mass is pulled in  even higher density

z=9.00 65 Mpc 50 million particle N-body simulation

Does a picture like this look familiar ?

Recent simulations (MPA group)
(Court. V. Springel)

Note: The simulations assume that most of the matter in the Universe is non-baryonic and “dark”!

Q: What is it ? A: MACHOs or WIMPs

MACHOs ? MAssive Compact Halo Objects
Brown dwarfs (stars not massive enough to shine) Dim white dwarfs (relics of stars like the Sun) Massive black holes (stars that massive that even light cannot escape) But: if the DM is really in MACHOs, something with the nucleosynthesis constraint must be wrong

How can we see MACHOs ? Gravitational lensing:
If foreground object has only little mass, the image split is too small to be observed But the amplification (brightening) is observable

How can we see MACHOs ? How likely is it for a star in the Milky Way to get amplified ? Once every 10 million years !!!

How did this work ? Monitor 10 million stars simultaneously !

Light curve of a MACHO event
Achromatic (!) magnification due to gravitational lensing There seem to be not enough brown dwarfs (or dark objects of similar mass) to account for the dark matter in the Milky Way !

WIMPs ? Weakly Interacting Massive Particles Massive neutrinos
at least we know that they exist their masses seem to be low they would be hot dark matter (hot: moving at speeds near the speed of light) Another (yet undiscovered) particle predicted by some particle physicists cold dark matter (cold: moving much slower than the speed of light)

WIMP candidate I: Massive neutrinos
What mass do we need to account for all the dark matter ? There are ~100 neutrinos per cm3 A mass of 20eV results in 0=0.3 Can we measure their mass ? tricky … use energy conservation. Measure all masses and velocities in the  + n  p+ + e- reaction with high precision. Difference between left and right hand side  neutrino mass

Direct measurements: β decays
Best value to date: m ≤ 4 eV

The KamLAND detector: Neutrino oscillations

WIMP candidate I: Massive neutrinos
Result: No clear (direct) detection, but upper limits. The mass of the (electron) neutrino is (much?) less than a few eV  electron neutrino is ruled out as a dark matter candidate. There are two more neutrino families, μ neutrinos and τ neutrinos (the muon and tauon are particles similar to the electron, but more massive and unstable). But: Their masses seem to be not too different from νe’s

WIMP candidate II: The least massive supersymmetric particle
Main goal of particle physics: to develop a theory that unifies the four forces of nature Those models predict a whole zoo of particles, some of them are already detected, but most of them still very speculative. Most of these particles are unstable. Supersymmetry is a particularly promising unifying theory The least massive supersymmetric particle (neutralino) should be stable

WIMP candidate II: The least massive supersymmetric particle
It’s mass should be > 150 GeV, otherwise its contribution would be irrelevant it should already have been detected But how to prove its existence ?

How can we find cold WIMPs ?
Cryogenic (ultra cold) detectors Search for annual modulation of the signal

Do we have already detected WIMPs ?
DAMA collabor- ation Results are very controversial and inconclusive

Can astronomy help to discriminate between neutrinos and neutralinos ?
Neutrinos: Hot Dark Matter (HDM) mass in the tens of eV  very low mass very low mass  high velocities  “hot” can travel several tens of Mpc over the age of the universe Neutralinos Cold Dark Matter (CDM) mass in the hundredst of GeV  very high mass very high mass  low velocities  “cold” cannot travel significant distances over the age of the universe Neutrinos: mass in the tens of eV  very low mass very low mass  high velocities  “hot” can travel several tens of Mpc over the age of the universe Neutralinos mass in the hundredst of GeV  very high mass very high mass  low velocities  “cold” cannot travel significant distances over the age of the universe

Can astronomy help to discriminate between hot and cold dark matter ?
CDM HDM

Structure formation: HDM vs CDM
Hot dark matter: initial small scale structure (anything smaller than a galaxy cluster) washed out due to the high velocities of neutrinos clusters and supercluster form first galaxies form due to fragmentation of collapsing clusters and superclusters top-down structure formation

Cold dark matter: plenty of small scale structure small galaxies form first, clusters last larger structures form due to merging of smaller structures bottom-up or hierarchical structure formation

CDM fits observations much better than HDM high-z galaxies are smaller irregular shape of galaxy clusters indicate that they formed recently there are only a very few clusters at high redshift, but many galaxies two-point correlation function is much better reproduced

Ingredients: gas, radiation, gravity Pick a model for the Universe
A galaxy formation recipe Ingredients: gas, radiation, gravity Pick a model for the Universe Add some seeds (perturbations) to trigger growth of structure Combine it with some recipe of your star formation cookbook

(Courtesy: M. Steinmetz)

(Court. V. Springel)

Hierarchical galaxy formation

first relaxed small disks
Phase I: Formation of First Galactic Disks (1Gyr) first relaxed small disks

Disks are destroyed by merging, formation of an elliptical
Phase II: Bulge Formation and Disk Reassembly (2 Gyr) Disks are destroyed by merging, formation of an elliptical Later on: disk reassemble

young stars and gas in thin disk, bulge of old stars
Phase III: Well Developed Disk+Bulge Structure (3 Gyr) slowly growing disk young stars and gas in thin disk, bulge of old stars

several minor mergers rapidly rotating bar
Phase IV: Tidally Triggered Bar Formation (5 Gyr) several minor mergers rapidly rotating bar

nuclear star burst consumes nearly all remaining gas
Phase V: Formation of a Giant Elliptical (7 Gyr) nuclear star burst consumes nearly all remaining gas

Summary

Timeline of the Universe
Backed by experi-ment & observations ???

Problems to be solved by quantum gravity
Combination of quantum mechanics and general relativity Dealing with singularities in general relativity and particle physics point like elementary particles black holes the very early Universe Nature of the Dark Energy?

Quantum cosmology Task: calculate the wave function of the Universe
Problem: observer is part of the system  the Copenhagen interpretation cannot be applied Alternative: many-worlds interpretation many universes exist, but mutually unobservable all possible outcomes are realized whenever a decision between two (or more) states has to be made, the universe splits into two (or more) branches

Many-worlds interpretation

“Close to solved” problems in cosmology
Present expansion rate (H0) Present acceleration, geometry (not topology!) (Ω0, q0) Primordial nucleosynthesis Cosmic microwave background Formation of large-scale structures and galaxies

Outstanding problems in cosmology
What is the dark matter? What is the dark energy/cosmological constant? Quantum gravity & Cosmology?

Observational Cosmology:

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