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Physics 270 The Universe Astrophysics, Gravity

and Cosmology

The History of Cosmology

- Mythology vs the scientific method
- Cosmos Earth ? solar system ? Milky Way ?

Hubble sphere - Copernicus, Brahe, Kepler, Galileo

Newton Cosmology as a Science

- Galileo The Scientific method the universality

of scientific laws - Newtons laws
- Newtons gravity The heavens and the Earth

follow the same scientific principles - Galileo Relativity before Einstein

Einsteins Theories of Special and General

Relativity

- Principle of Relativity
- Giving up absolute space and time
- Space and time where common sense makes no sense
- what is here and there or now and then ?

Special Relativity

- All inertial frames of reference are equivalent
- The speed of light is absolute (invariant)
- Maxwells equations are invariant under Lorentz

transformation - Newtons laws, which are based on absolute space

and time, need to be modified

Some open problems

- How to treat 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 ?

Non-inertial reference frame

- Non-inertial frames ? fictitious forces
- centrifugal force
- Coriolis force

Why is the Space Shuttle orbiting?

- The space Shuttle is continuously falling

towards the Earth

Is there no gravity in space ?

No, there is gravity (actu- ally Earths gravity

at the orbit of the Shuttle is still 80-90 of

its strength on the ground

- So why do astronauts appear to be weightless ?

What effect does mass have?

- Gravity tendency of massive bodies to attract

each other - Inertia resistance of a body against changes of

its current state of motion

Is gravity and inertia the same thing ?

- No. They are completely different physical

concepts. - There is no a priori reason, why they should be

identical. In fact, for the electromagnetic force

(Coulomb force), the source (the charge Q) and

inertia (m) are indeed different. - But for gravity they appear to be identical
- ? Equivalence Principle

Eötvös experiment

Coriolis

Gravity

Result of the Eötvös experiment

- Gravitational and inertial mass are identical to

one part in a billion - modern experiments identical to one part in a

hundred billion

What effect does mass have?

- Source of gravity
- Inertia

Principle of Equivalence

Weak equivalence principle

- The laws of mechanics are precisely
- the same in all inertial and freely
- falling frames. In particular, gravity is
- completely indistinguishable from
- any other acceleration.

Consequences of the equivalenceprinciple mass

bends light

Observer in freely falling reference frame

Consequences of the equivalenceprinciple mass

bends light

Outside Observer

Examples for light bending

Some effects predicted by the theory of general

relativity

- gravity bends light
- gravitational redshift
- gravitational time dilation
- gravitational length contraction

Least action principle

- light travels on a path that minimizes the

distance between two points? for flat space

straight line - a path that minimizes the distance between two

points is called a geodesic - Examples for geodesics
- plane straight line
- sphere great circle

What is the shortest way to Europe?

Spacetime

- Fourth coordinate ct
- time coordinate has different sign than spatial

coordinates - spacetime distance
- ?, ?, ? metric coefficients

Weak equivalence principle

- The laws of mechanics are precisely
- the same in all inertial and freely
- falling frames. In particular, gravity is
- completely indistinguishable from
- any other acceleration.

General relativity

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

Why does space curvature result in attraction ?

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?

Tidal forces (I)

Tidal forces (II)

Tidal forces (III)

Tidal forces (IV)

So does the existence of tidal forces violate the

equivalence principle ?

- there is no freely falling frame of reference in

which gravity vanishes globally - there is a freely falling frame of reference in

which gravity vanishes locally - equivalence principle holds for small labs,

small in comparison to distances over which the

gravitational field changes significantly. - spacetime is locally flat

Towards a new theory for gravity ...

- Requirements
- it should locally fulfill the equivalence

principle - it should relate geometry of space to the

distribution of mass and energy - it should be locally flat
- it should reduce to Newtonian gravity for small

velocities (compared to c) and for weak

gravitational fields

The entire Universe in one line

Why is general relativity (GR) difficult ?

- conceptually difficult (relativity of space and

time, curvature of spacetime) - set of 10 coupled partial differential equations
- non linear (solutions do not superpose)
- space and time are part of the solution
- ? exact solution known only for a very few

simple cases

Checklist

?

- 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 ?

?

?

?

So what is left to do ?

- Show that general relativity provides a

consistent and accurate description of nature?

test it by experiment/observation

Some open problems

- 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 ?

Boost factor

- special relativity

First test bending of light

- Star light should be bend as it passes through

the gravitational field of the Sun, i.e., it

should be possible to see a star behind the Sun

First test bending of light

- Star light should be bend as it passes through

the gravitational field of the Sun, i.e., it

should be possible to see a star behind the Sun - General relativity predicts an angle of 1.75,

twice as big as that predicted by Newtonian

gravity - measured by Arthur Eddington in 1919. Key event

for Einsteins elevation to a celebrity.

Test 2 Perihelion shift of Mercury

- Planets do not move on perfect ellipses, but

ellipses are precessing. This effect is due to

the gravitational force exerted by the other

planets

Test 2 Perihelion shift of Mercury

- Planets do not move on perfect ellipses, but

ellipses are precessing. This effects is caused

by the perturbing effect of the other planets

gravitational field. - Mercurys precession amounts to 5600 per

century, but only 5557 can be explained by

Newtonian gravity, leaves a discrepancy of 43

per century. - General relativity predicts exactly this

additional precession

Test 3 gravitational time dilation and redshift

- Can be measured by experiments on Earth

(challenging, but feasible) - Better White Dwarfs (very compact objects mass

comparable to that of the Sun, radius comparable

to that of the Earth), because they have a

stronger gravitational field - Even better Neutron Stars and Pulsars (very

compact objects mass comparable to that of the

Sun, radius only 10-100 km), because they have a

very strong gravitational field

Test 4 Binary pulsar PSR 191316

- Pulsar a rapidly rotating highly magnetized

neutron star that emits radio pulses at regular

intervals - Discovered by Bell and Hewish in 1967
- Nobel Prize in physics (1974)

Test 4 Binary pulsar PSR 191316

- Pulsar

Test 4 Binary pulsar PSR 191316

- Binary pulsar two pulsars orbiting each other
- Orbital time 7.75h
- Discovered by Hulse and Taylor in 1974
- Nobel Prize in physics (1993)

Test 4 Binary pulsar PSR 191316

- Precession 4.2º per year

Test 4 Binary pulsar PSR 191316

- Time delay Clocks tick slower in strong

gravitational fields

Test 4 Binary pulsar PSR 191316

- Gravitational Waves Orbital decay due to

emission of gravitational radiation

data points

Prediction of GR

Tests to come Gravity Probe B

Gravitational time dilation and redshift

- Can be measured by experiments on Earth

(challenging, but feasible) - Better White Dwarfs (very compact objects mass

comparable to that of the Sun, radius comparable

to that of the Earth), because they have a

stronger gravitational field - Even better Neutron Stars and Pulsars (very

compact objects mass comparable to that of the

Sun, radius only 10-100 km), because they have a

very strong gravitational field

Flash-back Newtonian gravity

- What velocity is required to leave the

gravitational field of a planet or star? - Example Earth
- Radius R 6470 km 6.47?106 m
- Mass M 5.97 ?1024 kg
- escape velocity vesc 11.1 km/s

Flash-back Newtonian gravity

- What velocity is required to leave the

gravitational field of a planet or star? - Example Sun
- Radius R 700 000 km 7?108 m
- Mass M 2?1030 kg
- escape velocity vesc 617 km/s

Flash-back Newtonian gravity

- What velocity is required to leave the

gravitational field of a planet or star? - Example a solar mass White Dwarf
- Radius R 5000 km 5?106 m
- Mass M 2?1030 kg
- escape velocity vesc 7300 km/s

Flash-back Newtonian gravity

- What velocity is required to leave the

gravitational field of a planet or star? - Example a solar mass neutron star
- Radius R 10 km 104 m
- Mass M 2?1030 kg
- escape velocity vesc 163 000 km/s ? ½ c

Flash-back Newtonian gravity

- Can an object be so small that even light cannot

escape ? ? Black Hole

- RS Schwarzschild Radius
- Example for a solar mass
- Mass M 2?1030 kg
- Schwarzschild Radius RS 3 km

Some definitions ... and Black Holes

- The Schwarzschild radius RS of an object of mass

M is the radius, at which the escape speed is

equal to the speed of light. - The event horizon is a sphere of radius RS.

Nothing within the event horizon, not even light,

can escape to the world outside the event

horizon. - A Black Hole is an object whose radius is smaller

than its event horizon.

Sizes of objects

Lets do it within the context of general

relativity spacetime

- spacetime distance (flat space)

- Fourth coordinate ct
- time coordinate has different sign than spatial

coordinates

Lets do it within the context of general

relativity spacetime

- spacetime distance (curved space of a point

mass)

What happens if R ? RS

- R gt RS everything o.k. time , space ? but

gravitational time dilation and length

contraction - R ? RS time ? 0 space ? ?
- R lt RS signs change!! time ?, space ?

space passes, everything falls to the center?

infinite density at the center, singularity

Structure of a Black Hole

What happens to an astronaut who falls into a

black hole?

- Far outside nothing special
- Falling in long before the astronaut reaches the

event horizon, he/she is torn apart by tidal

forces - For an outside observer
- astronaut becomes more and more redshifted
- The astronauts clock goes slower and slower
- An outside observer never sees the astronaut

crossing the event horizon.

What happens, if an astronaut falls into a black

hole?

- For the astronaut
- He/she reaches and crosses the event horizon in a

finite time. - Nothing special happens while crossing the event

horizon (except some highly distorted pictures of

the local environment) - After crossing the event horizon, the astronaut

has 10 microseconds to enjoy the view before

he/she reaches the singularity at the center.

Cosmic censorship

- Singularity a point at which spacetime diverges
- infinite forces are acting
- laws of physics break down
- quantum gravity may help ?
- no problem as long as a singularity is shielded

from the outside world by an event horizon - Hypothesis Every singularity is surrounded by an

event horizon. - There are no naked singularities

Near a black hole bending of light

The Photon sphere

- The photon sphere is a sphere of radius 1.5 RS.

On the photon sphere, light orbits a black hole

on a circular orbit.

Structure of a rotating black hole

- Within the ergosphere (or static sphere) nothing

can remain at rest. Spacetime is dragged around

the hole

No-Hair theorem

- Properties of a black hole
- it has a mass
- it has an electric charge
- it has a spin (angular momentum)
- thats it. Like an elementary particle, but much

more massive - Black holes have no hair

Hawking Radiation

- Heisenberg uncertainty principle
- DEDt gt h/2p
- Þ Energy need not be conserved over short

periods, only on average - Virtual particles particle-antiparticle pairs

created from vacuum energy fluctuations which

quickly disappear - Virtual particles that can "steal" energy from

elsewhere become real

Hawking Radiation

- Virtual pairs near a black hole can steal energy

from the gravitational field - Tidal stresses accelerate one particle outward,

one drops into event horizon - Energy of new particle comes from gravitational

energy of BH, so BH mass must decrease - Black hole evaporates!

Hawking Radiation

- Energy for new particles comes from tidal

stresses - Tidal effects must be large over short path

lengths of virtual pairs - Smaller black holes have steeper gravitational

gradients - gt Smaller black holes evaporate more quickly
- tevap 1010(MBH /1012 kg)3 yr
- tevap(1Msolar) 1065 yr

Hawking Radiation

- Black holes emit as black bodies
- Temperature of black hole proportional to rate of

radiation - TBH 10-7 (Msolar / MBH)
- T(1 Msolar) 10-7 K
- T(106 Msolar) 10-13 K

Exotica

- White holes - a phenomenon analogous to a black

hole from which light can only escape. No obvious

way to make or power one - Wormholes - conduits between two points in

spacetime. Unstable, difficult to avoid

singularity without going faster than c,

solutions with timelike paths only size of

elementary particles. If they exist, probably not

useful for travel since stable solutions require

"exotic matter"

A Practical Perspective

- Two main types of black hole in the universe
- Stellar mass black holes created by the collapse

of a massive star at the end of its life, - 3-100? Msolar
- Supermassive black holes (SMBH) found in the

centers of galaxies, power quasars and AGN, - a few times 106 - 109 M

Stellar Black Holes

- Created from stars of more than 30 Msolar
- Detectable in binary systems
- Normal or evolved star transfers mass to black

hole via accretion disk - Measure orbital period and velocity of companion

and use Kepler's laws to derive lower limits on

mass - Neutron stars lt 3 Msolar so any larger invisible

companion must be black hole or unknown physics

Stellar Black Holes

Stellar Black Holes

Stellar Black Holes

- X-Ray Binaries
- Viscosity (friction) of gas in disk heats up disk
- A few to 40 of gravitational potential energy (

rest mass energy) liberated - Temperatures of 105-106 K in inner disk
- Spectrum peaks in soft x-rays
- Optically thin material in corona or inner disk

at gt107 K gives hard x-ray emission - Some with relativistic jets
- Luminosities of order 105 Lsolar

Supermassive Black Holes

- Active Galactic Nuclei (AGN)
- Many types most commonly discussed are radio

galaxies, Seyferts, quasars, and QSOs - Large black holes at the centers of galaxies form

at early epochs, possibly from collapse of dense

stellar clusters, and grow by accretion over

lifetime of universe - Luminosity from accretion disks as in X-ray

binaries, but larger BH lower temperature

Supermassive Black Holes

- AGN structure
- Accretion disk at a few x 104 K, peak emission in

UV (R 100AU 100 RS) - Hot, rarefied gas in x-ray halo or corona (R

1-10 AU RS) - Broad emission line region (BLR) clouds with

velocities of 104 kms-1, indicate strong

gravitational field (R 0.01pc) - Dusty molecular torus in plane of disk (R

0.1-1pc) IR emission

Supermassive Black Holes

- AGN structure continued
- Narrow emission line region (NLR) clouds of

ionized gas with widths of a few hundred kms-1

Seen in cones extending from 50pc to 15kpc - Relativistic jets - accelerated by magnetic

fields in disk to significant fraction of c.

Looking head-on into quasar jets, see OVVs and BL

Lacs - Jets in radio galaxies may extend 1 Mpc

Supermassive Black Holes

Supermassive Black Holes

Supermassive Black Holes

Supermassive Black Holes

Supermassive Black Holes

- AGN characteristics
- Emission over 21 orders of magnitude in frequency

- from radio to g-rays - Range of luminosities, from barely discernable to

gt 1015 Lsolar, 10,000 times the luminosity of a

bright galaxy - Radio quiet and radio loud
- Often associated with starbursts, interacting

galaxies, Luminous Infrared Galaxies (LIRGs,

ULIRGs, HLIRGs)

Supermassive Black Holes

- Evidence
- Kinematic evidence
- Stellar motions in center of Milky Way
- Stellar and gas motions in other galaxies
- OH masers in NGC 4258
- All imply tremendous mass in a tiny area
- Images of dusty torii and accretion disks
- Only way of producing enough energy to make a

quasar in so little space

Supermassive Black Holes

Supermassive Black Holes

Supermassive Black Holes

Supermassive Black Holes

Questions

- Do they really exist ? (Observe gravitational

effects ) - How do we observe something that does not emit

light? (Light bends around them)

The cosmic distance ladder

- Parallax
- solar neighborhood (lt 1 kpc)
- Main sequence fitting
- distances within the Galaxy (lt100 kpc)
- Cepheids
- nearby galaxies (lt 20 Mpc)
- Tully-Fisher relation
- distant galaxies (lt 500 Mpc)
- Type 1a supernovae
- cosmological distances ( 1 Gpc)

Nature of spiral nebulae and the Milky Way (MW)

- 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

- 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. - ? Spiral nebulae are galaxies like the Milky Way.

Distance millions of parsec.

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Edwin Hubble (1889-1953)

- Four major accomplishments
- in extragalactic astronomy
- The establishment of the Hubble classification

scheme of galaxies - The convincing proof that galaxies are island

universes - The distribution of galaxies in space
- The discovery that the universe is expanding

The Hubble classification

The Hubble classification

- 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)

THE EXPANDING UNIVERSE Using the Doppler Effect

to Measure Velocity

T1

T2

T3

T4

Redshift

Blueshift

Galaxy Spectroscopy

- Spectra of a nearby star and a distant galaxy
- Star is nearby, approximately at rest
- Galaxy is distant, traveling away from us at

12,000 km/s

Stellar Spectrum

Sodium

Magnesium

The larger the redshift the greater the distance

from us

Galaxy Spectrum

Calcium

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

The redshift-distance relation

The redshift-distance relation

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 70 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. If the velocity of recession is

proportional to distance, then any point is at

the center of the expansion

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

History of the Universe (with Inflation)

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 ?

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

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

Example static universe

Example expanding at a constant rate

Example expansion is slowing down

Example expansion is accelerating

Example collapsing

How old is the universe?

- 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 65 km/s/Mpc

tHubble 15 Gyr

How big is the universe?

- 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 65 km/s/Mpc

dHubble 4.6 Gpc

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

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 ? changes.

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 z5.8

Lets switch to general relativity

- Friedmann equation
- k is the curvature constant

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

kgt0

klt0

k0

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

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

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 ?

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

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 - 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

- Acceleration according to Newton
- deceleration parameter

The fate of the Universe for ?gt0

k1

?gt0

?0

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

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 65 km/s/Mpc
- ?0 0.3 ?? 0.7 ? flat space

How old is the Universe?

- 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 65 km/s/Mpc

tHubble 15 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 15 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 15 Gyr

The age of the Universe revisited

- ?00, ?0 tHubble 1/H0 15 Gyr
- ?01, ?0 tHubble 2/(3H0) 10 Gyr
- open universes with 0lt?0lt1, ?0 are between 10

and 15 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 14.5 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
- ?0gt1 strongly disfavored

The life of a universe 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 ? - Flatness problem

The life of a universe 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

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)

Hoyles Big Bang

What are the consequences (Gamow)?

- 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 (-450 F) - 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."

The Big Bang and the Creation of the elements

(Hoyle Saltpeter)

- Atoms are mostly empty space
- Atoms consist of protons (), neutrons (o) and

electrons (-) - protons and neutrons form the atomic nucleus
- of protons deter-mines the element
- electrons in the outskirts determine chemistry

The structure of matter

- Neutrons and protons are very similar, but
- Protons are electrically charged, neutrons are

not - Neutrons have a slightly higher mass
- Electrons are much less massive than nucleons ?

most of the mass of an atom is in its nucleus - If charges of the same sign repel, and the

nucleus is made of protons, why dont the protons

fly apart ?

The four forces of nature

- gravity
- electromagnetism
- strong nuclear force
- keeps atomic nuclei together
- weak nuclear force
- decay of free neutrons into protons

n ? p

n ? p e-

? n ? p e-

The structure of matter

Abundance 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
- 3He 3H ? 7Li
- 3He 3He ? 7Be

Mass gap/stability gap at A5 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 A5 and 8

- Reaction chain
- 4He 4He ? 8B
- 8B 4He ? 12C
- so-called 3-body reaction (Saltpeter)
- 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

- Result
- abundance of H,He and Li is consistent
- but ?b 0.04

How far can we see ?

- Naked eye 2 million Light years (Andromeda

galaxy) - Large telescopes 14 billion Lyr (z5.8)
- 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 z5.8

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

Black body radiation

- A hot a 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

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

The Cosmic Background Explorer (COBE)

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

Main results from COBE

More results from the CMB

- The Earth is moving with respect to the CMB ?

Doppler shift - Earths motion around the Sun
- Suns motion around the Galaxy
- Motion of the Galaxy with respect to other

galaxies (large scale flows)

More results from the CMB

- The Earth is moving with respect to the CMB ?

Doppler shift - The emission of the Galaxy

More results from the CMB

- 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

The BOOMERANG mission

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

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

What comes next ?

WMAP

Planck

Can we see the sound of the universe ?

- Compressed gas heats up? temperature

fluctuations

Acoustic Oscillations in the CMB

- Although there are fluctuations on all scales,

there is a characteristic angular scale.

Acoustic Oscillations in the CMB

WMAP team (Bennett et al. 2003)

Last scattering surface

transparent

opaque

Sound Waves in the Early Universe

- After recombination
- Universe is neutral.
- Photons can travel freely past the baryons.
- Phase of oscillation at trec affects late-time

amplitude.

- Before recombination
- Universe is ionized.
- Photons provide enormous pressure and restoring

force. - Perturbations oscillate as acoustic waves.

Sound Waves

- Each initial overdensity (in DM gas) is an

overpressure that launches a spherical sound

wave. - This wave travels outwards at 57 of the speed

of light. - Pressure-providing photons decouple at

recombination. CMB travels to us from these

spheres. - Sound speed plummets. Wave stalls at a radius of

150 Mpc. - Overdensity in shell (gas) and in the original

center (DM) both seed the formation of galaxies.

Preferred separation of 150 Mpc.

A Statistical Signal

- The Universe is a super-position of these shells.
- The shell is weaker than displayed.
- Hence, you do not expect to see bullseyes in the

galaxy distribution. - Instead, we get a 1 bump in the correlation

function.

Cosmological Constraints

2-s

1-s

The History of the Universe

- The Concordance Model (not yet the Standard

Model) of - Cosmology
- The Universe is homogeneous and flat (horizon

problem - and flatness problem)
- The Universe evolved from a quantum fluctuation

no bigger - than 10-35 m in diameter.
- Since gravitational energy is negative and the

energy of a - massive object is positive, the total energy of

the quantum - fluctuation can be zero
- If the fluctuation now expands it may become the

entire universe - The Concordance Model postulates that the

initial expansion was - very rapid indeed (cosmic inflation)

History of the Universe (with Inflation)

Inflation (potential)

Matter era

- The energy of matter is nowadays 10000 times

higher than that of radiation - but temperature rises like (1z)
- 2.7K lt T lt 10000K matter era
- dominate particles (in order of decreasing

contribution - baryons, photons, neutrinos
- dominant forces
- gravity

Radiation era

- As the temperature exceeds 10000K, radiation

starts dominating - 10000K lt T lt 1010K radiation era
- dominate particles (in order of decreasing

contribution - photons, neutrinos, baryons
- dominant forces
- electromagnetism, gravity

Electron-positron annihilation

- As the temperature exceeds 1010K, creation of

electron-positron pairs - T gt 1010K equilibrium between electron-positron

pair creation and annihilation - T lt 1010K freeze-out. Remaining pairs annihilate

Lepton era

- 1010K lt T lt 1012K
- dominate particles (in order of decreasing

contribution - electrons, positrons, photons, neutrinos,

antineutrinos, baryons - dominant forces
- electromagnetism, weak nuclear, gravity

Hadron annihilation

- As the temperature exceeds 1012K, creation of

hadron-antihadron pairs (e.g. proton-antiproton) - T gt 1012K equilibrium between hadron pair

creation and annihilation - T lt 1012K freeze-out. Remaining pairs annihilate

Hadron era

- 1012K lt T lt 1013K
- dominate particles (in order of decreasing

contribution - baryonsantiparticles, mesonsantiparticles,

electrons, positrons, photons, neutrinos,

antineutrinos - dominant forces
- electromagnetism, strong nuclear, weak nuclear,

gravity

Still quark era

- 1013K lt T lt 1015K
- hadrons (baryons, mesons) break into quarks
- dominate particles (in order of decreasing

contribution - quarks, antiquarks, electrons, positrons,

photons, neutrinos, antineutrinos - dominant forces
- electromagnetism, strong nuclear, weak nuclear,

gravity

Electroweak phase transition

- As the temperature exceeds 1015K,

electromagnetism and weak nuclear force join to

form the electroweak force - T gt 1015K electroweak force
- T lt 1015K electromagnetism, weak nuclear force
- Limit of what we can test in particle

accelerators. - Nobel prizes 1979 (theory) and 1984 (experiment)

Quark era

- 1015K lt T lt 1029K
- dominate particles (in order of decreasing

contribution - quarks, antiquarks, electrons, positrons,

photons, neutrinos, antineutrinos - dominant forces
- electroweak, strong nuclear, gravity

GUT phase transition

- As the temperature exceeds 1029K, electroweak

force and strong nuclear force join to form the

GUT (grand unified theories) - T gt 1029K GUT
- T lt 1029K electroweak force, strong nuclear

force - relatively solid theoretical framework (but may

be wrong), but pretty much no constraint by

experiments

GUT era

- 1029K lt T lt 1032K
- dominate particles (in order of decreasing

contribution - Zillions of particles, most of them not detected

yet - dominant forces
- GUT, gravity

Planck epoch

- T gt 1032K unification of GUT and gravity
- Particles
- ???
- Forces
- TOE (theory of everything)
- The last frontier ...

Structure formation in the Big-Bang model

The Hubble sequence of galaxies

A galaxy census spiral galaxies

- Most common type among the luminous galaxies

(75) - two major classes, S and SB
- regular spirals (S)
- barred spirals (SB)
- further classified from a to d according to the

bulge-to-disk ratio - a very large, prominent bulge
- d essentially no bulge at all
- The Milky Way is a Sbc or a SBbc galaxy

A galaxy census spiral galaxies

- Spiral galaxies are disk like and in centrifugal

equilibrium - The are cold, i.e. the velocity dispersion

(random motion of individual stars) ? is much

smaller than the rotation velocity vrot (Milky

Way ?20 km/s vrot220 km/s) - They mainly consist of stars, but 10 of the

mass is gas and dust - They actively form stars (Milky Way 1 star per

year)

A galaxy census elliptical galaxies

- 20 of the luminous galaxies are ellipticals
- classified according to the flattening E0-E7

n10?(1-b/a) - E0 circular
- E7 minor axis only 30 of major axis
- They are hot, i.e. the velocity dispersion ? is

much larger than the rotation velocity vrot - flattened by an anisotropic velocity dispersion
- little gas, no recent star formation
- predominantly in clusters of galaxies

A galaxy census other galaxies

- Irregular galaxies ( 5 of the luminous

galaxies) - dwarf galaxies
- dwarf irregulars
- dwarf spheroidals
- dwarf ellipticals
- blue compact dwarfs
- ...

Toomre Toomre (mid 70s)

- 11 out of the 4000 galaxie

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