Midterm exam: date: March 17, 2006, 8:15 a.m. date: March 17, 2006, 8:15 a.m. location: Conrad Naber Hall location: Conrad Naber Hall bring pocket calculator bring pocket calculator NO text books, notes laptops etc. NO text books, notes laptops etc. do NOT bring your own paper do NOT bring your own paper write on exam sheets directly write on exam sheets directly astrophysics see web site Spacephysics: see web site

Sir Isaac Newton: ( ) Cosmology as a Science Mathematical description Mathematical description of the Universe of the Universe The same physical laws The same physical laws apply to earth and Universe apply to earth and Universe

Newton: Fundamental contributions Mathematics: - series expansionsMathematics: - series expansions - differential calculus - differential calculus - approximation methods - approximation methods - … - … Optics: - spectral analysis of white light Optics: - spectral analysis of white light Physics: - ‘Principia mathematica…’ Physics: - ‘Principia mathematica…’ Astronomy: - derive Kepler’s laws from Astronomy: - derive Kepler’s laws from gravitational forces gravitational forces ….. …..

A toy universe According to Newton, what is going to happen ? The model Universe is going to collapse under its own gravity The model Universe is going to collapse under its own gravity boundary constant density (homogeneous)

Newton’s Conclusion: In order to avoid collapse In order to avoid collapse  homogeneous  isotropic  infinite size  no center infinite in time infinite in time  has always been  will always be  perfect cosmological principle  perfect cosmological principle

The perfect cosmological principle homogeneous: the universe looks the same homogeneous: the universe looks the same everywhere on large scales  there is no special place (center) everywhere on large scales  there is no special place (center) isotropic: the universe looks the same in isotropic: the universe looks the same in all directions on the sky all directions on the sky  there is no special direction  there is no special direction unchanging: The universe looks the same at unchanging: The universe looks the same at all times  there is no special epoch all times  there is no special epoch

Olber’s Paradox If the universe is i) eternal If the universe is i) eternal ii) (more or less) uniformly filled ii) (more or less) uniformly filled with stars with stars iii) infinite iii) infinite then there is a star along each line of sight then there is a star along each line of sight so: Why is the night sky dark ? so: Why is the night sky dark ?

Shell of radius r 1 : Surface: S 1 =4  r 1 2 Volume: V 1 =4  r 1 2  x # of stars: N 1 = 4   r 1 2  x luminosity per star: l * luminosity of shell: L 1 = 4   r 1 2  x l * L 1 = 4   r 1 2  x l * Shell of radius r 2 = 2r 1 : Surface: S 2 =4  (2r 1 ) 2 Volume: V 2 =4  (2r 1 ) 2  x # of stars: N 2 = 4   (2r 1 ) 2  x luminosity per star: l * /4 luminosity of shell: L 2 = 4   (2r 1 ) 2  x l * /4 L 2 = 4   (2r 1 ) 2  x l * /4 = 4   r 1 2  x l * = L 1 Shell of radius r 3 = 4r 1 : Surface: S 3 =4  (4r 1 ) 2 Volume: V 3 =4  (4r 1 ) 2  x # of stars: N 3 = 4   (4r 1 ) 2  x luminosity per star: l * /16 luminosity of shell: L 3 = 4   (4r 1 ) 2  x l * /16 L 3 = 4   (4r 1 ) 2  x l * /16 = 4   r 1 2  x l * = L 1 Problems with an infinite universe Olber’s Paradox: Why is the night sky dark? Olber’s Paradox: Why is the night sky dark?

Olber’s Paradox: Each shell contributes L 1 = 4   r 1 2  x l * L 1 = 4   r 1 2  x l * infinite number of shells  infinite luminosity (at least) one of the assumptions must be wrong !

How to solve Olber’s paradox ? Universe is finite Universe is finite Universe has finite age Universe has finite age The distribution of stars throughout space is not uniform The distribution of stars throughout space is not uniform The wavelength of radiation increases with time The wavelength of radiation increases with time Note: for the big bang model, all these conditions are satisfied

Einstein: speed of light = const speed of light = const relativity of relativity of simultaneity, simultaneity, special relativity special relativity general relativity: general relativity: space-time is curved space-time is curved prediction of black holes prediction of black holes prediction of gravitational waves prediction of gravitational waves

Einstein Universe has to be static! Universe has to be static! only possible if extra-term is included in only possible if extra-term is included in equations to counter-balance attraction equations to counter-balance attraction cosmological constant cosmological constant Einstein’s “biggest blunder” Einstein’s “biggest blunder”

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

Doppler effect (for light) The light of an approaching source is shifted to the blue, the light of a receding source is shifted to the red The light of an approaching source is shifted to the blue, the light of a receding source is shifted to the red

Doppler effect red shift blue shift The light of an approaching source is shifted to the blue, the light of a receding source is shifted to the red.

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

The redshift-distance relation

Key results Most galaxies are moving away from us 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 = H 0  d The recession speed v is larger for more distant galaxies. The relation between recess velocity v and distance d fulfills a linear relation: v = H 0  d Hubble’s measurement of the constant H 0 : H 0 = 500 km/s/Mpc Hubble’s measurement of the constant H 0 : H 0 = 500 km/s/Mpc today’s best fit value of the constant: H 0 = 71 km/s/Mpc (WMAP) today’s best fit value of the constant: H 0 = 71 km/s/Mpc (WMAP)

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.

Einstein’s General Relativity + observation of expanding Universe: Universe started from a point: “Big Bang Model” “Big Bang Model”

Big Bang Model

Big Bang in a nutshell:

Cosmological redshift While a photon travels from a distant source to an observer on Earth, the Universe expands in size from R then to R now. While a photon travels from a distant source to an observer on Earth, the Universe expands in size from R then to R now. Not only the Universe itself expands, but also the wavelength of the photon. Not only the Universe itself expands, but also the wavelength of the photon.

Cosmological redshift General definition of redshift:  for cosmological redshift: General definition of redshift:  for cosmological redshift:

A large redshift z implies... The spectrum is strongly shifted toward red or even infrared colors The spectrum is strongly shifted toward red or even infrared colors The object is very far away The object is very far away We see the object at an epoch when the universe was much younger than the present day universe We see the object at an epoch when the universe was much younger than the present day universe most distant astrophysical object discovered so far: z= 6.3 (in 2005) most distant astrophysical object discovered so far: z= 6.3 (in 2005) z>5.8: “dark ages” z>5.8: “dark ages”

Are there any indications that this picture is correct? Yes ! Yes !  Primordial Nucleosynthesis  Cosmic Microwave background

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

The Cosmic Microwave Background (CMB) Last scattering surface transparent opaque

Penzias and Wilson 1965 Working at Bell labs Working at Bell labs Used a satellite dish to measure radio emission of the Milky Way Used a satellite dish to measure radio emission of the Milky Way They found some extra noise in the receiver, but couldn’t explain it  discovery of the background radiation They found some extra noise in the receiver, but couldn’t explain it  discovery of the background radiation Most significant cosmological observation since Hubble Most significant cosmological observation since Hubble Nobel prize for physics 1978 Nobel prize for physics 1978

The cosmic microwave background radiation (CMB) Temperature of 2.728±0.004 K Temperature of 2.728±0.004 K isotropic to 1 part in isotropic to 1 part in perfect black body perfect black body 1990ies: CMB is one of the major tools to study cosmology 1990ies: CMB is one of the major tools to study cosmology Note: ~1% of the noise in your TV is from the big bang Note: ~1% of the noise in your TV is from the big bang

More results from the CMB The Earth is moving with respect to the CMB  Doppler shift The Earth is moving with respect to the CMB  Doppler shift The emission of the Galaxy The emission of the Galaxy Fluctuations in the CMB Fluctuations in the CMB

Fluctuations in CMB responsible for structure formation in the universe

Cosmic Structure formation

New developments: Science discovery of the year 1998 q 0 = 0 q 0 = 0.5 more distant fainter Data indicates: q 0 < 0  Expansion is accelerating

From Supernova observations: The expansion of the universe is accelerating !!! The expansion of the universe is accelerating !!! But gravity is always attractive, so it only can decelerate But gravity is always attractive, so it only can decelerate  Revival of the cosmological constant 

k=+1  =0  >0 The fate of the Universe for  >0

Wilkinson Microwave Anisotropy Probe (WMAP) (2003) COBE (1992) WMAP (2003)

Summary of most important results of WMAP Age of the Universe: 13.7 billion years Age of the Universe: 13.7 billion years First stars: 200 million years First stars: 200 million years after Big Bang after Big Bang CMB: decoupled years CMB: decoupled years after Big Bang after Big Bang Hubble constant: H 0 = 71 (km/s)/Mpc Hubble constant: H 0 = 71 (km/s)/Mpc Content of the Universe: Content of the Universe: - 4% Atoms - 4% Atoms - 23 % cold, dark matter - 23 % cold, dark matter - 73 % ‘Dark Energy’ - 73 % ‘Dark Energy’