Part I: Expanding Universe Part II: What’s the matter in the Universe? July 27, 2004
Expanding Universe • Expanding Universe of Students • The farther things are, the faster they are moving away
Is the Universe really expanding? • Take a look at the handout • How do you interpret the 3 graphs? • Try to draw graphs of a Universe that has • Static galaxies (not moving) • Turbulent galaxies (random motion) • Rotating galaxies (like the planets around the Sun) • Uniformly contracting galaxies
Cepheid variables and Nebulae • In 1923, Hubble used new Mt. Wilson 100 inch telescope to observe Cepheid variables in the nearby “nebula” Andromeda. He recognized that the fuzzy patches called nebulae were actually distant galaxies, outside of our own Milky Way This relation was calibrated by Hertzsprung and Shapley L =K P1.3
Hubble Law The Hubble constant Ho = 558 km s -1Mpc -1 is the slope of these graphs Compared to modern measurements, Hubble’s results were off by a factor of ten!
v c l - lo Dl = = = z lo lo Recall Doppler Shift • Redshift z is a non-relativistic approximation that relates the Doppler shift to the velocity of the object • Redshift is determined by comparing laboratory wavelength lo to observed wavelength l
Hubble Law • v = Ho d = cz where • v = velocity from spectral line measurements • d = distance to object • Ho = Hubble constant in km s-1 Mpc -1 • z is the redshift Space between the galaxies expands while galaxies stay the same size
Expanding Universe • Expanding Universe of Dots • Why it looks as though you are at the center of the expanding universe
Doppler shifting spectral lines • When a star or galaxy is moving, its spectral lines are Doppler shifted by Dl = lobs – llab • The redshift Z = Dl/llab • The velocity of the star or galaxy is found from the redshift using v = ZAVG c H and K lines
Hubble constant • Contemporary Lab Experiences in Astronomy Project CLEA • You will plot the velocities (km/sec) vs. the distances (Mpc) that you obtain from a sample of galaxies • The slope of this line is known as the Hubble constant – it is given in km/sec/Mpc H = v/D
Contemporary Lab Experiences in Astronomy Project CLEA • Read through “The Hubble Redshift Distance Relation” student manual • This manual will walk you through the steps to running the lab. • Break up into 6 groups of four
The age of the Universe • What is the relationship to the Hubble constant and the age of the Universe? • What are the units? • D must be in km (animate) • V must be in km/sec (animate) • What does this give us? • How do we convert this number into years?
Break • Why did the Big Bang happen? • What happened in the Big Bang? • Where did the Big Bang happen?
Standard Big Bang Cosmology • Sometime in the distant past there was nothing – space and time did not exist • Vacuum fluctuations created a singularity that was very hot and dense • The Universe expanded from this singularity • As it expanded, it cooled • Photons became quarks • Quarks became neutrons and protons • Neutrons and protons made atoms • Atoms clumped together to make stars and galaxies
Standard Big Bang Cosmology • Top three reasons to believe big bang cosmology • Big Bang Nucleosynthesis • Cosmic Microwave Background • Hubble Expansion Big Bang by Physics Chanteuse Lynda Williams
Big Bang Timeline We are here Big Bang Nucleosynthesis
Big Bang Nucleosynthesis • Light elements (namely deuterium, helium, and lithium) were produced in the first few minutes of the Big Bang The predicted abundance of light elements heavier than hydrogen, as a function of the density of baryons in the universe (where 1 is critical) Note the steep dependence of deuterium on critical density. Goal is to find a critical density that explains all the abundances that are measured
Big Bang Nucleosynthesis • Heavier elements than 4He are produced in the stars and through supernovae • However, enough helium and deuterium cannot be produced in stars to match what is observed – in fact, stars destroy deuterium in their cores, which are too hot for deuterium to survive. • So all the deuterium we see must have been made around three minutes after the big bang, when T~109 K • BBN predicts that 25% of the matter in the Universe should be helium, and about 0.001% should be deterium, which is what we see. • BBN also predicts the correct amounts of 3He and 7Li
Big Bang Timeline Cosmic Microwave Background We are here
Cosmic Microwave Background • Discovered in 1965 by Arno Penzias and Robert Wilson who were working at Bell Labs • Clinched the hot big bang theory Excess noise in horned antennae was not due to pigeon dung!
CMB • Photons in CMB come from surface of last scattering – where they stop interacting with matter and travel freely through space • CMB photons emanate from a cosmic photosphere – like the surface of the Sun – except that we inside it looking out • The cosmic photosphere has a temperature which characterizes the radiation that is emitted • It has cooled since it was formed by more than 1000 to 2.73 degrees K
COBE data • “Wrinkles on the face of God”
COBE data • Fluctuations in CMB are at the level of one part in 100,000 Blue spots mean greater density Red spots mean lesser density (in the early Universe)
WMAP vs. COBE • The WMAP image brings the COBE picture into sharp focus. movie
Universe’s Baby Pictures Red is warmer Blue is cooler Credit: NASA/WMAP
Compare MAPs at other wavelengths • Visible to microwave galaxy images • Compare the dynamic range movie
Geometry See how parallel laser light beams fired by the space slug are affected by the geometry of space
Big Bang Timeline We are here Inflation
What is inflation? • Inflation refers to a class of cosmological models in which the Universe exponentially increased in size by about 1043 between about 10-35 and 10-32 s after the Big Bang (It has since expanded by another 1026) • Inflation is a modification of standard Big Bang cosmology • It was originated by Alan Guth in 1979 and since modified by Andreas Albrecht, Paul Steinhardt and Andre Linde (among others)
Alan Guth Why believe in inflation? • Inflation is a prediction of grand unified theories in particle physics that was applied to cosmology – it was not just invented to solve problems in cosmology • It provides the solution to two long standing problems with standard Big Bang theory • Horizon problem • Flatness problem
WMAP supports inflation • Inflation - a VERY rapid expansion in the first 10-35 s of the Universe – predicts: • That the density of the universe is close to the critical density, and thus the geometry of the universe is flat. • That the fluctuations in the primordial density in the early universe had the same amplitude on all physical scales. • That there should be, on average, equal numbers of hot and cold spots in the fluctuations of the cosmic microwave background temperature. • WMAP sees a geometrically flat Universe
Horizon Problem • The Universe looks the same everywhere in the sky that we look, yet there has not been enough time since the Big Bang for light to travel between two points on opposite horizons • This remains true even if we extrapolate the traditional big bang expansion back to the very beginning • So, how did the opposite horizons turn out the same (e.g., the CMBR temperature)?
Horizon Problem • Inflation allows the early Universe to be small enough so that light can easily cross it at early times
No inflation • At t=10-35 s, the Universe expands from about 1 cm to what we see today • 1 cm is much larger than the horizon, which at that time was 3 x 10-25 cm
With inflation • Space expands from 3 x 10-25 cm to much bigger than the Universe we see today
Flatness Problem • Why does the Universe today appear to have W between 0.1 and 1 – the critical dividing line between an open and closed Universe? • Density today will differ greatly from density of early Universe, due to expansion – if W starts out <1, it will get much lower and vice versa only values of W very near 1 can persist • A value for W =1also implies the existence of dark matter as well as the cosmological constant
Flatness Problem • Inflation flattens out spacetime the same way that blowing up a balloon flattens the surface • Since the Universe is far bigger than we can see, the part of it that we can see looks flat
Uncertainty Principle DE Dt = h Big Bang Revisited • Extrapolating back in time, we conclude that the Universe must have begun as a singularity – a place where the laws of physics and even space and time break down • However, our theories of space and time break down before the singularity, at a time of 10-43 s, a length of 10-33 cm, and a density of 1094 cm3 • This is known as the Planck scale
Uncertainty Principle DE Dt = h/2 Uncertainty Principle Dx Dp = h/2 Planck scale activity • The goal of this activity is to calculate the Planck mass, length, time and energy. • Remember
Lunch • What’s the matter in the universe? • Why are there so many more particles than anti-particles? • How do we know?
Big Bang Timeline This lecture We are here
Probing structure of matter • Given: a large wooden board, a mystery shape and marbles • Try to identify the shape that is hiding under the wooden board. You can only roll marbles against the hidden object and observe the deflected paths that the marbles take. Take at least five minutes to "observe" a shape. Then do a second shape. • Place a piece of paper under the board for sketching the paths of the marbles. Then analyze this information to determine the object's actual shape.
Analysis • Black vertical line shows path of incoming marble • Red line shows path of outgoing marble • Green dotted line bisects the angle made by the incoming and outgoing lines • Reflecting surface is perpendicular to bisecting line
Questions • Draw a small picture of each shape you studied in your lab notebook. • Can you tell the size of the object as well as its shape? • How could you find out whether the shape has features that are small compared to the size of your marbles? • Without looking, how can you be sure of your conclusions?
What Rutherford did • Rutherford shot alpha-particles (Helium nuclei) at a thin gold foil. He found that most went right through. However, some were deflected, and a percentage of those bounced right back at him! He said that “it was like firing a cannonball at tissue paper, and having it ricochet off!” • Can you see how he concluded that the nucleus was a hard small sphere, and that most of the atom was empty space? (As opposed to a plum pudding?)
nucleus Atomic Particles • Atoms are made of protons, neutrons and electrons • 99.999999999999% of the atom is empty space • Electrons have locations described by probability functions • Nuclei have protons and neutrons mp = 1836 me
Leptons • An electron is the most common example of a lepton – particles which appear pointlike • Neutrinos are also leptons • There are 3 generations of leptons, each has a massive particle and an associated neutrino • Each lepton also has an anti-lepton (for example the electron and positron) • Heavier leptons decay into lighter leptons plus neutrinos (but lepton number must be conserved in these decays)