… but the equilibrium is unstable. In order to prevent the universe from either expanding or contracting, Einstein introduced a scalar field that was called The Cosmological Constant in order to keep the universe static.

The Age of the Universe No gravity: v = H o r  t o = r/v = H o -1 Newtonian gravity for a flat universe: ½ mv 2 - GmM/r = 0  v = dr/dt = (2GM/r) ½ so we can integrate r ½ dr = (2GM) ½ dt to get t o = 2/3 (r 3 /2GM) ½ = 2/3 (r/v) = 2/3 H o -1 Ho = 73.8 ± 2.4 (km/s)/Mpc. t o = 13.7 billion years

Oscillations on many scales Source: Wayne Hu: background.chicago.edu

Power Spectrum cosmic variance limited for l<354 S/N>1 for l<658

Evidence for the Hot Big Bang Abundances of the light elements BBN measures the universe at approximately t = 200 s Hubble flow H o measures the universe at approximately t = yrs Cosmic microwave background radiation CMB measure the universe at approximately t = 4 x10 5 yrs

Galactic Rotation Curves For a star of mass m a distance r from the center of a galaxy, where the total mass interior to r is M(r): mv 2 /r = GM(r)m/r 2 so that we would expect v= [GM(r)/r] ½ so that v should go like r -½

Size and Scale of the Universe Image courtesy of The Cosmic Perspective by Bennett, Donahue, Schneider, & Voit; Addison Wesley, 2002

You Are Here The Milky Way Galaxy is a giant disk of stars 160,000 light-years across and 1,000 light-years thick. There are over 100 Billion stars in the Milky Way The Spiral arms are only 5% more dense than average, and are the locations of new star formation The Sun is located at the edge of a spiral arm, 30,000 light-years from the center It takes 250 Million years for the Sun to complete one orbit The Milky Way Galaxy

The Local Group Contains 3 large spiral galaxies--Milky Way, Andromeda (M31), and Triangulum (M33)—plus a few dozen dwarf galaxies with elliptical or irregular shapes. Gravitationally bound together—orbiting about a common center of mass Ellipsoidal in shape About 6.5 million light-years in diameter

The Local Supercluster A cluster of many groups and clusters of galaxies Largest cluster is the Virgo cluster containing over a thousand galaxies. Clusters and groups of galaxies are gravitationally bound together, however the clusters and groups spread away from each other as the Universe expands. The Local Supercluster gets bigger with time It has a flattened shape The Local Group is on the edge of the majority of galaxies The Local Supercluster is about 130 Million light-years across

The Universe 1.3 Billion light-years Surveys of galaxies reveal a web-like or honeycomb structure to the Universe Great walls and filaments of matter surrounding voids containing no galaxies Probably 100 Billion galaxies in the Universe The plane of the Milky Way Galaxy obscures our view of what lies beyond. This creates the wedge-shaped gaps in all-sky galaxy surveys such as those shown here.

The Universe Computer Simulation The observable Universe is ~26 Billion light-years in diameter.

The Universe

The distance to the center of the Milky Way is about 10 4 pc, whereas the size of the solar system is about pc. If the distance to the center of the Milky Way were scaled to the size of this room (10 meters), then on the same scale the solar system would be about the size of: A. An atom ( m); B. A molecule of DNA (10 -7 m); C. A pin head (10 -3 m); D. A foot (10 -1 m); E. You (1 meter).

Elements of an Interactive Classroom Feedback (Clicker questions) Peer education (Think pair share) Formative and summative assessment (JiTT) Inquiry based learning (workshop style classrooms) Web-based activities & resources (facebook, youtube, twitter & compadre) Visualizations (Phet Simulations, demos)

A "Hubble diagram" is a graph of: A. Brightness versus wavelength or frequency; B. Luminosity versus temperature; C. Mass versus radius; D. Size versus time; E. Velocity versus distance.

What is the principal observational evidence that the age of the Universe is about 14 billion years? A. The oldest rocks (carbonaceous chondrites) in the solar system indicate an age of 14 billion years; B. Radioactive decay of heavy elements created in the Big Bang indicates an age of 14 billion years; C. The main sequence turn-off point in the HR diagrams of globular clusters indicates ages of about 14 billion years; D. Light from the most distant galaxies and quasars appears to be about 14 billion years old; E. The reciprocal of Hubble's constant gives an estimate of the age of the Universe.

How can astronomers measure that a galaxy is rotating? A. From the rotating motion of the galaxy on the sky; B. From its redshift; C. From the difference in the redshift of the galaxy from one side to the other; D. From the swept back appearance of its spiral arms; E. From Cepheid variables in the galaxy.

The distance to the center of the Milky Way is about 10 4 pc, whereas the size of the solar system is about pc. If the distance to the center of the Milky Way were scaled to the size of this room (10 meters), then on the same scale the solar system would be about the size of: A. An atom ( m); B. A molecule of DNA (10 -7 m); C. A pin head (10 -3 m); D. A foot (10 -1 m); E. You (1 meter).

There was a revolution in cosmology, leading to the "Standard Model of Cosmology" (according to which the Universe contains 70% Dark Energy, 26% non-baryonic Dark Matter, 4% baryonic matter). What observational discovery caused the revolution? A. The redshifts of galaxies showed that the Universe is expanding; B. The discovery of the Cosmic Microwave Background. C. The rotation of spiral galaxies showed the existence of Dark Matter; D. All of the above