Geometries of space: flat, spherical, hyperbolic

Cosmology (Winter, 2013)

Lecture Playlist

  1. The expanding (Newtonian) universe

  2. Matter and radiation dominated universes

  3. Geometries of space: flat, spherical, hyperbolic

  4. Cosmological thermodynamics

  5. Vacuum energy

  6. Dark matter and allocation of energy density

  7. Temperature history of the universe

  8. Baryogenesis

  9. Inflation

  10. Inhomogeneities and quantum fluctuations

January 28, 2013

Professor Susskind presents three possible geometries of homogeneous space: flat (infinite), spherical (positively curved and finite), hyperbolic (negatively curved and infinite). He develops the metric for these three spatial geometries in spherical coordinates, and describes methodologies for determining which geometry represents our universe. To date, we have not been able to detect curvature in our universe. Professor Susskind concludes the lecture by introducing a time-dependent scale factor into the metric for each of these geometries.

References