Geometries of space: flat, spherical, hyperbolic

Cosmology (Winter, 2013)

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.