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Currently Playing: Relativity 110b: Cosmology - FLRW Metric Derivation (3 possible geometries)

Full relativity playlist: https://www.youtube.com/playlist?list=PLJHszsWbB6hqlw73QjgZcFh4DrkQLSCQa Powerpoint slide files: https://github.com/eigenchris/MathNotes/tree/master/Relativity Leave me a tip: https://ko-fi.com/eigenchris Ricci Curvature of 3-sphere: https://www.physics.mcgill.ca/~rhb/ph514/10sol6.pdf Ricci Curvature of Hyperbolic plane: https://thatsmaths.files.wordpress.com/2013/10/134-half-plane-curvature.pdf Info on Hyperboloid Model: https://en.wikipedia.org/wiki/Hyperboloid_model Hyperbolic Geometry video by Henry Segerman: https://www.youtube.com/watch?v=eGEQ_UuQtYs Alex Flournoy video on FLRW metric: https://www.youtube.com/watch?v=9WToQrPPeXs Dietterich Labs video on FLRW metric: https://www.youtube.com/watch?v=cbRy3sXDJ-U 0:00 Introduction 1:10 Cosmological Principle 4:03 Flat universe and scale factor a(t) 6:52 Closed/spherical universe 12:22 Open/hyperbolic universe 17:55 Unifying the 3 metrics 22:58 Reduced-Circumference Polar Coordinates