Relativity 110f: Cosmology - Friedmann Equations Derivation + Universe Evolution Models (FINALE)
Full relativity playlist: • Relativity by eigenchris
Powerpoint slide files: https://github.com/eigenchris/MathNot...
Leave me a tip: https://ko-fi.com/eigenchris
Links/Sources:
Sean Carroll's 15-page PDF on cosmology: https://preposterousuniverse.com/wp-c...
PDF with derivation of "3rd" Friedmann Equation based on Adiabatic expansion (page 19): https://www.uio.no/studier/emner/matn...
Article on Conservation of Energy in General Relativity: https://math.ucr.edu/home/baez/physic...
de Sitter's 1917 paper: https://academic.oup.com/mnras/articl...
Video on mathematics of de Sitter space: • The Cosmological Constant, Maulik Par...
Equation for de Sitter space: https://en.wikipedia.org/wiki/De_Sitt...
Equation for embedding Anti-de Sitter space: https://en.wikipedia.org/wiki/Anti-de...
PDF building up dS and AdS space from the basics: http://3dhouse.se/ingemar/relteori/Ku...
Physics Stack exchange post about values of cosmological parameters: https://physics.stackexchange.com/que...
Chronology of the Universe: https://en.wikipedia.org/wiki/Chronol...
Dark Energy Survey (estimated cosmological parameters): https://en.wikipedia.org/wiki/Dark_En...
Video intro to Dark Energy Survey: • Exploring 7 billion light years of sp...
Dr Becky talks about Dark Energy Survey: • Dark matter: smooth or clumpy?! | The...
Cosmic Inflation: https://en.wikipedia.org/wiki/Inflati...)
"Gravity in a Nutshell" by A. Zee also has chapters on de Sitter and anti-de Sitter spacetimes (IX.10 and IX.11)
Sources for the estimations of cosmological parameters:
WMAP: https://arxiv.org/pdf/0803.0732.pdf
BOOMERanG: https://arxiv.org/pdf/astro-ph/000440...
Planck: https://en.wikipedia.org/wiki/Lambda-...
Other topics I didn't cover:
Killing Vectors: https://en.wikipedia.org/wiki/Killing...
Kerr Metric (rotating black holes): https://en.wikipedia.org/wiki/Kerr_me...
Einstein-Hilbert Action (Lagrangian formulation of GR): https://en.wikipedia.org/wiki/Einstei...
0:00 Introduction
1:04 Review of FLRW metric and Perfect Fluid
3:09 Friedmann Equations Derivation
7:04 "3rd" Friedmann Equation (conservation of energy)
8:25 Universes dominated by matter, radiation, dark energy
14:25 Einstein Static Universe
17:51 de Sitter / anti-de Sitter Universes
25:16 Cosmological parameters
28:02 Cosmological Models with Λ = 0
33:08 Cosmological Models with Λ ≠ 0
36:43 The model for our universe
39:17 Conclusion
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