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Tuesday, 22 October 2024, (4:15 PM - 6:00 PM)
- Organizational matter
- Primer on intuition behind a “Tensor”
- Discussed CAT2
- Introduction to xAct package
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Tuesday, 29 October 2024, (4:15 PM - 6:00 PM)
- Crash course on Differential Geometry for GR
- Manifolds
- Vector fields and flows on manifolds
- Deep dive into Lie Derivative
Notes : I followed David Tong’s GR lecture notes, chapter 2 first half. Daniel Baumann’s GR lecture scripts have some nice diagrams.
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Tuesday, 5 November 2024, (4:15 PM - 6:00 PM)
- Exercise 1.1 : Gauge transformation law in GR for scalar, vector and tensors.
- Exercise 1.2 : Redefining Lie derivative in terms of Cov. derivative
- Exercise 2.2 : Lie Derivative of a scalar, vector and tensor
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Tuesday, 12 November 2024, (4:15 PM - 6:00 PM)
- Exercise 3.1 : Friedmann equations, De sitter and Einstein static universe
- Exercise 3.3 : Derivation of conservation of energy equation from Friedmann equations
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Tuesday, 19 November 2024, (4:15 PM - 5:45 PM)
- Exercise 4.1 : Observations of $z>6$ quasars indicate the necessity of a Universe with $a \in [0,1]$ (That the universe has a Big Bang Singularity at $a=0$)
- Exercise 4.2 : Derive the Luminosity distance in a curved universe (and compare with other distances)
- Exercise 2.3 : (Mathematica) Derive FLRW metric by taking the Lie derivative of the metric with respect to the translational and rotational killing vectors
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Tuesday, 26 November 2024, (4:05 PM - 5:35 PM)
- Exercise 3.2 : Deep dive into Newtonian cosmology
- Exercise 5.1 : Trajectory of a massive particle in FLRW universe
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Tuesday, 03 December 2024, (4:15 PM - 5:45 PM)
- Special lecture on Cosmological perturbation theory. Focus on diffeomorphism invariance and gauge degrees of freedom and metric perturbations.
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Tuesday, 10 December 2024, (4:15 PM - 5:45 PM)
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Tuesday, 17 December 2024, (4:15 PM - 5:45 PM)
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Tuesday, 7 Jan 2025, (4:15 PM - 5:45 PM)
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Tuesday, 14 Jan 2025, (4:15 PM - 5:45 PM)