Organizational details#

• M.Sc. Physics core course
• Standard course description can be found at the following link (on page 82) [https://www.physik.uni-heidelberg.de/c/image/d/studium/master/pdf/MScModuleManual.pdf](https://www.physik.uni-heidelberg.de/c/image/d/studium/master/pdf/MScModuleManual.pdf
• Course organization on PhU for registered students ( PhU link)

Course material#

• Lecture slides uploaded on PhU by Prof. Heisenberg
• Cosmology lecture notes
  • by Matthias Bartelmann (Primary)
  • by David Tong
  • by Daniel Baumann
• GR crash course
  • https://preposterousuniverse.com/wp-content/uploads/2015/08/grtinypdf.pdf

Tutorials#

1. Tuesday, 22 October 2024, (4:15 PM - 6:00 PM)

   • Organizational matter
   • Primer on intuition behind a “Tensor”
   • Discussed CAT2
   • Introduction to xAct package

2. 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.

3. 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

4. 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

5. 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

6. 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

7. 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.

8. Tuesday, 10 December 2024, (4:15 PM - 5:45 PM)

   • Exercise 7.1 : Show that Bardeen potentials are gauge invariant
   • Exercise 7.2 : Computation of $G_i^0$ in cosmological perturbation theory (specific case)
   • Exercise 7.3 : Dark matter fluctuations during matter domination

9. Tuesday,  7 Jan 2025, (4:15 PM - 5:45 PM)

   • Exercise 8.1 : Derivation of the cosmological Klein-Gordon equation
   • Exercise 8.2 : Slow roll inflation for a quadratic potential
   • Exercise 8.3 : Derive the relation between the slow-roll parameters

10. Tuesday, 14 Jan 2025, (4:15 PM - 5:45 PM)

    • Exercise 6 (Part 1) : Work out the dynamics of a three form : Gauge symmetry, Equations of motions, Physical degrees of freedom

11. Tuesday, 21 Jan 2024, (4:15 PM - 5:45 PM)

    • Exercise 6 (Part 2) : Work out the dynamics of a three form in an FLRW Universe : Background field configuration, Background equations of motions for a Homogeneous + Isotropic background

12. Tuesday, 28 Jan 2024, (4:15 PM - 5:45 PM)

    • Exercise 9.1 : Luminosity distance from an FLRW metric
    • Exercise 9.2 : Olbers paradox in FLRW universe
    • Crash course on CMB physics and anisotropies