Early universe cosmology

Questions

June 2024

Hertog:

1. a) Prove the Bardeen potentials are invariant under certain infinitesimal transformations. (The Bardeen potentials were not given, you had to know them by heart.) b) Could the QCD phase transition have created a stochastic gravitational wave background? What kind of detector would be suitable for its detection? (5 points)

2. a) Give the diagram for the gravitational potential as a function of the scale factor for small scales (large k) that entered the horizon in the radiation dominated era. Discuss the different physical mechanisms that explain the curve's features. b) Give a sketch of the Harrison-Zeldovich-Peebles power spectrum today. Discuss three important effects on the power spectrum of introducing dark energy. (5 points)

3. a) Giving an analysis of the comoving Hubble sphere, show how inflation solves the horizon problem. b) The Hartle-Hawking wave function solves the problem of the initial singularity. What are the main predictions of Hartle-Hawking? (4 points)

4. Homework question: the question on parametric resonance. (3 points)

Craps:

1. Homework related question: explain the Hubble tension. (2 points)

2. Explain why the simplest models of inflation predict Gaussian perturbations. (1,5 points)

3. Explain intuitively why there are such large error bars for low multipole moments in the CMB power spectrum. Then give a technical explanation using the relation <a_lm a*_l'm'> = d_ll' d_mm' C_l. (The 'd' here stands for a Kronecker delta.) (3 points)

4. What is the effect of photon diffusion on the CMB temperature power spectrum? (1,5 points)

June 2021

Examen 15 June 2021

June 2020

Fout bij het aanmaken van de miniatuurafbeelding: Bestand is zoek

Fout bij het aanmaken van de miniatuurafbeelding: Bestand is zoek

June 2017

Hertog:

Question 1)

• Given the transferfunction, derive the form of the power spectrum in the Harrison-Zel'dovich-Peebles theory. Discuss the influence of the cosmological parameters on the spectrum. (I don't recall which specifically)

Question 2)

• Derive the realtion between the CMB temperature and the temperature of the neutrino background radiation
• Calculate and discuss the deuterium number density when it falls out of equilibrium

Question 3) (Homework)

• Proof that the existence of a Big Bang if the SEC is satisfied. How does Quantum Cosmology solve this problem?

Craps

Question 4)

• Discuss the influence of reionisation. (Don't recall exactly what he asked, its the part about reionisation in Lesgourges)

Question 5) (Homework)

• Derive the identity (6.113) from Dodelson (The identity was given)
• Extra: discuss the spectral indices. (I recall deriving them using the previous identity)

August 2017

Hertog:

Question 1)

• Find the solution of the Meszaros equation. Discuss the Harrison-Zel'dovich-Peebles spectrum.

Craps Question 2)

• Derive the identities for the inflation parameters in a slow roll potential. (The identities that relate the parameters (\epsilon, \eta) with the potential V)

Question 3)

• Discuss cosmic variance