Starting on October 17th, lectures will be held on Mondays and Wednesdays starting at 9h.  Tutorials will be held by Marta Trini.

Literature/Notes:
Lecture Notes by Prof. Roman Scoccimarro (New York University), here
Book: Kolb&Turner "The Early Universe"

Grading:
homeworks 30%
written exam with oral discussion 70% (list of potential questions given before hand)

Topics

(we will typically cover one topic per week)

Introduction

• Relevant scales
• Cosmological Principle
• Co-moving observers

Tutorial:

• Short reminder of relevant concepts in general relativity: space-time interval, tensors, metric, indices, geodesics, ...

Robertson-Walker Metric

• Minkowski metric
• Kinematics of RW metric
• redshift
• luminosity distance

Tutorial:

• Short reminder of relevant concepts in general relativity: distance between two events, covariant derivative, conserved current

Einstein's equation

• Stress-energy tensor
• Friedman equations
• critical density
• flatness problem

Tutorial:

• Omega parameter, curvature

Cosmic Acceleration - Age of the Universe

• measurement of acceleration
• age of the universe
• horizon
• Hubble radius
  

Tutorial:

• Examples of horizon and age calculations

Thermal history of the Universe - Distribution functions

• number density/energy density/pressure
  
• thermal equilibrium
  
• thermal decoupling
  

Tutorial:

• Examples of thermal decoupling calculations

(Matter-radiation equality, Recombination, BBN, Inflation...)

Exam questions

1. What is the cosmological principle? What are the implication for the metric of the Universe. Write down the RFW metric.

2. Kinematics of RFW metric (define redshift, sketch the derivation of the Hubble Law)

3. Write down the Einstein equation and stress energy tensor. What are the three main ideal fluids/components of energy density and what are their equations of state.

4. Write down the Friedmann equations, define of the critical density and formulate the flatness problem.

5. Definition of horizon and Hubble radius. Express the horizon in terms of time and scale in matter and radiation dominated Universe?

6. What is the age of the Universe in matter dominated Universe?

7. Write down general expressions for number density, energy density and pressure. What are the values in the limit of relativistic and non-relativistic particles?

8. What is the condition for a particle interaction to stay in the equilibrium? Calculate the temperature of neutrino decoupling.

9. What is the definition of g* and its value at >200 GeV temperatures.

10. Derive the temperature of matter/radiation equality

11. Derive the temperature of the start of the Big-Bang Nuchleosyntesis. Describe how the the synthesis of nuclei proceeds. What are the main nuclei in the Universe after the end of BBN?

12. Derive the temperature of recombination and photon decoupling

13. What are the motivations for inflation and how does the inflation solve those problems. How long does the inflation need to last?

14. Draw the arrow of time/temperature of the thermal history of the Universe and mark the main events which we discussed in the class on it.