ADVANCED COSMOLOGY

At the end of the course, the student will achieve:
1. Expertise with the observations, the morphology and the statistical properties of the large-scale distribution of galaxies, the measurements of anisotropy in the cosmic microwave background and the overall state-of-the-art in this field.
2. Ability to characterize the observed inhomogeneities both in terms of two-point correlation functions and in terms of Fourier components and power spectrum, with knowledge of the standard estimators used to measure them from real samples; he will also know how to connect these to the theoretical description of density fluctuations in the matter, considered as a continuous field.
3. Knowledge of the linear equation of growth of density perturbations in the expanding Universe, of its derivation in the Newtonian approximation and its solutions in the cases of relativistic and non-relativistic matter.
4. Comprehension of the growth history of cosmological perturbations during the various evolutionary phases of the Universe, and how this generates the spectrum and the specific spectral features we observe today in the CMB and in the galaxy distribution.
5. Comprehension of the existence of a non-baryonic (dark) matter component with specific properties, as a necessary ingredient to make sense to the overall picture.
6. The ability of contribute autonomously to original research work in the study of large-scale structure and tests of the standard cosmological model

• General Relativity
• FRLW Cosmology 
• Dynamica of Isotropic and homogeneous universe 
• Extra-galactic Astronomy 
• Classical Electrodynamics
• Quantum mechanics

1. Introduction

Current status of cosmology: the Standard Model and its open questions 
Intro on General Relativity and Tensor calculus
Recap from Background Cosmology  and Astrophysics of necessary basic concepts: Friedmann equations, Robertson-Walker metric, distances in cosmology, magnitudes)
Standard candles and discovery of accelerated expansion
Big Bang nucleosynthesis 

2. Cosmological Perturbations

Boltzmann Equation and distribution function. Collision Term
Photon Perturbations
Baryons Perturbations
 Dark Matter Perturbations 
Neutrino Perturbations

3. Metric Perturbations

Scalar Perturbations
Tensor Perturbations

4. The primordial seeds

Initial conditions
Flatness problem
Horizon problem
Inflationary paradigm
Slow-roll solution
Inflaton particle field
Gravitational wave production 
Curvature fluctuation production
Power spectrum of primordial fluctuations
5. Large Scale Structures 
Gravitational instability
Matter Power spectrum

6. Cosmic Microwave Anisotropies

The photon-baryon fluid
Production of Acoustic oscillations
CMB power spectra
7. Observables and  future experimental efforts

• S. Dodelson, "Modern Cosmology", Academic Press
• S. Weinberg, "Cosmology", Oxford Press  
• E. Kolb & M. Turner, "The Early Universe", CRC Press
• J. Peebles, "The large scale structure of the universe", Princeton University Press

Warm up questions 

(a) What is conformal time? Why is it useful?

(b) How do the energy densities in radiation (ρr), matter (ρm) and a cosmological constant (ρΛ)evolve with the scale factora(t)?(

c) What is a(t) for a flat universe dominated by radiation, matter or a cosmological constant?What is a(η) for the same cases?

(d) What is the redshift of matter-radiation equality if Ωr= 9.4×10−5and Ωm= 0.32?

(e) Show in the context of expanding FRW models that if the combination ρ+ 3 Pis alwayspositive, then there was a Big Bang singularity in the past