Cosmology 2
A.Y. 2024/2025
Learning objectives
The course aims at providing the students with: (a) the theoretical background to describe the physics of the growth of density fluctuations and the formation of structure in the Universe; (b) the knowledge of experimental results and the statistical tools that allow us to test this theory and constrain its fundamental parameters, in particular using observations of the large-scale distribution of galaxies.
Expected learning outcomes
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
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
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course can be attended as a single course.
Course syllabus and organization
Single session
Responsible
Lesson period
First semester
Course syllabus
Course Syllabus
1. Introduction
-- Current status of cosmology: the standard model
-- Recap from Cosmology 1 and Astrophysics of necessary basic concepts: Friedmann equations, Robertson-Walker metric, distances in cosmology, magnitudes, colours and stellar masses of galaxies, K-correction)
-- Standard candles and discovery of accelerated expansion
2. The large-scale distribution of galaxies
-- Classical cosmological tests: Number counts, the luminosity function; and reated issues
-- Redshift surveys
-- Galaxy clustering statistics: two-point correlation function
-- The density fluctuation field: Fourier description and power spectrum
-- Comparison of observations and theory: the concept of galaxy bias:
3. Linear evolution of density perturbations
-- Jeans theory in an expanding medium: growth equation for a non-relativistic and a relativistic gas
-- General introduction to general relativistic perturbation theory
-- Adiabatic baryonic perturbations in Friedmann universes
-- Problems of the baryonic scenario: Silk damping
-- Hints at isothermal fluctuations, the need for dark matter
-- Problems of the hot dark-matter (neutrino) scenario: free streaming
-- Advantages of the Cold Dark Matter (CDM) model:
-- The evolved spectrum of density fluctuations: transfer function T(k) and the Harrison-Zeldovich primordial spectrum
-- Brush-up on CMB temperature anisotropies
-- Origin of Baryonic Acoustic Oscillations (BAO) in the fluctuation spectra of both CMB temperature and the galaxy distribution;
-- BAO as a standard ruler to measure the expansion history H(z)
-- Galaxy peculiar velocities and redshift-space distortions
-- Growth rate of structure as a test of General Relativity
4. Non-linear growth (hints)
-- Spherical collapse
-- Press-Schechter theory and cosmological tests with clusters of galaxies
-- Introduction to lagrangian perturbation theory
1. Introduction
-- Current status of cosmology: the standard model
-- Recap from Cosmology 1 and Astrophysics of necessary basic concepts: Friedmann equations, Robertson-Walker metric, distances in cosmology, magnitudes, colours and stellar masses of galaxies, K-correction)
-- Standard candles and discovery of accelerated expansion
2. The large-scale distribution of galaxies
-- Classical cosmological tests: Number counts, the luminosity function; and reated issues
-- Redshift surveys
-- Galaxy clustering statistics: two-point correlation function
-- The density fluctuation field: Fourier description and power spectrum
-- Comparison of observations and theory: the concept of galaxy bias:
3. Linear evolution of density perturbations
-- Jeans theory in an expanding medium: growth equation for a non-relativistic and a relativistic gas
-- General introduction to general relativistic perturbation theory
-- Adiabatic baryonic perturbations in Friedmann universes
-- Problems of the baryonic scenario: Silk damping
-- Hints at isothermal fluctuations, the need for dark matter
-- Problems of the hot dark-matter (neutrino) scenario: free streaming
-- Advantages of the Cold Dark Matter (CDM) model:
-- The evolved spectrum of density fluctuations: transfer function T(k) and the Harrison-Zeldovich primordial spectrum
-- Brush-up on CMB temperature anisotropies
-- Origin of Baryonic Acoustic Oscillations (BAO) in the fluctuation spectra of both CMB temperature and the galaxy distribution;
-- BAO as a standard ruler to measure the expansion history H(z)
-- Galaxy peculiar velocities and redshift-space distortions
-- Growth rate of structure as a test of General Relativity
4. Non-linear growth (hints)
-- Spherical collapse
-- Press-Schechter theory and cosmological tests with clusters of galaxies
-- Introduction to lagrangian perturbation theory
Prerequisites for admission
To fully benefit of this course, it will be useful to have previously attended "Introduction to General Relativity" and "Cosmology 1".
Teaching methods
Classroom lectures, using chalk and blackboard.
Teaching Resources
- M. Longair, "Galaxy Formation", 3rd Edition, Cambridge University Press
- S. Dodelson & F. Schmidt, "Modern Cosmology" 2nd ed., Academic Press (1st edition by Dodelson alone is also OK)
- Lecture notes and videos by the teacher
- S. Dodelson & F. Schmidt, "Modern Cosmology" 2nd ed., Academic Press (1st edition by Dodelson alone is also OK)
- Lecture notes and videos by the teacher
Assessment methods and Criteria
The oral exam has a duration of about 40 min. Its aim is to probe the level of comprehension of the central concepts and methods of the theory of structure formation and its link to observations.
FIS/05 - ASTRONOMY AND ASTROPHYSICS - University credits: 6
Lessons: 42 hours
Professor:
Guzzo Luigi
Educational website(s)
Professor(s)
Reception:
Upon email appointment
To be defined (either at the Department or via Zoom teleconference)