96388 - ADVANCED COSMOLOGY

Learning outcomes

This course is intended to present the current understanding of the main advanced topics in Cosmology. After completing the course, students will acquire a thorough and updated knowledge of modern cosmological frameworks, with particular focus on dark matter and dark energy models, and on all the main cosmological probes. Furthermore, they will learn the primary statistical methods of modern observational Cosmology.

Course contents

The course offers a comprehensive and rigorous overview of modern Cosmology, with a focus on both theoretical foundations and data analysis techniques. The topics are structured as follows:

• General Relativity and Gravitation: fundamentals of fields in curved spacetime; the geometrical structure of General Relativity; Einstein equations and their Newtonian limit; action principle, symmetries and physical interpretation; the gravitational field of a mass distribution.

• Statistical Analysis and Inference: Bayesian framework; likelihood, priors, and posteriors; practical methods for data analysis; Fisher information matrix; Markov Chain Monte Carlo techniques; introduction to machine learning applications in Cosmology.

• The Concordance Model: overview of the standard ΛCDM cosmological model; thermal history of the Universe; structure of the cosmic web; nature and evidence for dark matter and dark energy.

• The Expanding Universe: physical meaning of space expansion; cosmological distance measures; evolution of energy components; cosmic inventory and constraints from observations.

• Fundamental Equations of Cosmology: cosmological application of Einstein’s field equations and the Boltzmann equation; treatment of departures from homogeneity and isotropy.

• Inhomogeneities and Cosmic Perturbations: photon, baryon, neutrino and dark matter fluids; scalar-vector-tensor decomposition; Einstein equations for scalar perturbations; origin and evolution of tensor modes.

• Growth of Structures (Linear Regime): transfer function and growth factor; linear evolution of density fluctuations on large and small scales.

• Observational Probes of Structure: 3D clustering; bias; baryon acoustic oscillations; redshift-space and geometric distortions.

• Numerical Tools and Applications: hands-on sessions with the CosmoBolognaLib for statistical and theoretical analyses of cosmological data.

Readings/Bibliography

The course relies on the following materials:

Primary textbooks:

• General Relativity: The Essentials, Carlo Rovelli — Cambridge University Press.
  
• Modern Cosmology (Second Edition), Scott Dodelson and Fabian Schmidt — Academic Press.

Supporting material:

• Lecture slides and notes.

• Selected scientific papers.

Teaching methods

The course includes:

• Traditional lectures at the blackboard, focused on both theoretical foundations and their connection to observational cosmology;

• Demonstrations at the computer, where the fundamental concepts of C++ and Python are introduced and applied to cosmological problems using the CosmoBolognaLib free software numerical libraries.

All activities are held in person.

Assessment methods

The exam is oral and takes place in person. It is structured in two parts:

1. The student presents and discusses a topic of their choice, selected from those covered in the course. This part evaluates the ability to organize and communicate complex cosmological concepts clearly and autonomously.

2. A set of further questions follows, covering all topics discussed during the lectures and listed in the “Course content” section of this webpage. The “Course content” provides a general summary of the topics covered; however, the actual content of the lectures determines the scope of the exam. This part assesses the breadth and depth of the student's knowledge of theoretical and observational Cosmology.

The final grade (on a 30-point scale) is determined as follows:

• The exam is failed if the student is unable to demonstrate even a minimal understanding of any of the topics effectively covered during the lectures and selected during the exam.

• If the student is able to describe the main topics and conclusions but cannot reproduce or explain the key steps behind their derivation, the grade ranges from 18 to 20.

• If the student explains the content with reasonable clarity and recalls only some of the central arguments or proofs, the grade ranges from 21 to 24.

• If the student clearly and accurately presents all major topics together with their underlying derivations, the grade ranges from 25 to 28.

• If, in addition, the student demonstrates familiarity with CosmoBolognaLib by presenting original notebooks and basic cosmological plots, the grade ranges from 29 to 30.

• If the overall performance is outstanding, demonstrating complete mastery of the material along with clarity and precision, the student is awarded 30 cum laude.

Students may consult any material during the exam, only to support memory, not to compensate for lack of preparation.

Students may refuse the final grade up to two times, according to University regulations.

Students with learning disabilities or temporary/permanent impairments are encouraged to promptly contact the University's support service (https://site.unibo.it/studenti-con-disabilita-e-dsa/it). The office will provide guidance on possible accommodations, which must be submitted to the instructor at least 15 days before the exam. The proposed measures will be evaluated for compatibility with the academic objectives of the course.

Teaching tools

On the University’s Virtuale platform, PDF files corresponding approximately to the material written on the blackboard during lectures are made available to students. Additionally, supplementary materials, including detailed notes and selected articles, are regularly provided to support further study and deepen understanding of the topics covered.

Office hours

See the website of Federico Marulli