Advanced Gravitational Physics
A.Y. 2024/2025
Learning objectives
The goal of this course is to provide the students with the required theoretical background to understand modern applications of perturbation theory in General Relativity, with an emphasis on the production of gravitational waves of observational relevance and on the anisotropies of the Cosmic Microwave Background (CMB).
Expected learning outcomes
At the end of the course the student will:
· Have a deep knowledge of the metric describing an axisymmetric rotating object (Kerr Metric)
· Know how to formulate a relativistic perturbation theory in General Relativity and its gauge ambiguities;
· Know how to solve, perturbatively, for the emission of gravitational radiation by objects of astrophysical and cosmological relevance, e.g. black holes, pulsars, and neutron stars;
· Be familiar with the modern techniques to detect gravitational waves;
· Know how to solve the equations governing the evolution of density perturbations in the Early Universe in a regime where General Relativity cannot be ignored;
· Be familiar with the dependence of the anisotropies of the Cosmic Microwave background on cosmological parameters;
· Have basic knowledge of application of effective field theories to gravity;
· Be able to understand which astrophysical and cosmological problems require a relativistic description and which strategies to use in order to find a solution.
· Have a deep knowledge of the metric describing an axisymmetric rotating object (Kerr Metric)
· Know how to formulate a relativistic perturbation theory in General Relativity and its gauge ambiguities;
· Know how to solve, perturbatively, for the emission of gravitational radiation by objects of astrophysical and cosmological relevance, e.g. black holes, pulsars, and neutron stars;
· Be familiar with the modern techniques to detect gravitational waves;
· Know how to solve the equations governing the evolution of density perturbations in the Early Universe in a regime where General Relativity cannot be ignored;
· Be familiar with the dependence of the anisotropies of the Cosmic Microwave background on cosmological parameters;
· Have basic knowledge of application of effective field theories to gravity;
· Be able to understand which astrophysical and cosmological problems require a relativistic description and which strategies to use in order to find a solution.
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Lesson period
First semester
Course syllabus
Part I : Gravitational Waves
Recap of General Relativity. The Kerr metric.
Metric Perturbations in a flat spacetime. Gauge transformations, the TT gauge.
Propagation and interaction of Gravitational waves with test particles. Proper and detector frames.
The quadrupole formula: radiated energy and angular momentum.
Gravitational waves from the inspiral of compact objects: circular and elliptical orbits. Backreaction.
Discussion of some of the most relevant events detected by LIGO/Virgo/KAGRA.
Gravitational waves from rotating bodies.
Gravitational waves from objects infalling into a black hole. Tidal disruption.
Elements of Post-Newtonian theory. *
Effective Field theory of gravitational radiation from compact objects *.
Black hole perturbation theory*
Stochastic Gravitational waves backgrounds. First order cosmological phase transitions.
Pulsar Timing Arrays. Hellings and Downs curve.
Part II : Relativistic Cosmological perturbation theory
Cosmological Perturbation Theory. Scalar-Vector-Tensor decomposition. Gauge Transformations.
Perturbed Einstein's Equations and Boltzmann equations. Perturbed Compton Scattering.
The initial Value problem in Cosmology: Inflation.
Quantization of a free scalar field in de-Sitter. Generation of scalar and tensor perturbations.
Interactions during Inflation: the In-In formalism *
Evolution of cosmological perturbations outside the horizon.
Evolution of cosmological perturbations inside the horizon.
The tight-coupled limit of the baryon-photon fluid. Diffusion damping.
Free streaming and the line-of-sight solution.
The CMB temperature power spectrum.
Polarization from Compton Scattering.
The Boltzmann equation for polarizations.
The E and B mode power spectrum. Evidence for Inflation and Primordial Gravitational Waves.
The Legacy of WMAP and Planck.
Effective field theories for the clustering of dark matter on cosmological scales. UV divergences and counterterms.
Lagrangian Effective field theory of the Large Scale Structure *
Beyond 2-point function correlators *
Topics with an (*) could be covered upon request by the students.
Recap of General Relativity. The Kerr metric.
Metric Perturbations in a flat spacetime. Gauge transformations, the TT gauge.
Propagation and interaction of Gravitational waves with test particles. Proper and detector frames.
The quadrupole formula: radiated energy and angular momentum.
Gravitational waves from the inspiral of compact objects: circular and elliptical orbits. Backreaction.
Discussion of some of the most relevant events detected by LIGO/Virgo/KAGRA.
Gravitational waves from rotating bodies.
Gravitational waves from objects infalling into a black hole. Tidal disruption.
Elements of Post-Newtonian theory. *
Effective Field theory of gravitational radiation from compact objects *.
Black hole perturbation theory*
Stochastic Gravitational waves backgrounds. First order cosmological phase transitions.
Pulsar Timing Arrays. Hellings and Downs curve.
Part II : Relativistic Cosmological perturbation theory
Cosmological Perturbation Theory. Scalar-Vector-Tensor decomposition. Gauge Transformations.
Perturbed Einstein's Equations and Boltzmann equations. Perturbed Compton Scattering.
The initial Value problem in Cosmology: Inflation.
Quantization of a free scalar field in de-Sitter. Generation of scalar and tensor perturbations.
Interactions during Inflation: the In-In formalism *
Evolution of cosmological perturbations outside the horizon.
Evolution of cosmological perturbations inside the horizon.
The tight-coupled limit of the baryon-photon fluid. Diffusion damping.
Free streaming and the line-of-sight solution.
The CMB temperature power spectrum.
Polarization from Compton Scattering.
The Boltzmann equation for polarizations.
The E and B mode power spectrum. Evidence for Inflation and Primordial Gravitational Waves.
The Legacy of WMAP and Planck.
Effective field theories for the clustering of dark matter on cosmological scales. UV divergences and counterterms.
Lagrangian Effective field theory of the Large Scale Structure *
Beyond 2-point function correlators *
Topics with an (*) could be covered upon request by the students.
Prerequisites for admission
Knowledge of General Relativity (Introduction to General Relativity) and Cosmology (Cosmology I). Basic Quantum Mechanics. The Cosmology II class is a plus.
Teaching methods
The course consists of blackboard lectures. Interactions with students, through questions and discussions, are encouraged.
Teaching Resources
Michele Maggiore "Gravitational waves" Vol. 1 and 2
Steven Weinberg "Cosmology"
Scott Dodelson and Fabian Schmidt "Modern Cosmology"
Steven Weinberg "Cosmology"
Scott Dodelson and Fabian Schmidt "Modern Cosmology"
Assessment methods and Criteria
Exercises to be delivered by the end of the classes or at the exams, followed by a short oral discussion.
FIS/02 - THEORETICAL PHYSICS, MATHEMATICAL MODELS AND METHODS - University credits: 3
FIS/05 - ASTRONOMY AND ASTROPHYSICS - University credits: 3
FIS/05 - ASTRONOMY AND ASTROPHYSICS - University credits: 3
Lessons: 42 hours
Professor:
Castorina Emanuele
Professor(s)