# GRAVITATIONAL WAVES

OVERVIEW

The course presents the physics of gravitational waves, framing it in the context of the theory of general relativity, describing the experimental and data analysis techniques used for their observation and discussing their contribution in the field of astroparticle physics, astrophysics, cosmology and fundamental physics.

## AIMS AND CONTENT

LEARNING OUTCOMES

The course gives an updated overview on the activity of experimental research in the theory of gravitation based on its fundamentals (test of the weak equivalence principle: Eötvös experiment, experiment Roll, Dicke and Krotkov; experiment Braginsky and Panov) up to recent interferometric detectors of gravitational waves (Fabry-Perot interferometers with the cavity, the optical design of Virgo, noise sources and mitigation strategies, data analysis techniques). Part of the course is dedicated to gravitational astrophysics elements (compact astrophysical objects, rotating neutron stars, stellar collapse), with particular reference to general relativity tests.

AIMS AND LEARNING OUTCOMES

The course is aimed at students interested in the particular scientific topic of gravitational wave research, as well as those interested in a path in the field of astroparticle physics, astrophysics and cosmology. The course content is also a useful complement for students interested in the physics of fundamental interactions, as it concerns gravity physics issues not always covered in the curricular pathways. The elements of astrophysics, cosmology, classical optics, quantum optics and the data analysis techniques covered in the lessons provide a useful knowledge base also for the study of disciplines other than that covered by the course.

To achieve its objective, the course - of 48 hours in total - is structured in three modules of 16 hours each:

- Elements of general relativity and gravitational wave sources

The objective of this module is to provide students with the fundamental elements of the theory of general relativity, necessary for the study of the physics of gravitational waves. In addition to acquiring the fundamental concepts and tools of the theory, students will be able to understand the mechanisms underlying the generation of gravitational waves, useful for deepening the study of astrophysical sources, as well as the mechanisms of interaction of a gravitational wave with test masses, an essential prerequisite for understanding interferometric detection techniques.

- Interferometric detectors of gravitational waves and advanced detection techniques

The aim of this module is to provide students with a realistic description of the interferometric detection techniques of gravitational waves, starting from elements of classical optics, up to the study of advanced detection strategies based on on quantum optics techniques. Furthermore, the module deals with the study of the main noise sources that limit the sensitivity of the interferometer and the mitigation strategies adopted, with references to statistical physics (fluctuation-dissipation theorem) and the theory of quantum fluctuations (quantum noise). At the end of the module students will be able to read and deepen independently the technical/scientific literature on the subject.

- Elements of analysis of stochastic processes and data analysis strategies

The objective of this module is to provide students with the elements necessary to understand the advanced data analysis techniques used in experiments dedicated to the observation of gravitational waves. Starting from elements of probability and statistics, the course deals with the study of techniques used in the analysis of time series dominated by noise (Bayesian inference, adaptive filters, machine learning) to arrive at the discussion of the significance of the observed events. At the end of the module, students will be able to read and deepen the scientific literature on the subject independently.

PREREQUISITES

Three-year fundamental physics courses. Special relativity theory and tensor algebra in Minkowski space. Elements of probability and statistics covered in the three-year courses. Knowledge of elements of classical optics would be useful, but it is not considered an essential prerequisite.

Teaching methods

Theoretical frontal lessons. During the lessons, if possible, a visit to the Virgo interferometer will be organized.

SYLLABUS/CONTENT

- Elements of general relativity

Principle of equivalence. Tensor algebra. Tensorial equations. Geodesic curves. Covariant derivative. Geodesic deviation and curvature. Riemann tensor. Energy-momentum tensor. Einstein's equation. Weak field limit.

- Linear approximation and gravitational waves

Gravitational waves as solutions of Einstein's equations. Expression in Transverse-Traceless gauge and in the laboratory system. Effect on test masses. Generation of gravitational waves in linear approximation; quadrupole formula. Intensity and brightness of a gravitational wave source.

- Elements of gravitational astrophysics

Gravitational waves generated by compact binary systems in linear approximation. Back-action of the gravitational wave on the orbital dynamics of the system. Binary systems at cosmological distances. Standard candles and elements of gravitational cosmology.

- Interferometric gravitational wave detectors

A simple Michelson interferometer. Interferometers with Fabry-Pérot cavity. Power recycling. Virgo's optical scheme. Modes of propagation of laser beams, stability criteria for optical cavities. Thermal aberrations and mitigation methods. Noise sources and mitigation strategies (quantum noise; fluctuation-dissipation theorem and thermal noise; seismic noise; Newtonian noise). Interferometer control strategies: Pound-Drever-Hall technique, control of longitudinal degrees of freedom, control of angular degrees of freedom, locking. DC read-out. Elements of quantum optics, signal recycling, squeezing.

- Elements of analysis of stochastic processes

Introduction to data analysis; elements of probability; estimators. Bayes' theorem. Definition and properties of Power Spectral Density. Stochastic processes and their characterization; Gaussian processes. Linear systems. Hypothesis test. Matched filtering in linear systems and in general. Detection theory: parameter estimation; templates; checking the consistency of the waveforms; coherent analysis of two detectors. False alarm rate. Sampling in the parameter space. Notes on calculation problems. Location of the source; overview on sources and alternative methods to the matched filter. "First Detection". Population of events and merge rates. Elements of post-Newtonian formalism; tests of General Relativity. Deformability measurements for Neutron Stars and Equation of State limits through GW measurements. Notes on multi-messenger astronomy.

RECOMMENDED READING/BIBLIOGRAPHY

T.A. Moore, A General Relativity Workbook, University Science Books (2013)

M. Maggiore, Gravitational Waves. Volume 1: Theory and Experiments, Oxford University Press (2008)

PR Saulson, Fundamentals of Interferometric Gravitational WaveDetectors, World Scientific (1994)

M. Bassan (Ed.), Advanced Interferometers and the Search forGravitational Waves, Springer (2014)

J. D. E. Creighton, W. G. Anderson, Gravitational-Wave Physics and Astronomy: An Introduction to Theory, Experiment and Data Analysis, Wiley (2011)

## TEACHERS AND EXAM BOARD

Exam Board

GIANLUCA GEMME (President)

FIODOR SORRENTINO

ANDREA CHINCARINI

## LESSONS

Teaching methods

Theoretical frontal lessons. During the lessons, if possible, a visit to the Virgo interferometer will be organized.

LESSONS START

Second semester AY 2020/2021

## EXAMS

Exam description

Interview on the topics covered in the course starting from a topic chosen by the student.

Assessment methods

Oral exam starting from a topic chosen by the student and questions on the topics covered in the course. During the interview, the commission tries to stimulate the student to elaborate links between the topics and the information acquired during the course (and in the three-year courses) to evaluate the degree of learning, the synthesis ability and the clarity of the exposition.

## FURTHER INFORMATION

The students can agree on the reception hours by contacting the teachers by e-mail.

GEMME GIANLUCA

gianluca.gemme@ge.infn.it

CHINCARINI ANDREA

andrea.chincarini@ge.infn.it

SORRENTINO FIODOR

fiodor.sorrentino@ge.infn.it