Astrophysics and Cosmology

Experimental bases of Gravitation ------------------------------------------------------- - Inertial mass and gravitational mass, the Newtonian theory of gravitation and the 1/r2 trend of the gravitational field. Experimental checks. Gravity and other forces of nature. Isotropy and homogeneity of space and time. Gravitational red shift. Principle of equivalence in General Relativity. Roll, Krotkov and Dicke experiment. Homogeneity of time. Translation invariance and gravitational red shift. Pound and Rebka experiment. Vessot experiment. Lorentz invariance: the measure of g-2. - Theoretical implications and experimental verifications of the constancy over time of G. Classical verifications of General Relativity. Precession of Mercury, light deflection, radar echo delay. - Parametrized Post-Newtonian (PPN) formalism. Physical meaning of the parameters and their values in General Relativity. PPN tests in the solar system based on light deviation, radar echo delay, interferometry on a large basis, precession of the perihelion of Mercury. Test based on the observation of binary systems. Upper limits on the validity of the strong equivalence principle and lunar ranging experiment. The gravito-magnetic effect and the experimental basis for its detection. Gravitational waves and their effect on matter ------------------------------------------------------- - Gravitational Waves (GWs) as solutions of the Einstein equations. Effect on test masses. Intensity and brightness of the source. Generation of GWs: bond with the mass quadrupole moment, oscillating quadrupole and rotating quadrupole. Reduction of the orbital period by GW emission: the emblematic case of the PSR1913 + 16 system and the new double systems.Notes on astrophysical sources of GWs: coalescence of binary systems, rotating neutron stars, stellar collapse. Astrophysical and cosmological GW background. GW Detectors - Noise in measuring instruments. Stochastic processes. Average, variance, correlation, autocorrelation. Harmonic process. Poisson process. Stochastic process transformations. Systems without memory. Linear transformations. - Power spectrum. Fluctuation-Dissipation Theorem. Thermal noise in the circuits. Thermal noise in a pendulum. Attenuation of the seismic noise and of the thermal noise: the suspension systems. Wideband optical detectors ------------------------------------------------------- - Michelson interferometer and Fabry-Perot cavity. Light recirculation. Opto-mechanical systems with feedback: Pound-Drever-Hall technique for Fabry-Perot cavity control. Shot and radiation pressure noise reduction. Power and Signal Recycling. The Newtonian noise. Quantum limit of gravitational detectors and strategies to bypass this issue. Space detectors and pulsar timing technique. ------------------------------------------------------- Data Analysis: Theory and Applications ------------------------------------------------------- Elements of probability and statistics. Signals (continuous and discrete) and noise; Fourier transform. Spectral estimation (periodogram, auto-regressive estimates, spectrograms). The signal-to-noise ratio and the linear data filtering problem. Filtering (Wiener filter, adapted filter, triangular filters). Detection theory. Procedure in non-stationary noise. Image analysis. GW signal extraction. Parameter estimation. GW sources. Analysis of the open data collected by the LIGO-Virgo interferometric detectors (https://www.gw openscience.org/).

Basics Physics topics, matured through the standard courses during the three-year Bachelor in physics. Very useful also the knowledge of basic statistics tools and probability concepts. Tensor algebra is also used on some topics and is certainly quite useful.

• L. Landau, E.Lifshitz, Teoria dei campi, Editori Riuniti • Ciufoli, J. A. Wheeler : Gravitation and Inertia, Princeton University Press, 1995 • A. Papoulis, S. Unnikrishna Pillai , Probability, Random Variables and Stochastic Processes, McGraw-Hill, 2002 • H. C. Ohanian, R. Ruffini Gravitazione e spazio-tempo, Zanichelli, 1997 • Clifford M. Will, Theory and Experiment in Gravitational Physics, Cambridge University Press • P. Saulson, Fundamentals of Interferometric Detection of Gravitational waves, World Scientific 1994 • C.Will, Was Einstein Right? Testing Relativity at the Centenary; gr-qc/0504086 • C.M.Will, The Confrontation between General Relativity and Experiment; gr-qc/0103036 • E.G. Adelberger, B.R. Heckel, and A.E. Nelson: Tests of the Gravitational Inverse- Square law; ArXiv:hep-ph/0307284 • G.Pizzella, Fisica Sperimentale del Campo Gravitazionale, Nuova Italia, 1993 • A.M.Nobili, Precise gravitation measurements on Earth and in space: Tests of the Equivalence Principle - http://eotvos.dm.unipi.it/nobili/murst/varenna2000/nobili2.pdf • Fulvio Ricci’s notes: https://sites.google.com/a/uniroma1.it/fulvio-ricci/didattica/gravitazione-sperimentale • Sergio Frasca’s notes: https://drive.google.com/drive/folders/1-GfrpXDVYO5wj0MjcQoJKdma8SXrt_XN

optional but highly recommended

The exam consists of an oral dissertation on specific themes treated during the course and a dedicated in-depth presentation.