General

CONTENUTI: Elementi di Relatività Generale. Concetti base di astrofisica necessari per il corso. Principio cosmologico; metrica di Robertson e Walker, redshift, orizzonti; equazioni di Friedmann, modelli cosmologici con materia, radiazione e costante cosmologica; cosmologia osservativa: distanza di luminosità, distanza dal diametro angolare, conteggi di sorgenti, intensità specifica e redshift, assorbimento della radiazione; universo primordiale: lo Standard Big Bang, scale di energia, termodinamica, neutrini, nucleosintesi, bariogenesi; ricombinazione. Inflazione: problemi dello Standard Big Bang, elementi di teoria dei campi, relazione tra massa-energia e pressione, transizioni di fase, old e new inflation, dinamica dell'inflatone, slow roll e reheating; la costante cosmologica ed i problemi ad essa connessi, quintessenza.

CONTENT: (Details can change during the lectures)

 Introduction to General Relativity and basic astrophysics.

The metric of Robertson and Walker: expansion of the Universe and the cosmological principle,  comoving coordinates, scale factor, derivation of Robertson and Walker metrics . Topology of the Universe: cases k = 0, -1, +1. Proper distance, Hubble's law, the Hubble parameter, Hubble  radius , deceleration parameter. Conformal time , redshift and its interpretation.  Particle and  events Horizons. The  Milne model.

Cosmological models: Friedmann equations. Density of the universe, various contributions, existence of baryonic and non-baryonic dark matter, the contribution of the cosmological constant. Peculiar motions. The equation of state. Relations between the cosmological parameters, evolution of the Hubble parameter. The three epochs of the Universe. The Hubble time. Evolution of the density parameter (flatness problem) and the deceleration parameter. Qualitative and quantitative classification of cosmological models,  depending on the values of k and the cosmological constant. Our Universe. The age of the Universe. Horizons and cosmological models. Radial coordinate r as a function of redshift for different cosmological models.

Observational cosmology: Different kinds of distances. Luminosity distance, distance modulus, Hubble diagram, supernovae SNIa. Angular diameters and angular diameter distance, redhift-angle test , observational results, sound horizon, and its use as a standard rule, the horizon problem. Source counts. Specific intensity and redshift. Brightness of the sky background, Olbers paradox, radiation absorption, optical depth, Gunn-Peterson limit , reionization of the Universe.

The Standard Hot Big Bang: Basic observational evidences; particles, forces, couplings and their energy dependence, axions; grand unification; supersymmetry; Planck epoch. Thermodynamics of the early Universe: numerical density, density of mass-energy, pressure, ultra-relativistic  and non-relativistic cases, the total number of degrees of freedom; conditions for the thermodynamic equilibrium; entropy, entropy density, decoupling of relativistic particles and their temperature. Neutrino temperature, number density of photons and neutrinos today.  Cosmic relics:  "hot" dark matter (HDM) and its cosmological contribution ;  "warm" dark matter (WDM);  "cold" dark matter (CDM), freezing comoving density,  Lee - Weinberg limit; neutralino, DAMA experiment and  counts modulation. Recombination and decoupling of photons. Cosmological nucleosynthesis. Primordial baryogenesis : the three Sakharov conditions.

 Inflation: reminder of the horizon and flatness problems, the problem of monopoles; paradigm of inflation, expansion factor required to solve these problems. Equation of state and conditions for inflation. Spontaneous symmetry breaking and phase transitions,  true and false vacua, old inflation, new inflation,  slow-roll conditions, rapid oscillations and reheating. Orders of magnitude of energies and times involved. iInflaton's dynamic, number of e-foldings. Solution of  horizon and flatness problems.

Cosmological constant and dark energy: relativistic invariance of the equation of state of vacuum, estimate the  mass-energy density of the vacuum, the cosmological constant problem. Scalar fields that vary over time, quintessence equation of state and evolution; example: Ratra and Peebles potential .

SVOLGIMENTO DELL'ESAME ORALE: lo studente, durante i primi 15 minuti, espone, possibilmente in modo completo, un argomento a scelta trattato nel corso. Seguono poi le domande del docente.

ORAL EXAM: During the first 15 minutes the student speaks on a topic chosen by himself ; then we go on with my questions. Total time 45-60 minutes.