Francesco Bajardi


Assegnista in: SPACE (SPACE)

Titolo del progetto di ricerca: Foundations and Symmetries in Classical and Quantum Gravity, with Applications to Cosmology and Astrophysics

The main objective of the project is to investigate theories of gravity and related cosmological models, by searching for Noether symmetries. The existence of them allows: i) to fix the form of the interaction Lagrangians ii) to reduce dynamics and find, eventually, exact solutions iii) to compare these solutions with experimental data iv) to develop the quantum formalism and recover observable universes in the classical limit. According to this program, the existence of symmetries can be considered as a selection rule to discriminate between physical and unphysical theories and a sort of inverse scattering approach to reconstruct physically motivated models both at quantum and classical levels. The problem is urgent, from fundamental and cosmological points of view, because such modified theories represent a large class of alternatives to Einstein’s GR. Due to this state of art, general criterions to derive physically motivated models are required. Moreover, the presence of symmetries also allows to develop the Hamiltonian description, based on the Arnowitt-Deser-Misner (ADM) formalism, thank to which a Schroedinger-like equation for the gravitational field can be obtained. The latter is the so called Wheeler-DeWitt (WDW) equation, whose solution in cosmology is the Wave Function of the Universe. Despite this formalism is far from being a full theory of quantum gravity, it aims to find the initial conditions of our classical Universe, from which its evolution started. The application to cosmology gained great success, since could represent the semiclassical limit of a full, yet unknown, grand unified theory. Reducing the dynamics of the system, the Noether theorem implies the existence of a subset of analytic solutions of the WDW equation, where oscillating wave functions are physical information could permanently disappear inside, allowing many physical states to devolve into the same state. This is called “information paradox” and represents a serious problem in the interpretation of BHs. These kind of problems arise when GR is combined with Quantum Field Theory adopting a semi-classical approach, namely when gravity is considered at the classical level and matter at the quantum level selected (according to the Hartle Criterion). Consequently, by means of Hamilton-Jacobi equations, classical trajectories can be found even without solving the equations of motion directly.