Unveiling the expansion history of the universe with cosmic chronometers and gravitational waves

This Thesis explores two novel and independent cosmological probes, Cosmic Chronometers (CCs) and Gravitational Waves (GWs), to measure the expansion history of the Universe. CCs provide direct and cosmology-independent measurements of the Hubble parameter H(z) up to z∼2. In parallel, GWs provide a direct measurement of the luminosity distance without requiring additional calibration, thus yielding a direct measurement of the Hubble constant H0=H(z=0). This Thesis extends the methodologies of both of these probes to maximize their scientific yield. This is achieved by accounting for the interplay of cosmological and astrophysical parameters to derive them jointly, study possible degeneracies, and eventually minimize potential systematic effects. As a legacy value, this work also provides interesting insights into galaxy evolution and compact binary population properties. The first part presents a detailed study of intermediate-redshift passive galaxies as CCs, with a focus on the selection process and the study of their stellar population properties using specific spectral features. From their differential aging, we derive a new measurement of the Hubble parameter H(z) and thoroughly assess potential systematics. In the second part, we develop a novel methodology and pipeline to obtain joint cosmological and astrophysical population constraints using GWs in combination with galaxy catalogs. This is applied to GW170817 to obtain a measurement of H0. We then perform realistic forecasts to predict joint cosmological and astrophysical constraints from black hole binary mergers for upcoming gravitational wave observatories and galaxy surveys. Using these two probes we provide an independent reconstruction of H(z) with direct measurements of H0 from GWs and H(z) up to z∼2 from CCs and demonstrate that they can be powerful independent probes to unveil the expansion history of the Universe.

Cosmological perturbations in generalized theories of gravity

The first part of the thesis concerns the study of inflation in the context of a theory of gravity called "Induced Gravity" in which the gravitational coupling varies in time according to the dynamics of the very same scalar field (the "inflaton") driving inflation, while taking on the value measured today since the end of inflation. Through the analytical and numerical analysis of scalar and tensor cosmological perturbations we show that the model leads to consistent predictions for a broad variety of symmetry-breaking inflaton's potentials, once that a dimensionless parameter entering into the action is properly constrained. We also discuss the average expansion of the Universe after inflation (when the inflaton undergoes coherent oscillations about the minimum of its potential) and determine the effective equation of state. Finally, we analyze the resonant and perturbative decay of the inflaton during (p)reheating. The second part is devoted to the study of a proposal for a quantum theory of gravity dubbed "Horava-Lifshitz (HL) Gravity" which relies on power-counting renormalizability while explicitly breaking Lorentz invariance. We test a pair of variants of the theory ("projectable" and "non-projectable") on a cosmological background and with the inclusion of scalar field matter. By inspecting the quadratic action for the linear scalar cosmological perturbations we determine the actual number of propagating degrees of freedom and realize that the theory, being endowed with less symmetries than General Relativity, does admit an extra gravitational degree of freedom which is potentially unstable. More specifically, we conclude that in the case of projectable HL Gravity the extra mode is either a ghost or a tachyon, whereas in the case of non-projectable HL Gravity the extra mode can be made well-behaved for suitable choices of a pair of free dimensionless parameters and, moreover, turns out to decouple from the low-energy Physics.

Parameter estimation in a growth model for a biological population

The motivating problem concerns the estimation of the growth curve of solitary corals that follow the nonlinear Von Bertalanffy Growth Function (VBGF). The most common parameterization of the VBGF for corals is based on two parameters: the ultimate length L∞ and the growth rate k. One aim was to find a more reliable method for estimating these parameters, which can capture the influence of environmental covariates. The main issue with current methods is that they force the linearization of VBGF and neglect intra-individual variability. The idea was to use the hierarchical nonlinear model which has the appealing features of taking into account the influence of collection sites, possible intra-site measurement correlation and variance heterogeneity, and that can handle the influence of environmental factors and all the reliable information that might influence coral growth. This method was used on two databases of different solitary corals i.e. Balanophyllia europaea and Leptopsammia pruvoti, collected in six different sites in different environmental conditions, which introduced a decisive improvement in the results. Nevertheless, the theory of the energy balance in growth ascertains the linear correlation of the two parameters and the independence of the ultimate length L∞ from the influence of environmental covariates, so a further aim of the thesis was to propose a new parameterization based on the ultimate length and parameter c which explicitly describes the part of growth ascribable to site-specific conditions such as environmental factors. We explored the possibility of estimating these parameters characterizing the VBGF new parameterization via the nonlinear hierarchical model. Again there was a general improvement with respect to traditional methods. The results of the two parameterizations were similar, although a very slight improvement was observed in the new one. This is, nevertheless, more suitable from a theoretical point of view when considering environmental covariates.

Model reduction of stochastic groundwater flow and transport processes

This work presents a comprehensive methodology for the reduction of analytical or numerical stochastic models characterized by uncertain input parameters or boundary conditions. The technique, based on the Polynomial Chaos Expansion (PCE) theory, represents a versatile solution to solve direct or inverse problems related to propagation of uncertainty. The potentiality of the methodology is assessed investigating different applicative contexts related to groundwater flow and transport scenarios, such as global sensitivity analysis, risk analysis and model calibration. This is achieved by implementing a numerical code, developed in the MATLAB environment, presented here in its main features and tested with literature examples. The procedure has been conceived under flexibility and efficiency criteria in order to ensure its adaptability to different fields of engineering; it has been applied to different case studies related to flow and transport in porous media. Each application is associated with innovative elements such as (i) new analytical formulations describing motion and displacement of non-Newtonian fluids in porous media, (ii) application of global sensitivity analysis to a high-complexity numerical model inspired by a real case of risk of radionuclide migration in the subsurface environment, and (iii) development of a novel sensitivity-based strategy for parameter calibration and experiment design in laboratory scale tracer transport.

In vitro characterisation and expansion of human regulatory T cells for their in vivo application in the induction of tolerance in haematopoietic stem cell and solid organ transplantation

Solid organ transplantation (SOT) is considered the treatment of choice for many end-stage organ diseases. Thus far, short term results are excellent, with patient survival rates greater than 90% one year post-surgery, but there are several problems with the long term acceptance and use of immunosuppressive drugs. Hematopoietic Stem Cells Transplantation (HSCT) concerns the infusion of haematopoietic stem cells to re-establish acquired and congenital disorders of the hematopoietic system. The main side effect is the Graft versus Host Disease (GvHD) where donor T cells can cause pathology involving the damage of host tissues. Patients undergoing acute or chronic GvHD receive immunosuppressive regimen that is responsible for several side effects. The use of immunosuppressive drugs in the setting of SOT and GvHD has markedly reduced the incidence of acute rejection and the tissue damage in GvHD however, the numerous adverse side effects observed boost the development of alternative strategies to improve the long-term outcome. To this effect, the use of CD4+CD25+FOXP3+ regulatory T cells (Treg) as a cellular therapy is an attractive approach for autoimmunity disease, GvHD and limiting immune responses to allograft after transplantation. Treg have a pivotal role in maintaining peripheral immunological tolerance, by preventing autoimmunity and chronic inflammation. Results of my thesis provide the characterization and cell processing of Tregs from healthy controls and patients in waiting list for liver transplantation, followed by the development of an efficient expansion-protocol and the investigation of the impact of the main immunosuppressive drugs on viability, proliferative capacity and function of expanded cells after expansion. The conclusion is that ex vivo expansion is necessary to infuse a high Treg dose and although many other factors in vivo can contribute to the success of Treg therapy, the infusion of Tregs during the administration of the highest dose of immunosuppressants should be carefully considered.

NLGA based Active Control in Aerospace: fault tolerability, disturbance rejection, and parameter estimation

A new control scheme has been presented in this thesis. Based on the NonLinear Geometric Approach, the proposed Active Control System represents a new way to see the reconfigurable controllers for aerospace applications. The presence of the Diagnosis module (providing the estimation of generic signals which, based on the case, can be faults, disturbances or system parameters), mean feature of the depicted Active Control System, is a characteristic shared by three well known control systems: the Active Fault Tolerant Controls, the Indirect Adaptive Controls and the Active Disturbance Rejection Controls. The standard NonLinear Geometric Approach (NLGA) has been accurately investigated and than improved to extend its applicability to more complex models. The standard NLGA procedure has been modified to take account of feasible and estimable sets of unknown signals. Furthermore the application of the Singular Perturbations approximation has led to the solution of Detection and Isolation problems in scenarios too complex to be solved by the standard NLGA. Also the estimation process has been improved, where multiple redundant measuremtent are available, by the introduction of a new algorithm, here called "Least Squares - Sliding Mode". It guarantees optimality, in the sense of the least squares, and finite estimation time, in the sense of the sliding mode. The Active Control System concept has been formalized in two controller: a nonlinear backstepping controller and a nonlinear composite controller. Particularly interesting is the integration, in the controller design, of the estimations coming from the Diagnosis module. Stability proofs are provided for both the control schemes. Finally, different applications in aerospace have been provided to show the applicability and the effectiveness of the proposed NLGA-based Active Control System.