Menadeo, Nicola (2025) Probing the Early and Late Universe Through Gravitational Wave Propagation. [Tesi di dottorato]

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• Modelli di università in Europa e la questione dell'autonomia. (deposited 16 Nov 2009 11:57)
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Abstract

The past decade has witnessed a profound transformation in gravitational physics and cosmology, driven by the dawn of gravitational wave (GW) astronomy. The direct detection of GWs by the LIGO–Virgo–KAGRA collaboration has turned Einstein’s century-old prediction into a precision tool for testing gravity in dynamical, strong-field regimes. In parallel, the extraordinary success of the $\Lambda$CDM model in describing the large-scale structure and expansion history of the Universe has highlighted deep conceptual puzzles (most notably the nature of Dark Matter and Dark Energy) that may signal the limits of Einstein's General Relativity (GR) on cosmological scales. These two developments, observational and theoretical, have converged into a new paradigm: using GWs as messengers to test gravity across the entire cosmic history. This thesis explores two critical frontiers enabled by GW astronomy: \begin{itemize} \item \textbf{Probing the Primordial Universe.} Using the propagation of primordial GWs generated by the inflationary mechanism to access the earliest stages of cosmic history. By relaxing the assumption of perfect spatial flatness, this line of research investigates spatially curved cosmologies and examines how even a small curvature can affect GW evolution, leaving distinctive imprints on the primordial spectrum and unveiling information about the Universe’s geometry and initial conditions (Chapter~\ref{chapter:PGWs}). \item \textbf{Testing Gravity in Inhomogeneous Environments.} Analyzing how spacetime inhomogeneities, described by gravitational lenses, can modify the GW propagation through dispersive phenomena providing new methodologies to test GR and alternative theories of gravity (Chapters~\ref{chapter:ch3} and~\ref{chapter:ch4}). \end{itemize} This thesis work is organized as follows. Chapter~\ref{chapter:ch1} outlines the core concepts and formalism of General Relativity that are most relevant to the study of GWs. It presents the linearization of Einstein’s field equations, identifies the physical degrees of freedom associated with GW polarizations, and discusses wave propagation in both Minkowski and general spacetimes. The chapter reviews the main classes of GW sources together with the corresponding detection strategies across the GW frequency spectrum. It concludes with an overview of tests of gravity focusing on emission and propagation of GWs. Chapter~\ref{chapter:ch2} reviews the basic principles of cosmology based on the cosmological principle, focusing on the Friedmann–Lemaître–Robertson–Walker metric consistent with large-scale homogeneity and isotropy. It examines the energy budget of the Universe within the $\Lambda$CDM model including radiation, matter and the cosmological constant $\Lambda$. It follows with a discussion about the conceptual challenges posed by $\Lambda$, which motivate an overview of alternative explanations such as Dark Energy and extensions of Einstein’s gravity. Particular attention is given to scalar–tensor frameworks and the Horndeski class of theories, which provide a broad and consistent arena for exploring deviations from GR. Chapter~\ref{chapter:PGWs} investigates the primordial Universe within the framework of GR. It begins with a pedagogical overview of the inflationary paradigm and its resolution of the horizon and flatness problems. The analysis then challenges the assumption of perfect spatial flatness, exploring the role of spatial curvature in the evolution of primordial GWs generated during inflation. The chapter derives the evolution equations for tensor modes in open, flat, and closed cosmological backgrounds, computes the resulting primordial tensor power spectrum, and assesses the impact of evolving relativistic degrees of freedom. Finally, it discusses the observational consequences, emphasizing that curvature-induced features on the power spectrum could leave measurable imprints accessible to upcoming cosmological observations. Chapter~\ref{chapter:ch3} marks the beginning of the second part of the thesis, moving beyond the homogeneous and isotropic cosmological framework to investigate how spacetime inhomogeneities and modified gravity affect GW propagation. It develops a general framework to describe frequency- and polarization-dependent corrections collectively referred to as Lens-Induced Dispersion (LID), which arise when GWs interact with matter distributions through wave-optics phenomena such as diffraction and dispersion. The formulation is based on the short-wave approximation. The analysis focuses on the Brans–Dicke theory, where the framework is used to analytically compute beyond geometric optics corrections to scalar and tensor perturbations induced by a point-like gravitational lens. The results show that LID effects to the standard GW polarizations constitute a clear and testable signature of modified gravity. Chapter~\ref{chapter:ch4} extends the framework presented in the previous Chapter to more complex mass distributions and to screened scalar–tensor models, focusing in particular on the Symmetron theory. It reviews the Symmetron screening mechanism and the corresponding scalar-field solutions for a homogeneous spherical lens. The chapter computes dispersive corrections for this extended configuration, showing that such a lens induces non-trivial dispersion even for standard GW polarizations in GR. For the Symmetron case, it demonstrates that the scalar field profile can significantly amplify dispersive effects, leading to the emergence of a critical GW frequency beyond which propagation is inhibited, thus offering a novel means of constraining screened modified-gravity models. Chapter~\ref{chapter:conclusions} synthesizes the results across both early- and late-Universe regimes. It summarizes the key contributions of this work, including the analysis of spatial curvature effects on primordial GWs and the development of the LID framework, which reveals the universal nature of dispersive phenomena in curved spacetime.

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