Primordial gravitational waves offer unique insights into the inflationary period and subsequent thermal history of the Universe. The spectrum of primordial high-frequency gravitational waves is...Show morePrimordial gravitational waves offer unique insights into the inflationary period and subsequent thermal history of the Universe. The spectrum of primordial high-frequency gravitational waves is highly sensitive to the processes in the early Universe and can be significantly suppressed during an epoch of early matter domination (EMD) induced by new long-lived massive particles. This damping effect is studied with numerical and analytic methods. The relative energy density of gravitational waves today is found to scale with the wavenumber k as k^(-2) for waves crossing the horizon during the EMD epoch. The overall damping between the start and the end of the EMD epoch is given by m^(4/3) Γ^(-2/3)M^(-2/3), where m and Γ are the mass and decay width of the long-lived particles correspondingly, and M is the Planck mass. For concrete examples of EMD, models with inflaton decay and heavy neutral leptons are considered. Experimental observation of stochastic gravitational wave background could probe early cosmological events and constrain new physics scenarios.Show less
In recent years, deep neural networks have attracted the attention of both the academic community and the general public. An effort to theoretically understand the intricacies of these systems is...Show moreIn recent years, deep neural networks have attracted the attention of both the academic community and the general public. An effort to theoretically understand the intricacies of these systems is ongoing and physics-inspired approaches may have a part to play. In this thesis, we will discuss recent results in the theoretical study of deep linear neural networks. This class of neural networks has very limited real-world applications, but it could provide a good training ground for developing theoretical techniques that could prove useful beyond the simple linear case. We will also argue that Fisher information, and in particular “sloppy model” logic, can be a useful tool for future research on deep neural networks, in particular for network architecture optimization.Show less
