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There is some observational evidence that the dark energy may not be smooth on large scales. This makes it worth while to try and get as simple and as intuitive a picture of how dark energy perturbations behave so as to be able to better…

Cosmological perturbation theory is crucial for our understanding of the universe. The linear theory has been well understood for some time, however developing and applying the theory beyond linear order is currently at the forefront of…

The recent robust and homogeneous analysis of the world's supernova distance-redshift data, together with cosmic microwave background and baryon acoustic oscillation data, provides a powerful tool for constraining cosmological models. Here…

In modern cosmology, the discovery of the universe's accelerated expansion has significantly transformed our understanding of cosmic evolution and expansion history. The unknown properties of dark energy, the driver of this acceleration,…

The normal mode model is important in computational atmospheric acoustics. It is often used to compute the atmospheric acoustic field under a harmonic point source. Its solution consists of a set of discrete modes radiating into the upper…

Detailed knowledge of the primordial power spectrum of curvature perturbations is essential both in order to elucidate the physical mechanism (`inflation') which generated it, and for estimating the cosmological parameters from observations…

We develop a higher-order perturbation theory for large-scale structure formation involving a free-streaming hot or warm dark matter species. We focus on the case of mixed cold dark matter and massive neutrinos, although our approach is…

Observational searches for large-scale vorticity modes in the late time Universe are underexplored. Within the standard $\Lambda$CDM model, this is well motivated given the observed properties of the cosmic microwave background (CMB).…

Scale transformations have played an extremely successful role in studies of cosmological large-scale structure by relating the non-linear spectrum of cosmological density fluctuations to the linear primordial power at longer wavelengths.…

Increasingly accurate observations are driving theoretical cosmology toward the use of more sophisticated descriptions of matter and the study of nonlinear perturbations of FL cosmologies, whose governing equations are notoriously…

The increasing integration of power electronic devices is driving the development of more advanced tools and methods for the modeling, analysis, and control of modern power systems to cope with the different time-scale oscillations. In this…

Interacting dark sector (IDS) models provide a commonly explored extension of the standard $\Lambda$CDM cosmology, allowing for non-gravitational energy--momentum exchange between cold dark matter (CDM) and dark energy (DE). Although such…

We investigate a cosmological scenario in which the dark matter particles can be created during the evolution of the Universe. By regarding the Universe as an open thermodynamic system and using non-equilibrium thermodynamics, we examine…

We investigate the role played by symmetries in the perturbative expansion of the large-scale structure. In particular, we establish which of the coefficients of the perturbation theory kernels are dictated by symmetries and which not. Up…

Exponential divided differences arise in numerical linear algebra, matrix-function evaluation, and quantum Monte Carlo simulations, where they serve as kernel weights for time evolution and observable estimation. Efficient and numerically…

The use of Variational Autoencoders in different Machine Learning tasks has drastically increased in the last years. They have been developed as denoising, clustering and generative tools, highlighting a large potential in a wide range of…

Computational procedures for the stationary probability distribution, the group inverse of the Markovian kernel and the mean first passage times of an irreducible Markov chain, are developed using perturbations. The derivation of these…

In this thesis, we discuss some of the applications of cosmological perturbation theory in the late universe. We begin by reviewing the tools used to understand the standard model of cosmology theoretically and to compute its observational…

Combining cosmological probes has consolidated the standard cosmological model with percent precision, but some tensions have recently emerged when certain parameters are estimated from the local or primordial Universe. The origin of this…

In this paper we introduce PERTURB-c, a correlation-aware framework for interpreting black box regression models with one-dimensional structured inputs. We demonstrate this framework on a simulated case study with machine learning based…