Enlargements of Categories

In order to apply nonstandard methods to modern algebraic geometry, as a first step in this paper we study the applications of nonstandard constructions to category theory. It turns out that many categorial properties are well behaved under enlargements.Comment: 34 page

Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory

The goal of this present manuscript is to introduce the reader to the nonstandard method and to provide an overview of its most prominent applications in Ramsey theory and combinatorial number theory.Comment: 126 pages. Comments welcom

Cosmology intertwined: a review of the particle physics, astrophysics, and cosmology associated with the cosmological tensions and anomalies

The standard ¿ Cold Dark Matter (¿CDM) cosmological model provides a good description of a wide range of astrophysical and cosmological data. However, there are a few big open questions that make the standard model look like an approximation to a more realistic scenario yet to be found. In this paper, we list a few important goals that need to be addressed in the next decade, taking into account the current discordances between the different cosmological probes, such as the disagreement in the value of the Hubble constant , the – tension, and other less statistically significant anomalies. While these discordances can still be in part the result of systematic errors, their persistence after several years of accurate analysis strongly hints at cracks in the standard cosmological scenario and the necessity for new physics or generalisations beyond the standard model. In this paper, we focus on the tension between the Planck CMB estimate of the Hubble constant and the SH0ES collaboration measurements. After showing the evaluations made from different teams using different methods and geometric calibrations, we list a few interesting new physics models that could alleviate this tension and discuss how the next decade's experiments will be crucial. Moreover, we focus on the tension of the Planck CMB data with weak lensing measurements and redshift surveys, about the value of the matter energy density , and the amplitude or rate of the growth of structure (). We list a few interesting models proposed for alleviating this tension, and we discuss the importance of trying to fit a full array of data with a single model and not just one parameter at a time. Additionally, we present a wide range of other less discussed anomalies at a statistical significance level lower than the – tensions which may also constitute hints towards new physics, and we discuss possible generic theoretical approaches that can collectively explain the non-standard nature of these signals. Finally, we give an overview of upgraded experiments and next-generation space missions and facilities on Earth that will be of crucial importance to address all these open questionsPeer ReviewedArticle signat per 202 autors/esPostprint (published version

Advances in Fundamental Physics

This Special Issue celebrates the opening of a new section of the journal Foundation: Physical Sciences. Theoretical and experimental studies related to various areas of fundamental physics are presented in this Special Issue. The published papers are related to the following topics: dark matter, electron impact excitation, second flavor of hydrogen atoms, quantum antenna, molecular hydrogen, molecular hydrogen ion, wave pulses, Brans-Dicke theory, hydrogen Rydberg atom, high-frequency laser field, relativistic mean field formalism, nonlocal continuum field theories, parallel universe, charge exchange, van der Waals broadening, greenhouse effect, strange and unipolar electromagnetic pulses, quasicrystals, Wilhelm-Weber’s electromagnetic force law, axions, photoluminescence, neutron stars, gravitational waves, diatomic molecular spectroscopy, information geometric measures of complexity. Among 21 papers published in this Special Issue, there are 5 reviews and 16 original research papers

Cosmology with underdensities of the cosmic web

This thesis explores the utilisation of underdense regions of the Cosmic Web as a tool for studying cosmology. Underdensities, known as cosmic voids, provide a complementary approach for understanding the large-scale structure of our Universe, as well as providing a unique environment to explore the effects of dark energy. An application of the spherical model to void evolution is presented, showcasing its ability to provide non-linear density and velocity profiles for voids. This methodology is then applied in order to reconstruct the initial conditions of the void using a late-time void density profile. Using this reconstruction, the spherical model yields non-linear late-time velocity profiles which are used to predict redshift-space distortions around voids, showing the capacity to constrain cosmological parameters using measurements in the non-linear regime. Furthermore, this thesis investigates how cosmologists can utilise the advances of weak gravitational lensing to exploit the underdensities of the Universe. A study of the weak lensing measurement around voids is presented with a focus on the SLICS simulation suite and the KiDS and GAMA surveys. A watershed void finding algorithm, zobov, is applied to both the simulations and data, showing that the geometry of the GAMA survey does not lend well to extracting a weak lensing signal from voids due to limitations from both the survey volume and geometry. In contrast, projected underdensities, known as troughs, and the full, projected density spectrum, known as Density Split Statistics, are both shown to yield great potential as cosmological tools. The final chapter of this thesis investigates the use of this novel approach to explore non-ΛCDM cosmologies using the cosmo-SLICS simulations, showing how underdensities can potentially constrain the equation-of-state of dark energy with a higher precision than overdense regions. Chapter 1 of this thesis provides a brief overview of cosmology, while Chapter 2 introduces the theory of weak gravitational lensing. Chapter 3 discusses the spherical model applied to void evolution and redshift-space distortions around voids, while Chapter 4 explores the weak gravitational lensing signal around voids in simulations and data. Chapter 5 utilises a suite of simulations to investigate the sensitivity of Density Split Statistics to dark energy models

Cosmology intertwined: A review of the particle physics, astrophysics, and cosmology associated with the cosmological tensions and anomalies

The standard Cold Dark Matter (CDM) cosmological model provides a good description of a wide range of astrophysical and cosmological data. However, there are a few big open questions that make the standard model look like an approximation to a more realistic scenario yet to be found. In this paper, we list a few important goals that need to be addressed in the next decade, taking into account the current discordances between the different cosmological probes, such as the disagreement in the value of the Hubble constant H0, the σ8–S8 tension, and other less statistically significant anomalies. While these discordances can still be in part the result of systematic errors, their persistence after several years of accurate analysis strongly hints at cracks in the standard cosmological scenario and the necessity for new physics or generalisations beyond the standard model. In this paper, we focus on the 5.0 σ tension between the Planck CMB estimate of the Hubble constant H0 and the SH0ES collaboration measurements. After showing the H0 evaluations made from different teams using different methods and geometric calibrations, we list a few interesting new physics models that could alleviate this tension and discuss how the next decade’s experiments will be crucial. Moreover, we focus on the tension of the Planck CMB data with weak lensing measurements and redshift surveys, about the value of the matter energy density m, and the amplitude or rate of the growth of structure (σ8, f σ8). We list a few interesting models proposed for alleviating this tension, and we discuss the importance of trying to fit a full array of data with a single model and not just one parameter at a time. Additionally, we present a wide range of other less discussed anomalies at a statistical significance level lower than the H0–S8 tensions which may also constitute hints towards new physics, and we discuss possible generic theoretical approaches that can collectively explain the non-standard nature of these signals. Finally, we give an overview of upgraded experiments and next-generation space missions and facilities on Earth that will be of crucial importance to address all these open questions

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 24th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2021, which was held during March 27 until April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The 28 regular papers presented in this volume were carefully reviewed and selected from 88 submissions. They deal with research on theories and methods to support the analysis, integration, synthesis, transformation, and verification of programs and software systems