Beyond the Cosmological Standard Model

After a decade and a half of research motivated by the accelerating universe, theory and experiment have a reached a certain level of maturity. The development of theoretical models beyond \Lambda, or smooth dark energy, often called modified gravity, has led to broader insights into a path forward, and a host of observational and experimental tests have been developed. In this review we present the current state of the field and describe a framework for anticipating developments in the next decade. We identify the guiding principles for rigorous and consistent modifications of the standard model, and discuss the prospects for empirical tests. We begin by reviewing attempts to consistently modify Einstein gravity in the infrared, focusing on the notion that additional degrees of freedom introduced by the modification must screen themselves from local tests of gravity. We categorize screening mechanisms into three broad classes: mechanisms which become active in regions of high Newtonian potential, those in which first derivatives become important, and those for which second derivatives are important. Examples of the first class, such as f(R) gravity, employ the familiar chameleon or symmetron mechanisms, whereas examples of the last class are galileon and massive gravity theories, employing the Vainshtein mechanism. In each case, we describe the theories as effective theories. We describe experimental tests, summarizing laboratory and solar system tests and describing in some detail astrophysical and cosmological tests. We discuss future tests which will be sensitive to different signatures of new physics in the gravitational sector. Parts that are more relevant to theorists vs. observers/experimentalists are clearly indicated, in the hope that this will serve as a useful reference for both audiences, as well as helping those interested in bridging the gap between them.Comment: 175 pages, 24 figures. v2: Minor corrections, added references. Review article, comments welcom

Spatial variations of the fine-structure constant in symmetron models

We investigate the variation of the fine-structure constant, {\alpha}, in symmetron models using N-body simulations in which the full spatial distribution of {\alpha} at different redshifts has been calculated. In particular, we obtain simulated sky maps for this variation, and determine its power spectrum. We find that in high-density regions of space (such as deep inside dark matter halos) the value of {\alpha} approaches the value measured on Earth. In the low-density outskirts of halos the scalar field value can approach the symmetry breaking value and leads to significantly different values of {\alpha}. If the scalar-photon coupling strength {\beta}{\gamma} is of order unity we find that the variation of {\alpha} inside dark matter halos can be of the same magnitude as the recent claims by Webb et al. of a dipole variation. Importantly, our results also show that with low-redshift symmetry breaking these models exhibit some dependence of {\alpha} on lookback time (as opposed to a pure spatial dipole) which could in principle be detected by sufficiently accurate spectroscopic measurements, such as those of ALMA and the ELT-HIRES.Comment: 11 pages, 9 figure

Examining the validity of the minimal varying speed of light model through cosmological observations: relaxing the null curvature constraint

We revisit a consistency test for the speed of light variability, using the latest cosmological observations. This exercise can serve as a new diagnostics for the standard cosmological model and distinguish between the minimal varying speed of light in the Friedmann-Lema\^{i}tre-Robertson-Walker universe. We deploy Gaussian processes to reconstruct cosmic distances and ages in the redshift range $0<z<2$ utilizing the Pantheon compilation of type-Ia supernova luminosity distances (SN), cosmic chronometers from differential galaxy ages (CC), and measurements of both radial and transverse modes of baryon acoustic oscillations ($r$-BAO and $a$-BAO) respectively. Such a test has the advantage of being independent of any non-zero cosmic curvature assumption - which can be degenerated with some variable speed of light models - as well as any dark energy model. We also examine the impact of cosmological priors on our analysis, such as the Hubble constant, supernova absolute magnitude, and the sound horizon scale. We find null evidence for the speed of light variability hypothesis for most choices of priors and data-set combinations. However, mild deviations are seen at $\sim 2\sigma$ confidence level for redshifts $z<1$ with some specific prior choices when $r$-BAO data is employed, and at $z>1$ with a particular reconstruction kernel when $a$-BAO data are included. Still, we ascribe no statistical significance to this result bearing in mind the degeneracy between the associated priors for combined analysis, and incompleteness of the $a$-BAO data set at higher $z$.Comment: 15 pages, 8 sets of figures, revised version, including a change in title, to appear in Phys. Dark Uni

Color Superconductivity in Compact Stars

After a brief review of the phenomena expected in cold dense quark matter, color superconductivity and color-flavor locking, we sketch some implications of recent developments in our understanding of cold dense quark matter for the physics of compact stars. We give a more detailed summary of our recent work on crystalline color superconductivity and the consequent realization that (some) pulsar glitches may originate in quark matter.Comment: 19 pages. 2 figures. To appear in the proceedings of the ECT Workshop on Neutron Star Interiors, Trento, Italy, June 2000. Shorter versions contributed to the proceedings of Strong and Electroweak Matter 2000, Marseille, France, June 2000 and to the proceedings of Strangeness 2000, Berkeley, CA, July 2000. KR was the speaker at all three meeting

Soft computing applied to optimization, computer vision and medicine

Artificial intelligence has permeated almost every area of life in modern society, and its significance continues to grow. As a result, in recent years, Soft Computing has emerged as a powerful set of methodologies that propose innovative and robust solutions to a variety of complex problems. Soft Computing methods, because of their broad range of application, have the potential to significantly improve human living conditions. The motivation for the present research emerged from this background and possibility. This research aims to accomplish two main objectives: On the one hand, it endeavors to bridge the gap between Soft Computing techniques and their application to intricate problems. On the other hand, it explores the hypothetical benefits of Soft Computing methodologies as novel effective tools for such problems. This thesis synthesizes the results of extensive research on Soft Computing methods and their applications to optimization, Computer Vision, and medicine. This work is composed of several individual projects, which employ classical and new optimization algorithms. The manuscript presented here intends to provide an overview of the different aspects of Soft Computing methods in order to enable the reader to reach a global understanding of the field. Therefore, this document is assembled as a monograph that summarizes the outcomes of these projects across 12 chapters. The chapters are structured so that they can be read independently. The key focus of this work is the application and design of Soft Computing approaches for solving problems in the following: Block Matching, Pattern Detection, Thresholding, Corner Detection, Template Matching, Circle Detection, Color Segmentation, Leukocyte Detection, and Breast Thermogram Analysis. One of the outcomes presented in this thesis involves the development of two evolutionary approaches for global optimization. These were tested over complex benchmark datasets and showed promising results, thus opening the debate for future applications. Moreover, the applications for Computer Vision and medicine presented in this work have highlighted the utility of different Soft Computing methodologies in the solution of problems in such subjects. A milestone in this area is the translation of the Computer Vision and medical issues into optimization problems. Additionally, this work also strives to provide tools for combating public health issues by expanding the concepts to automated detection and diagnosis aid for pathologies such as Leukemia and breast cancer. The application of Soft Computing techniques in this field has attracted great interest worldwide due to the exponential growth of these diseases. Lastly, the use of Fuzzy Logic, Artificial Neural Networks, and Expert Systems in many everyday domestic appliances, such as washing machines, cookers, and refrigerators is now a reality. Many other industrial and commercial applications of Soft Computing have also been integrated into everyday use, and this is expected to increase within the next decade. Therefore, the research conducted here contributes an important piece for expanding these developments. The applications presented in this work are intended to serve as technological tools that can then be used in the development of new devices

Einstein and Beyond: A Critical Perspective on General Relativity

An alternative approach to Einstein's theory of General Relativity (GR) is reviewed, which is motivated by a range of serious theoretical issues inflicting the theory, such as the cosmological constant problem, presence of non-Machian solutions, problems related with the energy-stress tensor $T^{ik}$ and unphysical solutions. The new approach emanates from a critical analysis of these problems, providing a novel insight that the matter fields, together with the ensuing gravitational field, are already present inherently in the spacetime without taking recourse to $T^{ik}$. Supported by numerous evidences, the new insight revolutionizes our views on the representation of the source of gravitation and establishes the spacetime itself as the source, which becomes crucial for understanding the unresolved issues in a unified manner. This leads to a new paradigm in GR by establishing equation $R^{ik}=0$ as the field equation of gravitation plus inertia in the very presence of matter.Comment: An invited review accepted for publication by `Universe' in its Special Issue "100 Years of Chronogeometrodynamics: the Status of the Einstein's Theory of Gravitation in Its Centennial Year

Computational Electromagnetism and Acoustics

It is a moot point to stress the significance of accurate and fast numerical methods for the simulation of electromagnetic fields and sound propagation for modern technology. This has triggered a surge of research in mathematical modeling and numerical analysis aimed to devise and improve methods for computational electromagnetism and acoustics. Numerical techniques for solving the initial boundary value problems underlying both computational electromagnetics and acoustics comprise a wide array of different approaches ranging from integral equation methods to finite differences. Their development faces a few typical challenges: highly oscillatory solutions, control of numerical dispersion, infinite computational domains, ill-conditioned discrete operators, lack of strong ellipticity, hysteresis phenomena, to name only a few. Profound mathematical analysis is indispensable for tackling these issues. Many outstanding contributions at this Oberwolfach conference on Computational Electromagnetism and Acoustics strikingly confirmed the immense recent progress made in the field. To name only a few highlights: there have been breakthroughs in the application and understanding of phase modulation and extraction approaches for the discretization of boundary integral equations at high frequencies. Much has been achieved in the development and analysis of discontinuous Galerkin methods. New insight have been gained into the construction and relationships of absorbing boundary conditions also for periodic media. Considerable progress has been made in the design of stable and space-time adaptive discretization techniques for wave propagation. New ideas have emerged for the fast and robust iterative solution for discrete quasi-static electromagnetic boundary value problems