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Combining research methods from various areas of mathematics and physics, Probabilistic Models of Cosmic Backgrounds describes the isotropic random sections of certain fiber bundles and their applications to creating rigorous mathematical models of both discovered and hypothetical cosmic backgrounds. Previously scattered and hard-to-find mathematical and physical theories have been assembled from numerous textbooks, monographs, and research papers, and explained from different or even unexpected points of view. This consists of both classical and newly discovered results necessary for understanding a sophisticated problem of modelling cosmic backgrounds. The book contains a comprehensive description of mathematical and physical aspects of cosmic backgrounds with a clear focus on examples and explicit calculations. Its reader will bridge the gap of misunderstanding between the specialists in various theoretical and applied areas who speak different scientific languages. The audience of the book consists of scholars, students, and professional researchers. A scholar will find basic material for starting their own research. A student will use the book as supplementary material for various courses and modules. A professional mathematician will find a description of several physical phenomena at the rigorous mathematical level. A professional physicist will discover mathematical foundations for well-known physical theories.
Book Synopsis Probabilistic Models of Cosmic Backgrounds by : Anatoliy Malyarenko
Download or read book Probabilistic Models of Cosmic Backgrounds written by Anatoliy Malyarenko and published by CRC Press. This book was released on 2024-06-30 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combining research methods from various areas of mathematics and physics, Probabilistic Models of Cosmic Backgrounds describes the isotropic random sections of certain fiber bundles and their applications to creating rigorous mathematical models of both discovered and hypothetical cosmic backgrounds. Previously scattered and hard-to-find mathematical and physical theories have been assembled from numerous textbooks, monographs, and research papers, and explained from different or even unexpected points of view. This consists of both classical and newly discovered results necessary for understanding a sophisticated problem of modelling cosmic backgrounds. The book contains a comprehensive description of mathematical and physical aspects of cosmic backgrounds with a clear focus on examples and explicit calculations. Its reader will bridge the gap of misunderstanding between the specialists in various theoretical and applied areas who speak different scientific languages. The audience of the book consists of scholars, students, and professional researchers. A scholar will find basic material for starting their own research. A student will use the book as supplementary material for various courses and modules. A professional mathematician will find a description of several physical phenomena at the rigorous mathematical level. A professional physicist will discover mathematical foundations for well-known physical theories.
The author describes the current state of the art in the theory of invariant random fields. This theory is based on several different areas of mathematics, including probability theory, differential geometry, harmonic analysis, and special functions. The present volume unifies many results scattered throughout the mathematical, physical, and engineering literature, as well as it introduces new results from this area first proved by the author. The book also presents many practical applications, in particular in such highly interesting areas as approximation theory, cosmology and earthquake engineering. It is intended for researchers and specialists working in the fields of stochastic processes, statistics, functional analysis, astronomy, and engineering.
Book Synopsis Invariant Random Fields on Spaces with a Group Action by : Anatoliy Malyarenko
Download or read book Invariant Random Fields on Spaces with a Group Action written by Anatoliy Malyarenko and published by Springer Science & Business Media. This book was released on 2012-10-26 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author describes the current state of the art in the theory of invariant random fields. This theory is based on several different areas of mathematics, including probability theory, differential geometry, harmonic analysis, and special functions. The present volume unifies many results scattered throughout the mathematical, physical, and engineering literature, as well as it introduces new results from this area first proved by the author. The book also presents many practical applications, in particular in such highly interesting areas as approximation theory, cosmology and earthquake engineering. It is intended for researchers and specialists working in the fields of stochastic processes, statistics, functional analysis, astronomy, and engineering.
Book Synopsis Background Due to Cosmic Protons in Gamma-Ray Telescopes (Final Report) by :
Download or read book Background Due to Cosmic Protons in Gamma-Ray Telescopes (Final Report) written by and published by DIANE Publishing. This book was released on with total page 59 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Probes of the Early Universe by : Max Tegmark
Download or read book Probes of the Early Universe written by Max Tegmark and published by . This book was released on 1994 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt:
From ancient soothsayers and astrologists to today’s pollsters and economists, probability theory has long been used to predict the future on the basis of past and present knowledge. Mathematical Models of Information and Stochastic Systems shows that the amount of knowledge about a system plays an important role in the mathematical models used to foretell the future of the system. It explains how this known quantity of information is used to derive a system’s probabilistic properties. After an introduction, the book presents several basic principles that are employed in the remainder of the text to develop useful examples of probability theory. It examines both discrete and continuous distribution functions and random variables, followed by a chapter on the average values, correlations, and covariances of functions of variables as well as the probabilistic mathematical model of quantum mechanics. The author then explores the concepts of randomness and entropy and derives various discrete probabilities and continuous probability density functions from what is known about a particular stochastic system. The final chapters discuss information of discrete and continuous systems, time-dependent stochastic processes, data analysis, and chaotic systems and fractals. By building a range of probability distributions based on prior knowledge of the problem, this classroom-tested text illustrates how to predict the behavior of diverse systems. A solutions manual is available for qualifying instructors.
Book Synopsis Mathematical Models of Information and Stochastic Systems by : Philipp Kornreich
Download or read book Mathematical Models of Information and Stochastic Systems written by Philipp Kornreich and published by CRC Press. This book was released on 2018-10-03 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: From ancient soothsayers and astrologists to today’s pollsters and economists, probability theory has long been used to predict the future on the basis of past and present knowledge. Mathematical Models of Information and Stochastic Systems shows that the amount of knowledge about a system plays an important role in the mathematical models used to foretell the future of the system. It explains how this known quantity of information is used to derive a system’s probabilistic properties. After an introduction, the book presents several basic principles that are employed in the remainder of the text to develop useful examples of probability theory. It examines both discrete and continuous distribution functions and random variables, followed by a chapter on the average values, correlations, and covariances of functions of variables as well as the probabilistic mathematical model of quantum mechanics. The author then explores the concepts of randomness and entropy and derives various discrete probabilities and continuous probability density functions from what is known about a particular stochastic system. The final chapters discuss information of discrete and continuous systems, time-dependent stochastic processes, data analysis, and chaotic systems and fractals. By building a range of probability distributions based on prior knowledge of the problem, this classroom-tested text illustrates how to predict the behavior of diverse systems. A solutions manual is available for qualifying instructors.
This graduate textbook describes the physics of the Cosmic Microwave Background, arguably the most important topic in modern cosmology.
Book Synopsis The Cosmic Microwave Background by : Ruth Durrer
Download or read book The Cosmic Microwave Background written by Ruth Durrer and published by Cambridge University Press. This book was released on 2020-12-17 with total page 519 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate textbook describes the physics of the Cosmic Microwave Background, arguably the most important topic in modern cosmology.
Book Synopsis Statistical Analysis of Cosmic Microwave Background Anisotropy by : Emory Freeman Bunn
Download or read book Statistical Analysis of Cosmic Microwave Background Anisotropy written by Emory Freeman Bunn and published by . This book was released on 1995 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt:
A thorough introduction to modern ideas on cosmology and on the physical basis of the general theory of relativity, An Introduction to the Science of Cosmology explores various theories and ideas in big bang cosmology, providing insight into current problems. Assuming no previous knowledge of astronomy or cosmology, this book takes you beyond introductory texts to the point where you are able to read and appreciate the scientific literature, which is broadly referenced in the book. The authors present the standard big bang theory of the universe and provide an introduction to current inflationary cosmology, emphasizing the underlying physics without excessive technical detail. The book treats cosmological models without reliance on prior knowledge of general relativity, the necessary physics being introduced in the text as required. It also covers recent observational evidence pointing to an accelerating expansion of the universe. The first several chapters provide an introduction to the topics discussed later in the book. The next few chapters introduce relativistic cosmology and the classic observational tests. One chapter gives the main results of the hot big bang theory. Next, the book presents the inflationary model and discusses the problem of the origin of structure and the correspondingly more detailed tests of relativistic models. Finally, the book considers some general issues raised by expansion and isotropy. A reference section completes the work by listing essential formulae, symbols, and physical constants. Beyond the level of many elementary books on cosmology, An Introduction to the Science of Cosmology encompasses numerous recent developments and ideas in the area. It provides more detailed coverage than many other titles available, and the inclusion of problems at the end of each chapter aids in self study and makes the book suitable for taught courses.
Book Synopsis An Introduction to the Science of Cosmology by : Derek Raine
Download or read book An Introduction to the Science of Cosmology written by Derek Raine and published by CRC Press. This book was released on 2018-10-03 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: A thorough introduction to modern ideas on cosmology and on the physical basis of the general theory of relativity, An Introduction to the Science of Cosmology explores various theories and ideas in big bang cosmology, providing insight into current problems. Assuming no previous knowledge of astronomy or cosmology, this book takes you beyond introductory texts to the point where you are able to read and appreciate the scientific literature, which is broadly referenced in the book. The authors present the standard big bang theory of the universe and provide an introduction to current inflationary cosmology, emphasizing the underlying physics without excessive technical detail. The book treats cosmological models without reliance on prior knowledge of general relativity, the necessary physics being introduced in the text as required. It also covers recent observational evidence pointing to an accelerating expansion of the universe. The first several chapters provide an introduction to the topics discussed later in the book. The next few chapters introduce relativistic cosmology and the classic observational tests. One chapter gives the main results of the hot big bang theory. Next, the book presents the inflationary model and discusses the problem of the origin of structure and the correspondingly more detailed tests of relativistic models. Finally, the book considers some general issues raised by expansion and isotropy. A reference section completes the work by listing essential formulae, symbols, and physical constants. Beyond the level of many elementary books on cosmology, An Introduction to the Science of Cosmology encompasses numerous recent developments and ideas in the area. It provides more detailed coverage than many other titles available, and the inclusion of problems at the end of each chapter aids in self study and makes the book suitable for taught courses.
"Mass tells spacetime how to curve, spacetime tells mass how to move". This famous quote by physicist John Archibald Wheeler succinctly summarizes General Relativity, the most successful theory that describes our universe at large scale. However, most of the mass that General Relativity describes, namely dark matter (DM), remains a mystery. We have solid evidence of the existence of DM from various observations, but we know little or nothing about the particle nature of DM and how DM particles interact with different particles. Completing this knowledge gap would improve or revolutionize our established cosmological model, the Lambda Cold-Dark Matter (CDM) model, and give directions to theories beyond the standard particle physics model.This work attempts to study DM by examining and extending existing modeling approaches of DM and its visible tracers in a probabilistic way. The single verified form of DM interaction is gravitational. Currently, the only way to infer the properties of DM is through visible tracers. Most of these indirect detections either have low signal-to-noise, sparse coverage, or missing variables. These limitations introduce additional modeling choices and uncertainties. A probabilistic approach allows us to propagate the uncertainties appropriately and marginalize any missing variables. There are two recurring types of visible tracers that my work uses. The first type of tracers are galaxies and observables in the overdense regions of DM. These tracers allow usto infer the macroscopic dynamical properties of DM distribution that we want to study. The second type of tracers, on the hand, are in the background, i.e. further away than the foreground dark matter, from us observers. The gravity of DM can bend spacetime such that the path of light traveling in the vicinity would also curve, leaving distortions in the galaxy images. The gravitational distortion of the images of the background galaxies is also known as gravitational lensing. In the introduction (first chapter) of this thesis, I will layout the technical history, terminology and the reasons behind choosing the various data sets and give an overview of the analysis methods for my thesis work. In chapter two, I will present the study based on the observational data of El Gordo, one of the most massive, most ancient, merging galaxy clusters. Under the extreme collision speeds during a merger of a galaxy cluster, it is more probable for DM particles in the cluster to manifest eects of self-interaction. Thus, if DM particles can interact with one another, some preliminary simulations have shown that large-scale spatial distribution of DM can show discrepancies from its galaxy-counterparts. This discrepancy is also known as the galaxy-DM offset, with a caveat. The long duration (millions of years) of a merger means that we cannot detect the direction of motions of the components directly to confirm the offset as a lag. My work on El Gordo was the first to show a quantitative method of estimating how likely the DM components of El Gordo are to be moving in a certain direction. This study was made possible by utilizing informative observables in various wavelengths, including a pair of radio shockwaves on the outer skirt of the cluster, enhanced X-ray emissivity and the decrement of the Sunyaev-Zel'Dovich effect for the infra-red observations. This comprehensive set of observables allowed us to formulate probabilistic constraints in our Monte Carlo simulation of El Gordo. Furthermore, the study also brought up several questions about the modeling choices for comparing the DM and the member-galaxy distributions of a cluster. For instance, do the DM maps and the galaxy maps have high enough resolution to show the delicate offset signal produced by the possible self-interaction of DM (SIDM)? To address my concerns from the study of El Gordo, I conducted a second investigation of galaxy clusters in a cosmological simulation, which is described in chapter 3. The dataset I chose was from the Illustris simulation. As this simulation assumes a Cold-Dark-Mattermodel (CDM) without requiring an SIDM model, any offset between DM and the member galaxies in a galaxy cluster provides an estimate of the variability of the galaxy-DM offset. My study shows that the variability in this setting is non-negligible compared to the small observed offsets, it is likely that random variation can account for the galaxy-DM offsets inobservations. The result weakens our belief that SIDM is the cause of the offsets. The fourth chapter of my dissertation builds on top of my previous experience with analyzing the weak lensing data for El Gordo. This time, I performed the weak lensing study for a dataset of a much larger spatial scale, such that, galaxy clusters look like parts of a homogeneous and isotropic DM web. At this scale, it is possible to compare the spatial distribution of DM to simulations to give competitive constraints on cosmological parameters. Using weak lensing signals for estimating cosmological parameters is also known as cosmic shear inference. While I used a parametric technique to estimate the mass of El Gordo in chapter 2, my work in chapter 4 introduces a new non-parametric model using a Gaussian Process. A Gaussian Process is a generalization of the multivariate normal distribution to higher dimensions. We can draw functional models from a Gaussian Process to describe our data. While the realizations are drawn from a multivariate normal distribution, we can specify the parameters and the functional structure of the covariance (kernel) matrix of the underlying distribution. This generative model gives us the ability to put probabilistic estimates of DM density in regions without any background galaxies. As I have built the lensing physics into the very core of the covariance kernel matrix, we can also simultaneously infer the several important lensing observables, such as shear and convergence, given some lensed galaxy shapes. More importantly, this technique relies on fewer assumptions about the photometric redshift than traditional cosmic shear analysis technique. This may reduce the bias towards a ducial cosmology and lead to interesting discoveries. However, this new technique is not without its challenges. Computationally, this technique requires an O(n3) runtime. Despite my best attempts to parallelize the computation, the algorithm takes longer for generating DM mass maps than traditional approaches. My work here marks the beginning of an alternative method for cosmic shear inference. Many promising approximation techniques have emerged to drastically speed up the runtime of doing inference with a Gaussian Process. Incorporating these approximations may make it possible to use this method to give tighter cosmological constraints from future sky surveys such as the Large Synoptic Survey Telescope. I conclude my work in Chapter 5 and discuss the implications of my work. This includes some future directions for analyzing DM by using simulations with different underlying DM models and real data.
Book Synopsis Probabilistic Inference of Dark Matter Properties in Galaxy Clusters and the Cosmic Web by : Yin-Yee Ng
Download or read book Probabilistic Inference of Dark Matter Properties in Galaxy Clusters and the Cosmic Web written by Yin-Yee Ng and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "Mass tells spacetime how to curve, spacetime tells mass how to move". This famous quote by physicist John Archibald Wheeler succinctly summarizes General Relativity, the most successful theory that describes our universe at large scale. However, most of the mass that General Relativity describes, namely dark matter (DM), remains a mystery. We have solid evidence of the existence of DM from various observations, but we know little or nothing about the particle nature of DM and how DM particles interact with different particles. Completing this knowledge gap would improve or revolutionize our established cosmological model, the Lambda Cold-Dark Matter (CDM) model, and give directions to theories beyond the standard particle physics model.This work attempts to study DM by examining and extending existing modeling approaches of DM and its visible tracers in a probabilistic way. The single verified form of DM interaction is gravitational. Currently, the only way to infer the properties of DM is through visible tracers. Most of these indirect detections either have low signal-to-noise, sparse coverage, or missing variables. These limitations introduce additional modeling choices and uncertainties. A probabilistic approach allows us to propagate the uncertainties appropriately and marginalize any missing variables. There are two recurring types of visible tracers that my work uses. The first type of tracers are galaxies and observables in the overdense regions of DM. These tracers allow usto infer the macroscopic dynamical properties of DM distribution that we want to study. The second type of tracers, on the hand, are in the background, i.e. further away than the foreground dark matter, from us observers. The gravity of DM can bend spacetime such that the path of light traveling in the vicinity would also curve, leaving distortions in the galaxy images. The gravitational distortion of the images of the background galaxies is also known as gravitational lensing. In the introduction (first chapter) of this thesis, I will layout the technical history, terminology and the reasons behind choosing the various data sets and give an overview of the analysis methods for my thesis work. In chapter two, I will present the study based on the observational data of El Gordo, one of the most massive, most ancient, merging galaxy clusters. Under the extreme collision speeds during a merger of a galaxy cluster, it is more probable for DM particles in the cluster to manifest eects of self-interaction. Thus, if DM particles can interact with one another, some preliminary simulations have shown that large-scale spatial distribution of DM can show discrepancies from its galaxy-counterparts. This discrepancy is also known as the galaxy-DM offset, with a caveat. The long duration (millions of years) of a merger means that we cannot detect the direction of motions of the components directly to confirm the offset as a lag. My work on El Gordo was the first to show a quantitative method of estimating how likely the DM components of El Gordo are to be moving in a certain direction. This study was made possible by utilizing informative observables in various wavelengths, including a pair of radio shockwaves on the outer skirt of the cluster, enhanced X-ray emissivity and the decrement of the Sunyaev-Zel'Dovich effect for the infra-red observations. This comprehensive set of observables allowed us to formulate probabilistic constraints in our Monte Carlo simulation of El Gordo. Furthermore, the study also brought up several questions about the modeling choices for comparing the DM and the member-galaxy distributions of a cluster. For instance, do the DM maps and the galaxy maps have high enough resolution to show the delicate offset signal produced by the possible self-interaction of DM (SIDM)? To address my concerns from the study of El Gordo, I conducted a second investigation of galaxy clusters in a cosmological simulation, which is described in chapter 3. The dataset I chose was from the Illustris simulation. As this simulation assumes a Cold-Dark-Mattermodel (CDM) without requiring an SIDM model, any offset between DM and the member galaxies in a galaxy cluster provides an estimate of the variability of the galaxy-DM offset. My study shows that the variability in this setting is non-negligible compared to the small observed offsets, it is likely that random variation can account for the galaxy-DM offsets inobservations. The result weakens our belief that SIDM is the cause of the offsets. The fourth chapter of my dissertation builds on top of my previous experience with analyzing the weak lensing data for El Gordo. This time, I performed the weak lensing study for a dataset of a much larger spatial scale, such that, galaxy clusters look like parts of a homogeneous and isotropic DM web. At this scale, it is possible to compare the spatial distribution of DM to simulations to give competitive constraints on cosmological parameters. Using weak lensing signals for estimating cosmological parameters is also known as cosmic shear inference. While I used a parametric technique to estimate the mass of El Gordo in chapter 2, my work in chapter 4 introduces a new non-parametric model using a Gaussian Process. A Gaussian Process is a generalization of the multivariate normal distribution to higher dimensions. We can draw functional models from a Gaussian Process to describe our data. While the realizations are drawn from a multivariate normal distribution, we can specify the parameters and the functional structure of the covariance (kernel) matrix of the underlying distribution. This generative model gives us the ability to put probabilistic estimates of DM density in regions without any background galaxies. As I have built the lensing physics into the very core of the covariance kernel matrix, we can also simultaneously infer the several important lensing observables, such as shear and convergence, given some lensed galaxy shapes. More importantly, this technique relies on fewer assumptions about the photometric redshift than traditional cosmic shear analysis technique. This may reduce the bias towards a ducial cosmology and lead to interesting discoveries. However, this new technique is not without its challenges. Computationally, this technique requires an O(n3) runtime. Despite my best attempts to parallelize the computation, the algorithm takes longer for generating DM mass maps than traditional approaches. My work here marks the beginning of an alternative method for cosmic shear inference. Many promising approximation techniques have emerged to drastically speed up the runtime of doing inference with a Gaussian Process. Incorporating these approximations may make it possible to use this method to give tighter cosmological constraints from future sky surveys such as the Large Synoptic Survey Telescope. I conclude my work in Chapter 5 and discuss the implications of my work. This includes some future directions for analyzing DM by using simulations with different underlying DM models and real data.
We live in an age of trusting the “experts.” But what happens when the so-called experts are wrong…and their misinformation is allowing us to destroy ourselves? In Science Myths We Tell Ourselves, William Barbat demonstrates the incorrect reasoning behind “facts” we have been taught, including the Big Bang, instant creation, continental drift, and spreading sea floors. Skeptics’ assertions that the climate is not changing are disproven by Barbat’s update of his 1973 climate study, which definitively proves that the world’s desert belts are expanding poleward, like the expansion of the Sahara Desert of North Africa, which ended the Ice Age. The recent drought in the midcontinental US, and the pervasive droughts in California and Brazil may be previews of climate disasters brought on by mankind, unless we can halt climate change by rethinking our energy protocols. We’ve been told that energy cannot be created in nature, or by man…but the stunning central thesis of Science Myths We Tell Ourselves is that the “law” on which this belief is based (Helmholtz’s Energy Conservation Law) is completely untrue—in fact, it was rejected as “metaphysics” in 1847 by the Berlin Physics Society. Scientists unwilling to examine the facts continue to propagate this misinformation while ignoring the potential for unlimited, non-polluting energy from low-mass electrons. This enlightening and fascinating book will challenge what you think you know, as well as providing hope and direction for a different future.
Book Synopsis Science Myths We Tell Ourselves by : William N. Barbat
Download or read book Science Myths We Tell Ourselves written by William N. Barbat and published by Outskirts Press. This book was released on 2015-03-27 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: We live in an age of trusting the “experts.” But what happens when the so-called experts are wrong…and their misinformation is allowing us to destroy ourselves? In Science Myths We Tell Ourselves, William Barbat demonstrates the incorrect reasoning behind “facts” we have been taught, including the Big Bang, instant creation, continental drift, and spreading sea floors. Skeptics’ assertions that the climate is not changing are disproven by Barbat’s update of his 1973 climate study, which definitively proves that the world’s desert belts are expanding poleward, like the expansion of the Sahara Desert of North Africa, which ended the Ice Age. The recent drought in the midcontinental US, and the pervasive droughts in California and Brazil may be previews of climate disasters brought on by mankind, unless we can halt climate change by rethinking our energy protocols. We’ve been told that energy cannot be created in nature, or by man…but the stunning central thesis of Science Myths We Tell Ourselves is that the “law” on which this belief is based (Helmholtz’s Energy Conservation Law) is completely untrue—in fact, it was rejected as “metaphysics” in 1847 by the Berlin Physics Society. Scientists unwilling to examine the facts continue to propagate this misinformation while ignoring the potential for unlimited, non-polluting energy from low-mass electrons. This enlightening and fascinating book will challenge what you think you know, as well as providing hope and direction for a different future.
