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Books > Science & Mathematics > Astronomy, space & time > Cosmology & the universe

Origins - Fourteen Billion Years of Cosmic Evolution (Paperback): Neil De Grasse Tyson, Donald Goldsmith Origins - Fourteen Billion Years of Cosmic Evolution (Paperback)
Neil De Grasse Tyson, Donald Goldsmith
R465 R437 Discovery Miles 4 370 Save R28 (6%) Ships in 18 - 22 working days

Our true origins are not only human, or even terrestrial, but in fact cosmic. Drawing on recent scientific breakthroughs and cross-pollination among geology, biology, astrophysics and cosmology, Origins illuminates the soul-stirring leaps in our understanding of the cosmos. This newly revised and updated edition features such startling discoveries as the more than 5,000 newly detected exoplanets that shed light on the origins of and possibilities for life in the cosmos, and data from a host of new ground-based and spaceborne observatories that has fundamentally changed what we know about the expanding universe-and maybe even the laws of physics. From the first image of a galaxy's birth to tantalising evidence of water not only on Mars but also on the asteroid Ceres, as well as moons of Jupiter and Saturn, coauthors Neil deGrasse Tyson and Donald Goldsmith conduct an exhilarating tour of the cosmos with clarity and exuberance.

Physical Foundations of Cosmology (Hardcover, New): Viatcheslav Mukhanov Physical Foundations of Cosmology (Hardcover, New)
Viatcheslav Mukhanov
R2,565 Discovery Miles 25 650 Ships in 10 - 15 working days

Inflationary cosmology has been developed over the last twenty years to remedy serious shortcomings in the standard hot big bang model of the universe. This textbook, first published in 2005, explains the basis of modern cosmology and shows where the theoretical results come from. The book is divided into two parts; the first deals with the homogeneous and isotropic model of the Universe, the second part discusses how inhomogeneities can explain its structure. Established material such as the inflation and quantum cosmological perturbation are presented in great detail, however the reader is brought to the frontiers of current cosmological research by the discussion of more speculative ideas. An ideal textbook for both advanced students of physics and astrophysics, all of the necessary background material is included in every chapter and no prior knowledge of general relativity and quantum field theory is assumed.

Center, Bulge and Disk of the Milky Way (Hardcover): Leo Blitz Center, Bulge and Disk of the Milky Way (Hardcover)
Leo Blitz
R2,411 Discovery Miles 24 110 Ships in 18 - 22 working days

Our view of the Galaxy has recently been undergoing an increasing divergence from the traditional standpoint. In this book, ten authors discuss in eight chapters how the conceptions of the Milky Way have moved in new directions. Starting with the inner parsec and the Centre of the Galaxy, the book gradually moves on to the bulge and its relation to the globular clusters and to the disk, of which the presence of a bar is argued. A new look on the HI distribution in the disk, a synthesis of molecular line surveys and the study of stellar populations are discussed in the last three chapters.

Godel Meets Einstein - Time Travel in the Godel Universe (Paperback, Expanded ed.): Palle Yourgrau Godel Meets Einstein - Time Travel in the Godel Universe (Paperback, Expanded ed.)
Palle Yourgrau
R653 R603 Discovery Miles 6 030 Save R50 (8%) Ships in 10 - 15 working days

What happens when the country's greatest logician meets the century's greatest physicist? In the case of Kurt Godel and Albert Einstein the result in Godel's revolutioinary new model of the cosmos. In the 'Godel Universe' the philosophical fantasy of time travel becomes a scientific reality. For Godel, however, the reality of time travel signals the unreality of time. If Godel is right, the real meaning of the Einstein revolution had remained, for half a century, a secret. Now, half-century after Godel met Einstein, the real meaning of time travel in the Godel universe can be revealed.

The Sun (Paperback): Brendan Owens, Royal Observatory Greenwich The Sun (Paperback)
Brendan Owens, Royal Observatory Greenwich
R238 Discovery Miles 2 380 Ships in 10 - 15 working days

An enthralling exploration of the star on our doorstep, charting the journey from ancient superstition to the deep scientific mysteries yet to be resolved. The Sun examines how we've come to understand the features and processes at work in our star, starting with the earliest observations of mysterious sunspots and ending with the rich and complex investigation of the connected Sun-Earth system. It reveals the interconnected sciences involved in finding out more about the Sun and the practical importance of doing so for our modern world. It's a slow-burn tale of scientific discovery!

Discovering the Expanding Universe (Hardcover): Harry Nussbaumer, Lydia Bieri Discovering the Expanding Universe (Hardcover)
Harry Nussbaumer, Lydia Bieri; Foreword by Allan Sandage
R1,973 Discovery Miles 19 730 Ships in 18 - 22 working days

The discovery of the expanding universe is one of the most exciting exploits in astronomy. This book explores its history, from the beginnings of modern cosmology with Einstein in 1917, through Lemaitre's discovery of the expanding universe in 1927 and his suggestion of a Big Bang origin, to Hubble's contribution of 1929 and the subsequent years when Hubble and Humason provided the essential observations for further developing modern cosmology, and finally to Einstein's conversion to the expanding universe in 1931. As a prelude the book traces the evolution of some of the notions of modern cosmology from the late Middle Ages up to the final acceptance of the concept of galaxies in 1925. Written in non-technical language, with a mathematical appendix, the book will appeal to scientists, students, and anyone interested in the history of astronomy and cosmology.

Non-linear Data Analysis on the Sphere - The Quest for Anomalies in the Cosmic Microwave Background (Hardcover, 2013 ed.):... Non-linear Data Analysis on the Sphere - The Quest for Anomalies in the Cosmic Microwave Background (Hardcover, 2013 ed.)
Gregor Rossmanith
R3,182 Discovery Miles 31 820 Ships in 18 - 22 working days

This work deals with the search for signatures of non-Gaussianities in the cosmic microwave background (CMB). Probing Gaussianity in the CMB addresses one of the key questions in modern cosmology because it allows us to discriminate between different models of inflation, and thus concerns a fundamental part of the standard cosmological model. The basic goal here is to adapt complementary methods stemming from the field of complexity science to CMB data analysis. Two key concepts, namely the method of surrogates and estimators for local scaling properties, are applied to CMB data analysis. All results show strong non-Gaussianities and pronounced asymmetries. The consistency of the full sky and cut sky results shows convincingly for the first time that the influence of the Galactic plane is not responsible for these deviations from Gaussianity and isotropy. The findings seriously call into question predictions of isotropic cosmologies based on the widely accepted single field slow roll inflation model.

Atoms, Stars, and Nebulae (Hardcover, Revised): Lawrence H. Aller Atoms, Stars, and Nebulae (Hardcover, Revised)
Lawrence H. Aller
R3,020 Discovery Miles 30 200 Ships in 18 - 22 working days

This book, first published in 1991, tells the story of how astronomy and physics work together to unravel many mysteries of stars and nebulae. Stress is laid on a non-technical description of how an understanding of these objects is obtained, not on just a mere review of facts. After a succinct, non-mathematical excursion into the principles of radiation and atomic structure, the text explains in simple terms the physical processes at work in stars and gaseous nebulae. A survey of masses, dimensions, luminosities, temperatures and chemical composition of stars is followed by an exploration of their interiors and how stars generate energy. An account of the exciting new field of high energy astronomy and the origin of cosmic rays is given at the end of the book. This is the ideal introduction for physics and astronomy students to the important field of modern astronomics. It should also appeal to amateur astronomers and the reader interested in the life history of a star.

From Strange Simplicity to Complex Familiarity - A Treatise on Matter, Information, Life and Thought (Paperback): Manfred Eigen From Strange Simplicity to Complex Familiarity - A Treatise on Matter, Information, Life and Thought (Paperback)
Manfred Eigen
R2,509 Discovery Miles 25 090 Ships in 10 - 15 working days

This book presents a vivid argument for the almost lost idea of a unity of all natural sciences. It starts with the "strange" physics of matter, including particle physics, atomic physics and quantum mechanics, cosmology, relativity and their consequences (Chapter I), and it continues by describing the properties of material systems that are best understood by statistical and phase-space concepts (Chapter II). These lead to entropy and to the classical picture of quantitative information, initially devoid of value and meaning (Chapter III). Finally, "information space" and dynamics within it are introduced as a basis for semantics (Chapter IV), leading to an exploration of life and thought as new problems in physics (Chapter V). Dynamic equations - again of a strange (but very general) nature - bring about the complex familiarity of the world we live in. Surprising new results in the life sciences open our eyes to the richness of physical thought, and they show us what can and what cannot be explained by a Darwinian approach. The abstract physical approach is applicable to the origins of life, of meaningful information and even of our universe.

In Search of the True Universe - The Tools, Shaping, and Cost of Cosmological Thought (Hardcover, New): Martin Harwit In Search of the True Universe - The Tools, Shaping, and Cost of Cosmological Thought (Hardcover, New)
Martin Harwit
R1,160 Discovery Miles 11 600 Ships in 18 - 22 working days

Astrophysicist and scholar Martin Harwit examines how our understanding of the cosmos advanced rapidly during the twentieth century and identifies the factors contributing to this progress. Astronomy, whose tools were largely imported from physics and engineering, benefited mid-century from the US policy of coupling basic research with practical national priorities. This strategy, initially developed for military and industrial purposes, provided astronomy with powerful tools yielding access - at virtually no cost - to radio, infrared, X-ray, and gamma-ray observations. Today, astronomers are investigating the new frontiers of dark matter and dark energy, critical to understanding the cosmos but of indeterminate socio-economic promise. Harwit addresses these current challenges in view of competing national priorities and proposes alternative new approaches in search of the true Universe. This is an engaging read for astrophysicists, policy makers, historians, and sociologists of science looking to learn and apply lessons from the past in gaining deeper cosmological insight.

The Universe (Paperback): Greg Brown The Universe (Paperback)
Greg Brown
R238 Discovery Miles 2 380 Ships in 10 - 15 working days

Ever wondered how it all began? How it will all end? And while we're waiting, what's been going on in the meantime? From the Big Bang to the Big Crunch, dark matter to antimatter, The Universe is your pocket guide to everything that ever was and ever will be - a statement that places no undue pressure on the author whatsoever.

Stars (Paperback): Greg Brown, Royal Observatory Greenwich Stars (Paperback)
Greg Brown, Royal Observatory Greenwich
R236 Discovery Miles 2 360 Ships in 10 - 15 working days

Whether stargazing with the naked eye or observing deep space with the largest telescopes in the world, humans have a seemingly neverending fascination with the stars. Our ancestors saw patterns in their random arrangement, inventing both tales of legendary heroes and the pastime of dot-to-dot in one fell swoop. But it's only in the last century or so that the natures of these distant lights have been revealed - and it's more incredible than any legend. How are stars born? How long do they live? And just how many times can you read the word 'trillion' before it starts sounding made up? Find out as astronomer Dr Greg Brown of Royal Observatory Greenwich takes a short diversion from obsessing over black holes to illuminate us about the lives of stars - ending in black holes, naturally.

Stars And Space With Matlab Apps (With Companion Media Pack) (Hardcover): Daniel Green Stars And Space With Matlab Apps (With Companion Media Pack) (Hardcover)
Daniel Green
R2,393 Discovery Miles 23 930 Ships in 18 - 22 working days

Recent advances in the understanding of star formation and evolution have been impressive and aspects of that knowledge are explored in this volume. The black hole stellar endpoints are studied and geodesic motion is explored. The emission of gravitational waves is featured due to their very recent experimental discovery.The second aspect of the text is space exploration which began 62 years ago with the Sputnik Earth satellite followed by the landing on the Moon just 50 years ago. Since then Mars has been explored remotely as well as flybys of the outer planets and probes which have escaped the solar system. The text explores many aspects of rocket travel. Finally possibilities for interstellar travel are discussed.All these topics are treated in a unified way using the Matlab App to combine text, figures, formulae and numeric input and output. In this way the reader may vary parameters and see the results in real time. That experience aids in building up an intuitive feel for the many specific problems given in this text.

Astrobiology and Society in Europe Today (Paperback, 1st ed. 2018): Klara Anna Capova, Erik Persson, Tony Milligan, David Duner Astrobiology and Society in Europe Today (Paperback, 1st ed. 2018)
Klara Anna Capova, Erik Persson, Tony Milligan, David Duner
R1,353 Discovery Miles 13 530 Ships in 18 - 22 working days

This White Paper describes the state of astrobiology in Europe today and its relation to the European society at large. With contributions from authors in twenty countries and over thirty scientific institutions worldwide, the document illustrates the societal implications of astrobiology and the positive contribution that astrobiology can make to European society. The White paper has two main objectives: 1. It recommends the establishment of a European Astrobiology Institute (EAI) as an answer to a series of challenges relating to astrobiology but also European research, education and the society at large. 2. It also acknowledges the societal implications of astrobiology, and thus the role of the social sciences and humanities in optimizing the positive contribution that astrobiology can make to the lives of the people of Europe and the challenges they face. This book is recommended reading for science policy makers, the interested public, and the astrobiology community.

The Universe - Visions and Perspectives (Hardcover): N.J. Dadhich, Ajit K. Kembhavi The Universe - Visions and Perspectives (Hardcover)
N.J. Dadhich, Ajit K. Kembhavi
R2,937 Discovery Miles 29 370 Ships in 18 - 22 working days

This volume contains a number of essays by experts in areas of theoretical physics and astrophysics including cosmology, classical and quantum gravity, string theory and relativistic astrophysics. It will provide the reader with excellent reviews of current research in these frontier areas. Several of the essays emphasise alternative views of the Universe by leading astronomers and physicists who are known for their pioneering contributions. The volume is dedicated to Professor Jayant Narlikar, who has concerned himself with fundamental issues in cosmology and gravitation theory over a long and distinguished research career.

Galaxies at High Redshift (Hardcover): I. Perez-Fournon, M. Balcells, F. Moreno-Insertis, F. Sanchez Galaxies at High Redshift (Hardcover)
I. Perez-Fournon, M. Balcells, F. Moreno-Insertis, F. Sanchez
R3,623 Discovery Miles 36 230 Ships in 18 - 22 working days

This book covers normal galaxies, distant galaxies, studies based on far-infrared diagnostics, quasar absorption lines, and the properties of nearby galaxies. The timely volume provides an essential reference for astronomers working in the field of high-redshift galaxies. It includes the lectures delivered at the XI Canary Islands Winter School of Astrophysics, and reviews scientific results as well as main questions in the field.

Bang!! 2 - The Complete History of the Universe (Hardcover, Revised): Brian May, Patrick Moore, Chris Lintott, Hannah Wakeford Bang!! 2 - The Complete History of the Universe (Hardcover, Revised)
Brian May, Patrick Moore, Chris Lintott, Hannah Wakeford
R601 R542 Discovery Miles 5 420 Save R59 (10%) Ships in 9 - 17 working days

In 2004 a rock star, a TV astronomer and a young research astronomer sat down to write the story of the Universe in the order in which it happened, from its birth at the Big Bang 13.7 billion years ago, through to its ultimate demise in the infinitely far future. The aim of this book is to explain the Big Bang and everything that followed in a way that made sense, in the strict order in which events occurred, and without using maths, so it would be understandable to everyone, regardless of educational background. The original edition of Bang! was a bestseller, and a go-to for anyone wanting to understand the story of the origins and evolution of our Universe that did not duck the science. Since the first edition, thousands of planets have been discovered, the 'habitable zone' has expanded and a flotilla of new satellites has explored our own solar system, bringing back fresh images and new science. In this book all the latest findings about the evolution of stars and galaxies are included, and the current thinking about our ultimate origins. The latest ideas about Dark Matter and Dark Energy are explained, all illustrated with new images from the world's largest telescopes and space missions. This is the new, updated, popular guide to 'Life, the Universe, and Everything' - The Complete History of the Universe.

The Physics of Galaxy Formation (Paperback, Softcover reprint of the original 1st ed. 2014): Claudia Del P. Lagos The Physics of Galaxy Formation (Paperback, Softcover reprint of the original 1st ed. 2014)
Claudia Del P. Lagos
R3,303 Discovery Miles 33 030 Ships in 18 - 22 working days

This thesis addresses two of the central processes which underpin the formation of galaxies: the formation of stars and the injection of energy into the interstellar medium from supernovae, called feedback. In her work Claudia Lagos has completely overhauled the treatment of these processes in simulations of galaxy formation. Her thesis makes two major breakthroughs, and represents the first major steps forward in these areas in more than a decade. Her work has enabled, for the first time, predictions to be made which can be compared against new observations which probe the neutral gas content of galaxies, opening up a completely novel way to constrain the models. The treatment of feedback from supernovae, and how this removes material from the interstellar medium, is also likely to have a lasting impact on the field. Claudia Lagos Ph.D. thesis was nominated by the Institute for Computational Cosmology at Durham University as an outstanding Ph.D. thesis 2012.

The Future of Theoretical Physics and Cosmology - Celebrating Stephen Hawking's Contributions to Physics (Hardcover, New):... The Future of Theoretical Physics and Cosmology - Celebrating Stephen Hawking's Contributions to Physics (Hardcover, New)
G. W. Gibbons, E. P. S. Shellard, S.J. Rankin
R3,604 Discovery Miles 36 040 Ships in 18 - 22 working days

Based on lectures given in honor of Stephen Hawking's 60th birthday, this book comprises contributions from the world's leading theoretical physicists. Popular lectures progress to a critical evaluation of more advanced subjects in modern cosmology and theoretical physics. Topics covered include the origin of the universe, warped spacetime, cosmological singularities, quantum gravity, black holes, string theory, quantum cosmology and inflation. The volume provides a fascinating overview of the variety of subjects to which Stephen Hawking has contributed.

Defect Evolution in Cosmology and Condensed Matter - Quantitative Analysis with the Velocity-Dependent One-Scale Model... Defect Evolution in Cosmology and Condensed Matter - Quantitative Analysis with the Velocity-Dependent One-Scale Model (Paperback, 1st ed. 2016)
C.J.A.P. Martins
R1,698 Discovery Miles 16 980 Ships in 18 - 22 working days

This book sheds new light on topological defects in widely differing systems, using the Velocity-Dependent One-Scale Model to better understand their evolution. Topological defects - cosmic strings, monopoles, domain walls or others - necessarily form at cosmological (and condensed matter) phase transitions. If they are stable and long-lived they will be fossil relics of higher-energy physics. Understanding their behaviour and consequences is a key part of any serious attempt to understand the universe, and this requires modelling their evolution. The velocity-dependent one-scale model is the only fully quantitative model of defect network evolution, and the canonical model in the field. This book provides a review of the model, explaining its physical content and describing its broad range of applicability.

Non-linear Data Analysis on the Sphere - The Quest for Anomalies in the Cosmic Microwave Background (Paperback, 2013 ed.):... Non-linear Data Analysis on the Sphere - The Quest for Anomalies in the Cosmic Microwave Background (Paperback, 2013 ed.)
Gregor Rossmanith
R2,975 Discovery Miles 29 750 Ships in 18 - 22 working days

This work deals with the search for signatures of non-Gaussianities in the cosmic microwave background (CMB). Probing Gaussianity in the CMB addresses one of the key questions in modern cosmology because it allows us to discriminate between different models of inflation, and thus concerns a fundamental part of the standard cosmological model. The basic goal here is to adapt complementary methods stemming from the field of complexity science to CMB data analysis. Two key concepts, namely the method of surrogates and estimators for local scaling properties, are applied to CMB data analysis. All results show strong non-Gaussianities and pronounced asymmetries. The consistency of the full sky and cut sky results shows convincingly for the first time that the influence of the Galactic plane is not responsible for these deviations from Gaussianity and isotropy. The findings seriously call into question predictions of isotropic cosmologies based on the widely accepted single field slow roll inflation model.

The Amazing Unity of the Universe - And Its Origin in the Big Bang (Paperback, 2nd ed. 2016): Edward Van Den Heuvel The Amazing Unity of the Universe - And Its Origin in the Big Bang (Paperback, 2nd ed. 2016)
Edward Van Den Heuvel
R2,114 Discovery Miles 21 140 Ships in 18 - 22 working days

In the first chapters the author describes how our knowledge of the position of Earth in space and time has developed, thanks to the work of many generations of astronomers and physicists. He discusses how our position in the Galaxy was discovered, and how in 1929, Hubble uncovered the fact that the Universe is expanding, leading to the picture of the Big Bang. He then explains how astronomers have found that the laws of physics that were discovered here on Earth and in the Solar System (the laws of mechanics, gravity, atomic physics, electromagnetism, etc.) are valid throughout the Universe. This is illustrated by the fact that all matter in the Universe consists of atoms of the same chemical elements that we know on Earth. This unity is all the more surprising when one realizes that in the original Big Bang theory, different parts of the Universe could never have communicated with each other. It then is a mystery how they could have shared the same physical laws. This problem was solved by the introduction of the idea of inflation, a phase of extremely rapid expansion of the Universe during the first fraction of a second following the Big Bang. The author explains how the unity of the Universe finds its origin in the Big Bang prior to inflation. The book addresses the many fundamental questions about the Universe and its contents from the perspective of the Big Bang: the formation of structure in the Universe, the questions of the mysterious dark matter and dark energy, the possibilities of other Universes (the Multiverse) and of the existence of intelligent life elsewhere in the Universe.

Fantastic Numbers and Where to Find Them - A Journey to the Edge of Physics (Paperback): Antonio Padilla Fantastic Numbers and Where to Find Them - A Journey to the Edge of Physics (Paperback)
Antonio Padilla
R295 R272 Discovery Miles 2 720 Save R23 (8%) Ships in 5 - 10 working days

What are the mysterious numbers that unlock the secrets of the universe? In Fantastic Numbers and Where to Find Them, leading theoretical physicist and YouTube star Antonio Padilla takes us on an irreverent cosmic tour of nine of the most extraordinary numbers in physics. These include Graham's number, which is so large that if you thought about it in the wrong way, your head would collapse into a singularity; TREE(3), whose finite value could never be reached before the universe reset itself; and 10^{-120}, which measures the desperately unlikely balance of energy the universe needs to exist. . . Leading us down the rabbit hole to the inner workings of reality, Padilla demonstrates how these unusual numbers are the key to unlocking such mind-bending phenomena as black holes, entropy and the problem of the cosmological constant, which shows that our two best ways of understanding the universe contradict one another. Combining cutting-edge science with an entertaining cosmic quest, Fantastic Numbers and Where to Find Them is an electrifying, head-twisting guide to the most fundamental truths of the universe.

Philip's Stargazing 2023 Month-by-Month Guide to the Night Sky Britain & Ireland (Paperback): Nigel Henbest Philip's Stargazing 2023 Month-by-Month Guide to the Night Sky Britain & Ireland (Paperback)
Nigel Henbest
R205 R188 Discovery Miles 1 880 Save R17 (8%) Ships in 9 - 17 working days

"If you buy just one guide...you won't do better than this" BBC Sky at Night Magazine "I will continue to enjoy 'Philip's Stargazing' as the months go by" Helen Sharman, Astronaut "Very useful indeed" Chris Lintott, Sky at Night presenter Now including the top astronomical places to visit, star festivals and the latest on star parties in Britain and Ireland, the new 2023 edition is totally up-to-date for exploring the wonder of the night skies, month-by-month and day-by-day. Whether you're a seasoned astronomer or just starting out, Philip's Stargazing 2023 is the only book you'll need. Compiled by experts and specially designed for easy and daily use, Stargazing 2023 acts as a handily illustrated and comprehensive companion. - 12 updated sky charts for year-round astronomical discovery - Month-to-Month information. Daily Moon Phase Calendar, highlighting special lunar events throughout the year - Planet Watch for ideal viewing days in 2023 - The best places to experience Dark Skies, along with the latest on Star Festivals and Star Parties - Top places to visit for astronomical insights - Expert advice and insight throughout from internationally renowned Prof Nigel Henbest - The latest on electronic telescopes from expert Robin Scagell - Complete calendar of major astronomical events, including the Top 20 Sky Sights of 2023 - Jargon Buster, explaining common or confusing terms - The planets' movements explained from solar and lunar eclipses to meteor showers and comets

Advanced Statistical Methods for Astrophysical Probes of Cosmology (Paperback, 2013 ed.): Marisa Cristina March Advanced Statistical Methods for Astrophysical Probes of Cosmology (Paperback, 2013 ed.)
Marisa Cristina March
R1,408 Discovery Miles 14 080 Ships in 18 - 22 working days

This thesis explores advanced Bayesian statistical methods for extracting key information for cosmological model selection, parameter inference and forecasting from astrophysical observations. Bayesian model selection provides a measure of how good models in a set are relative to each other - but what if the best model is missing and not included in the set? Bayesian Doubt is an approach which addresses this problem and seeks to deliver an absolute rather than a relative measure of how good a model is. Supernovae type Ia were the first astrophysical observations to indicate the late time acceleration of the Universe - this work presents a detailed Bayesian Hierarchical Model to infer the cosmological parameters (in particular dark energy) from observations of these supernovae type Ia.

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