Astrophysics in a Nutshell, Second Edition
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3 the Friedmann-Robertson-Walker Metric
3 The Friedmann-Robertson-Walker metric 3.1 Three dimensions The most general isotropic and homogeneous metric in three dimensions is similar to the two dimensional result of eq. (43): dr2 ds2 = a2 + r2dΩ2 ; dΩ2 = dθ2 + sin2 θdφ2 ; k = 0; 1 : (46) 1 kr2 − The angles φ and θ are the usual azimuthal and polar angles of spherical coordinates, with θ [0; π], φ [0; 2π). As before, the parameter k can take on three different values: for k = 0, 2 2 the above line element describes ordinary flat space in spherical coordinates; k = 1 yields the metric for S , with constant positive curvature, while k = 1 is AdS and has constant 3 − 3 negative curvature. As in the two dimensional case, the change of variables r = sin χ (k = 1) or r = sinh χ (k = 1) makes the global nature of these manifolds more apparent. For example, − for the k = 1 case, after defining r = sin χ, the line element becomes ds2 = a2 dχ2 + sin2 χdθ2 + sin2 χ sin2 θdφ2 : (47) This is equivalent to writing ds2 = dX2 + dY 2 + dZ2 + dW 2 ; (48) where X = a sin χ sin θ cos φ ; Y = a sin χ sin θ sin φ ; Z = a sin χ cos θ ; W = a cos χ ; (49) which satisfy X2 + Y 2 + Z2 + W 2 = a2. So we see that the k = 1 metric corresponds to a 3-sphere of radius a embedded in 4-dimensional Euclidean space. One also sees a problem with the r = sin χ coordinate: it does not cover the whole sphere. -
Dark Matter and the Early Universe: a Review Arxiv:2104.11488V1 [Hep-Ph
Dark matter and the early Universe: a review A. Arbey and F. Mahmoudi Univ Lyon, Univ Claude Bernard Lyon 1, CNRS/IN2P3, Institut de Physique des 2 Infinis de Lyon, UMR 5822, 69622 Villeurbanne, France Theoretical Physics Department, CERN, CH-1211 Geneva 23, Switzerland Institut Universitaire de France, 103 boulevard Saint-Michel, 75005 Paris, France Abstract Dark matter represents currently an outstanding problem in both cosmology and particle physics. In this review we discuss the possible explanations for dark matter and the experimental observables which can eventually lead to the discovery of dark matter and its nature, and demonstrate the close interplay between the cosmological properties of the early Universe and the observables used to constrain dark matter models in the context of new physics beyond the Standard Model. arXiv:2104.11488v1 [hep-ph] 23 Apr 2021 1 Contents 1 Introduction 3 2 Standard Cosmological Model 3 2.1 Friedmann-Lema^ıtre-Robertson-Walker model . 4 2.2 A quick story of the Universe . 5 2.3 Big-Bang nucleosynthesis . 8 3 Dark matter(s) 9 3.1 Observational evidences . 9 3.1.1 Galaxies . 9 3.1.2 Galaxy clusters . 10 3.1.3 Large and cosmological scales . 12 3.2 Generic types of dark matter . 14 4 Beyond the standard cosmological model 16 4.1 Dark energy . 17 4.2 Inflation and reheating . 19 4.3 Other models . 20 4.4 Phase transitions . 21 5 Dark matter in particle physics 21 5.1 Dark matter and new physics . 22 5.1.1 Thermal relics . 22 5.1.2 Non-thermal relics . -
The State of the Multiverse: the String Landscape, the Cosmological Constant, and the Arrow of Time
The State of the Multiverse: The String Landscape, the Cosmological Constant, and the Arrow of Time Raphael Bousso Center for Theoretical Physics University of California, Berkeley Stephen Hawking: 70th Birthday Conference Cambridge, 6 January 2011 RB & Polchinski, hep-th/0004134; RB, arXiv:1112.3341 The Cosmological Constant Problem The Landscape of String Theory Cosmology: Eternal inflation and the Multiverse The Observed Arrow of Time The Arrow of Time in Monovacuous Theories A Landscape with Two Vacua A Landscape with Four Vacua The String Landscape Magnitude of contributions to the vacuum energy graviton (a) (b) I Vacuum fluctuations: SUSY cutoff: ! 10−64; Planck scale cutoff: ! 1 I Effective potentials for scalars: Electroweak symmetry breaking lowers Λ by approximately (200 GeV)4 ≈ 10−67. The cosmological constant problem −121 I Each known contribution is much larger than 10 (the observational upper bound on jΛj known for decades) I Different contributions can cancel against each other or against ΛEinstein. I But why would they do so to a precision better than 10−121? Why is the vacuum energy so small? 6= 0 Why is the energy of the vacuum so small, and why is it comparable to the matter density in the present era? Recent observations Supernovae/CMB/ Large Scale Structure: Λ ≈ 0:4 × 10−121 Recent observations Supernovae/CMB/ Large Scale Structure: Λ ≈ 0:4 × 10−121 6= 0 Why is the energy of the vacuum so small, and why is it comparable to the matter density in the present era? The Cosmological Constant Problem The Landscape of String Theory Cosmology: Eternal inflation and the Multiverse The Observed Arrow of Time The Arrow of Time in Monovacuous Theories A Landscape with Two Vacua A Landscape with Four Vacua The String Landscape Many ways to make empty space Topology and combinatorics RB & Polchinski (2000) I A six-dimensional manifold contains hundreds of topological cycles. -
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A&A 561, L12 (2014) Astronomy DOI: 10.1051/0004-6361/201323020 & c ESO 2014 Astrophysics Letter to the Editor Possible structure in the GRB sky distribution at redshift two István Horváth1, Jon Hakkila2, and Zsolt Bagoly1,3 1 National University of Public Service, 1093 Budapest, Hungary e-mail: [email protected] 2 College of Charleston, Charleston, SC, USA 3 Eötvös University, 1056 Budapest, Hungary Received 9 November 2013 / Accepted 24 December 2013 ABSTRACT Context. Research over the past three decades has revolutionized cosmology while supporting the standard cosmological model. However, the cosmological principle of Universal homogeneity and isotropy has always been in question, since structures as large as the survey size have always been found each time the survey size has increased. Until 2013, the largest known structure in our Universe was the Sloan Great Wall, which is more than 400 Mpc long located approximately one billion light years away. Aims. Gamma-ray bursts (GRBs) are the most energetic explosions in the Universe. As they are associated with the stellar endpoints of massive stars and are found in and near distant galaxies, they are viable indicators of the dense part of the Universe containing normal matter. The spatial distribution of GRBs can thus help expose the large scale structure of the Universe. Methods. As of July 2012, 283 GRB redshifts have been measured. Subdividing this sample into nine radial parts, each contain- ing 31 GRBs, indicates that the GRB sample having 1.6 < z < 2.1differs significantly from the others in that 14 of the 31 GRBs are concentrated in roughly 1/8 of the sky. -
An Analysis of Gravitational Redshift from Rotating Body
An analysis of gravitational redshift from rotating body Anuj Kumar Dubey∗ and A K Sen† Department of Physics, Assam University, Silchar-788011, Assam, India. (Dated: July 29, 2021) Gravitational redshift is generally calculated without considering the rotation of a body. Neglect- ing the rotation, the geometry of space time can be described by using the spherically symmetric Schwarzschild geometry. Rotation has great effect on general relativity, which gives new challenges on gravitational redshift. When rotation is taken into consideration spherical symmetry is lost and off diagonal terms appear in the metric. The geometry of space time can be then described by using the solutions of Kerr family. In the present paper we discuss the gravitational redshift for rotating body by using Kerr metric. The numerical calculations has been done under Newtonian approximation of angular momentum. It has been found that the value of gravitational redshift is influenced by the direction of spin of central body and also on the position (latitude) on the central body at which the photon is emitted. The variation of gravitational redshift from equatorial to non - equatorial region has been calculated and its implications are discussed in detail. I. INTRODUCTION from principle of equivalence. Snider in 1972 has mea- sured the redshift of the solar potassium absorption line General relativity is not only relativistic theory of grav- at 7699 A˚ by using an atomic - beam resonance - scat- itation proposed by Einstein, but it is the simplest theory tering technique [5]. Krisher et al. in 1993 had measured that is consistent with experimental data. Predictions of the gravitational redshift of Sun [6]. -
The Age of the Universe Transcript
The Age of the Universe Transcript Date: Wednesday, 6 February 2013 - 1:00PM Location: Museum of London 6 February 2013 The Age of The Universe Professor Carolin Crawford Introduction The idea that the Universe might have an age is a relatively new concept, one that became recognised only during the past century. Even as it became understood that individual objects, such as stars, have finite lives surrounded by a birth and an end, the encompassing cosmos was always regarded as a static and eternal framework. The change in our thinking has underpinned cosmology, the science concerned with the structure and the evolution of the Universe as a whole. Before we turn to the whole cosmos then, let us start our story nearer to home, with the difficulty of solving what might appear a simpler problem, determining the age of the Earth. Age of the Earth The fact that our planet has evolved at all arose predominantly from the work of 19th century geologists, and in particular, the understanding of how sedimentary rocks had been set down as an accumulation of layers over extraordinarily long periods of time. The remains of creatures trapped in these layers as fossils clearly did not resemble any currently living, but there was disagreement about how long a time had passed since they had died. The cooling earth The first attempt to age the Earth based on physics rather than geology came from Lord Kelvin at the end of the 19th Century. Assuming that the whole planet would have started from a completely molten state, he then calculated how long it would take for the surface layers of Earth to cool to their present temperature. -
A Study of John Leslie's Infinite Minds, a Philosophical Cosmology
Document généré le 1 oct. 2021 09:18 Laval théologique et philosophique Infinite Minds, Determinism & Evil A Study of John Leslie’s Infinite Minds, A Philosophical Cosmology Leslie Armour La question de Dieu Volume 58, numéro 3, octobre 2002 URI : https://id.erudit.org/iderudit/000634ar DOI : https://doi.org/10.7202/000634ar Aller au sommaire du numéro Éditeur(s) Faculté de philosophie, Université Laval Faculté de théologie et de sciences religieuses, Université Laval ISSN 0023-9054 (imprimé) 1703-8804 (numérique) Découvrir la revue Citer cette note Armour, L. (2002). Infinite Minds, Determinism & Evil: A Study of John Leslie’s Infinite Minds, A Philosophical Cosmology. Laval théologique et philosophique, 58(3), 597–603. https://doi.org/10.7202/000634ar Tous droits réservés © Laval théologique et philosophique, Université Laval, Ce document est protégé par la loi sur le droit d’auteur. L’utilisation des 2002 services d’Érudit (y compris la reproduction) est assujettie à sa politique d’utilisation que vous pouvez consulter en ligne. https://apropos.erudit.org/fr/usagers/politique-dutilisation/ Cet article est diffusé et préservé par Érudit. Érudit est un consortium interuniversitaire sans but lucratif composé de l’Université de Montréal, l’Université Laval et l’Université du Québec à Montréal. Il a pour mission la promotion et la valorisation de la recherche. https://www.erudit.org/fr/ Laval théologique et philosophique, 58, 3 (octobre 2002) : 597-603 ◆ note critique INFINITE MINDS, DETERMINISM & EVIL A STUDY OF JOHN LESLIE’S INFINITE MINDS, A PHILOSOPHICAL COSMOLOGY * Leslie Armour The Dominican College of Philosophy and Theology Ottawa ohn Leslie’s Infinite Minds is a refreshingly daring book. -
Science and Religion in the Face of the Environmental Crisis
Roger S. Gottlieb, ed., The Oxford Handbook of Religion and Ecology. New York and Oxford: Oxford University Press, 2006. Pages 376-397. CHAPTER 17 .................................................................................................. SCIENCE AND RELIGION IN THE FACE OF THE ENVIRONMENTAL CRISIS ..................................................................................................... HOLMES ROLSTON III BOTH science and religion are challenged by the environmental crisis, both to reevaluate the natural world and to reevaluate their dialogue with each other. Both are thrown into researching fundamental theory and practice in the face of an upheaval unprecedented in human history, indeed in planetary history. Life on Earth is in jeopardy owing to the behavior of one species, the only species that is either scientific or religious, the only species claiming privilege as the "wise spe- cies," Homo sapiens. Nature and the human relation to nature must be evaluated within cultures, classically by their religions, currently also by the sciences so eminent in Western culture. Ample numbers of theologians and ethicists have become persuaded that religion needs to pay more attention to ecology, and many ecologists recognize religious dimensions to caring for nature and to addressing the ecological crisis. Somewhat ironically, just when humans, with their increasing industry and technology, seemed further and further from nature, having more knowledge about natural processes and more power to manage them, just when humans were more and more rebuilding their environments, thinking perhaps to escape nature, the natural world has emerged as a focus of concern. Nature remains the milieu of 376 SCIENCE AND RELIGION 377 culture—so both science and religion have discovered. In a currently popular vocabulary, humans need to get themselves "naturalized." Using another meta- phor, nature is the "womb" of culture, but a womb that humans never entirely leave. -
Hubble's Law and the Expanding Universe
COMMENTARY COMMENTARY Hubble’s Law and the expanding universe Neta A. Bahcall1 the expansion rate is constant in all direc- Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544 tions at any given time, this rate changes with time throughout the life of the uni- verse. When expressed as a function of cos- In one of the most famous classic papers presented the observational evidence for one H t in the annals of science, Edwin Hubble’s of science’s greatest discoveries—the expand- mic time, ( ), it is known as the Hubble 1929 PNAS article on the observed relation inguniverse.Hubbleshowedthatgalaxiesare Parameter. The expansion rate at the pres- between distance and recession velocity of receding away from us with a velocity that is ent time, Ho, is about 70 km/s/Mpc (where 1 Mpc = 106 parsec = 3.26 × 106 light-y). galaxies—the Hubble Law—unveiled the proportional to their distance from us: more The inverse of the Hubble Constant is the expanding universe and forever changed our distant galaxies recede faster than nearby gal- Hubble Time, tH = d/v = 1/H ; it reflects understanding of the cosmos. It inaugurated axies. Hubble’s classic graph of the observed o the time since a linear cosmic expansion has the field of observational cosmology that has velocity vs. distance for nearby galaxies is begun (extrapolating a linear Hubble Law uncovered an amazingly vast universe that presented in Fig. 1; this graph has become back to time t = 0); it is thus related to has been expanding and evolving for 14 bil- a scientific landmark that is regularly repro- the age of the Universe from the Big-Bang lion years and contains dark matter, dark duced in astronomy textbooks. -
The Universe As a Laboratory: Fundamental Physics
The Universe as a Laboratory: Fundamental Physics The universe serves as an unparalleled laboratory for frontier physics, providing extreme conditions and unique opportunities to test theoretical models. Astronomical observations can yield invaluable information for physicists across the entire spectrum of the science, studying everything from the smallest constituents of mat- ter to the largest known structures. Astronomy is the principal player in the quest to uncover the full story about the origin, evolution and ultimate fate of the universe. The earliest “baby picture” of the universe is the map of the cosmic microwave background (CMB) radiation, predicted in 1948 and discovered in 1964. For years, physicists insisted that this radiation, seen coming from all directions in space, had to have irregularities in order for the universe as we know it to exist. These irregularities were not discovered until the COBE satellite mapped the radiation in 1992. Later, the WMAP satellite refined the measurement, allowing cosmologists to pinpoint the age of the universe at 13.7 billion years. Continued studies, including ground-based observations, seek to glean clues from the CMB about the basic nature of the universe and of its fundamental constituents. New telescopes and new technology promise to give astronomers better information about extremely distant objects—objects seen as they were in the early history of the universe. This, in turn, will provide valuable clues about how the first stars and galaxies developed and evolved into the objects we see in the universe today. The biggest mysteries in physics—and the biggest challenges for cosmologists—are the nature of dark matter and dark energy, which together constitute 95 percent of the universe. -
Neutrino Decoupling Beyond the Standard Model: CMB Constraints on the Dark Matter Mass with a Fast and Precise Neff Evaluation
KCL-2018-76 Prepared for submission to JCAP Neutrino decoupling beyond the Standard Model: CMB constraints on the Dark Matter mass with a fast and precise Neff evaluation Miguel Escudero Theoretical Particle Physics and Cosmology Group Department of Physics, King's College London, Strand, London WC2R 2LS, UK E-mail: [email protected] Abstract. The number of effective relativistic neutrino species represents a fundamental probe of the thermal history of the early Universe, and as such of the Standard Model of Particle Physics. Traditional approaches to the process of neutrino decoupling are either very technical and computationally expensive, or assume that neutrinos decouple instantaneously. In this work, we aim to fill the gap between these two approaches by modeling neutrino decoupling in terms of two simple coupled differential equations for the electromagnetic and neutrino sector temperatures, in which all the relevant interactions are taken into account and which allows for a straightforward implementation of BSM species. Upon including finite temperature QED corrections we reach an accuracy on Neff in the SM of 0:01. We illustrate the usefulness of this approach to neutrino decoupling by considering, in a model independent manner, the impact of MeV thermal dark matter on Neff . We show that Planck rules out electrophilic and neutrinophilic thermal dark matter particles of m < 3:0 MeV at 95% CL regardless of their spin, and of their annihilation being s-wave or p-wave. We point out arXiv:1812.05605v4 [hep-ph] 6 Sep 2019 that thermal dark matter particles with non-negligible interactions with both electrons and neutrinos are more elusive to CMB observations than purely electrophilic or neutrinophilic ones. -
The Reionization of Cosmic Hydrogen by the First Galaxies Abstract 1
David Goodstein’s Cosmology Book The Reionization of Cosmic Hydrogen by the First Galaxies Abraham Loeb Department of Astronomy, Harvard University, 60 Garden St., Cambridge MA, 02138 Abstract Cosmology is by now a mature experimental science. We are privileged to live at a time when the story of genesis (how the Universe started and developed) can be critically explored by direct observations. Looking deep into the Universe through powerful telescopes, we can see images of the Universe when it was younger because of the finite time it takes light to travel to us from distant sources. Existing data sets include an image of the Universe when it was 0.4 million years old (in the form of the cosmic microwave background), as well as images of individual galaxies when the Universe was older than a billion years. But there is a serious challenge: in between these two epochs was a period when the Universe was dark, stars had not yet formed, and the cosmic microwave background no longer traced the distribution of matter. And this is precisely the most interesting period, when the primordial soup evolved into the rich zoo of objects we now see. The observers are moving ahead along several fronts. The first involves the construction of large infrared telescopes on the ground and in space, that will provide us with new photos of the first galaxies. Current plans include ground-based telescopes which are 24-42 meter in diameter, and NASA’s successor to the Hubble Space Telescope, called the James Webb Space Telescope. In addition, several observational groups around the globe are constructing radio arrays that will be capable of mapping the three-dimensional distribution of cosmic hydrogen in the infant Universe.