Towards Relativistic Astrophysics
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Frame Covariance and Fine Tuning in Inflationary Cosmology
FRAME COVARIANCE AND FINE TUNING IN INFLATIONARY COSMOLOGY A thesis submitted to the University of Manchester for the degree of Doctor of Philosophy in the Faculty of Science and Engineering 2019 By Sotirios Karamitsos School of Physics and Astronomy Contents Abstract 8 Declaration 9 Copyright Statement 10 Acknowledgements 11 1 Introduction 13 1.1 Frames in Cosmology: A Historical Overview . 13 1.2 Modern Cosmology: Frames and Fine Tuning . 15 1.3 Outline . 17 2 Standard Cosmology and the Inflationary Paradigm 20 2.1 General Relativity . 20 2.2 The Hot Big Bang Model . 25 2.2.1 The Expanding Universe . 26 2.2.2 The Friedmann Equations . 29 2.2.3 Horizons and Distances in Cosmology . 33 2.3 Problems in Standard Cosmology . 34 2.3.1 The Flatness Problem . 35 2.3.2 The Horizon Problem . 36 2 2.4 An Accelerating Universe . 37 2.5 Inflation: More Questions Than Answers? . 40 2.5.1 The Frame Problem . 41 2.5.2 Fine Tuning and Initial Conditions . 45 3 Classical Frame Covariance 48 3.1 Conformal and Weyl Transformations . 48 3.2 Conformal Transformations and Unit Changes . 51 3.3 Frames in Multifield Scalar-Tensor Theories . 55 3.4 Dynamics of Multifield Inflation . 63 4 Quantum Perturbations in Field Space 70 4.1 Gauge Invariant Perturbations . 71 4.2 The Field Space in Multifield Inflation . 74 4.3 Frame-Covariant Observable Quantities . 78 4.3.1 The Potential Slow-Roll Hierarchy . 81 4.3.2 Isocurvature Effects in Two-Field Models . 83 5 Fine Tuning in Inflation 88 5.1 Initial Conditions Fine Tuning . -
AST 541 Lecture Notes: Classical Cosmology Sep, 2018
ClassicalCosmology | 1 AST 541 Lecture Notes: Classical Cosmology Sep, 2018 In the next two weeks, we will cover the basic classic cosmology. The material is covered in Longair Chap 5 - 8. We will start with discussions on the first basic assumptions of cosmology, that our universe obeys cosmological principles and is expanding. We will introduce the R-W metric, which describes how to measure distance in cosmology, and from there discuss the meaning of measurements in cosmology, such as redshift, size, distance, look-back time, etc. Then we will introduce the second basic assumption in cosmology, that the gravity in the universe is described by Einstein's GR. We will not discuss GR in any detail in this class. Instead, we will use a simple analogy to introduce the basic dynamical equation in cosmology, the Friedmann equations. We will look at the solutions of Friedmann equations, which will lead us to the definition of our basic cosmological parameters, the density parameters, Hubble constant, etc., and how are they related to each other. Finally, we will spend sometime discussing the measurements of these cosmological param- eters, how to arrive at our current so-called concordance cosmology, which is described as being geometrically flat, with low matter density and a dominant cosmological parameter term that gives the universe an acceleration in its expansion. These next few lectures are the foundations of our class. You might have learned some of it in your undergraduate astronomy class; now we are dealing with it in more detail and more rigorously. 1 Cosmological Principles The crucial principles guiding cosmology theory are homogeneity and expansion. -
PDF Solutions
Solutions to exercises Solutions to exercises Exercise 1.1 A‘stationary’ particle in anylaboratory on theEarth is actually subject to gravitationalforcesdue to theEarth andthe Sun. Thesehelp to ensure that theparticle moveswith thelaboratory.Ifstepsweretaken to counterbalance theseforcessothatthe particle wasreally not subject to anynet force, then the rotation of theEarth andthe Earth’sorbital motionaround theSun would carry thelaboratory away from theparticle, causing theforce-free particle to followacurving path through thelaboratory.Thiswouldclearly show that the particle didnot have constantvelocity in the laboratory (i.e.constantspeed in a fixed direction) andhence that aframe fixed in the laboratory is not an inertial frame.More realistically,anexperimentperformed usingthe kind of long, freely suspendedpendulum known as a Foucaultpendulum couldreveal the fact that a frame fixed on theEarth is rotating andthereforecannot be an inertial frame of reference. An even more practical demonstrationisprovidedbythe winds,which do not flowdirectly from areas of high pressure to areas of lowpressure because of theEarth’srotation. - Exercise 1.2 TheLorentzfactor is γ(V )=1/ 1−V2/c2. (a) If V =0.1c,then 1 γ = - =1.01 (to 3s.f.). 1 − (0.1c)2/c2 (b) If V =0.9c,then 1 γ = - =2.29 (to 3s.f.). 1 − (0.9c)2/c2 Notethatitisoften convenient to write speedsinterms of c instead of writingthe values in ms−1,because of thecancellation between factorsofc. ? @ AB Exercise 1.3 2 × 2 M = Theinverse of a matrix CDis ? @ 1 D −B M −1 = AD − BC −CA. Taking A = γ(V ), B = −γ(V )V/c, C = −γ(V)V/c and D = γ(V ),and noting that AD − BC =[γ(V)]2(1 − V 2/c2)=1,wehave ? @ γ(V )+γ(V)V/c [Λ]−1 = . -
Expanding Space, Quasars and St. Augustine's Fireworks
Universe 2015, 1, 307-356; doi:10.3390/universe1030307 OPEN ACCESS universe ISSN 2218-1997 www.mdpi.com/journal/universe Article Expanding Space, Quasars and St. Augustine’s Fireworks Olga I. Chashchina 1;2 and Zurab K. Silagadze 2;3;* 1 École Polytechnique, 91128 Palaiseau, France; E-Mail: [email protected] 2 Department of physics, Novosibirsk State University, Novosibirsk 630 090, Russia 3 Budker Institute of Nuclear Physics SB RAS and Novosibirsk State University, Novosibirsk 630 090, Russia * Author to whom correspondence should be addressed; E-Mail: [email protected]. Academic Editors: Lorenzo Iorio and Elias C. Vagenas Received: 5 May 2015 / Accepted: 14 September 2015 / Published: 1 October 2015 Abstract: An attempt is made to explain time non-dilation allegedly observed in quasar light curves. The explanation is based on the assumption that quasar black holes are, in some sense, foreign for our Friedmann-Robertson-Walker universe and do not participate in the Hubble flow. Although at first sight such a weird explanation requires unreasonably fine-tuned Big Bang initial conditions, we find a natural justification for it using the Milne cosmological model as an inspiration. Keywords: quasar light curves; expanding space; Milne cosmological model; Hubble flow; St. Augustine’s objects PACS classifications: 98.80.-k, 98.54.-h You’d think capricious Hebe, feeding the eagle of Zeus, had raised a thunder-foaming goblet, unable to restrain her mirth, and tipped it on the earth. F.I.Tyutchev. A Spring Storm, 1828. Translated by F.Jude [1]. 1. Introduction “Quasar light curves do not show the effects of time dilation”—this result of the paper [2] seems incredible. -
On the Concept of Degenerate Stars: the Case of White Dwarfs
On the concept of degenerate stars: the case of white dwarfs Michael Rotondo - Istituto di Istruzione Superiore Statale “Pacinotti-Archimede”, Roma - [email protected] Abstract: In this work we briefly review the history of degenerate stars from the first introduction of Fermi-Dirac quantum statistics to the first unified approach of white dwarfs, based on the relativistic generalization of the Feynman-Metropolis-Teller of compressed atoms, which takes into account consistently the gravitational, the weak, the strong and the electromagnetic interactions. Keywords:History of astrophysics, Compact stars, Degenerate Fermi gas 1. Prologue: Adams and Eddington Exactly one century ago Walter S. Adams published a paper entitled “The Spectrum of the Companion of Sirius” in which he concludes that: …the companion of Sirius has a color index not appreciably different from that of the principal star (Adams 1915, p. 237). This conclusion would lead to a dramatic consequence as summarized by Arthur S. Ed- dington: …a ton of [companion of Sirius] material would be a little nugget that you could put in a match-box. What reply can one make to such a message? The reply which most of us made in 1914 was - ‘Shut up. Don’t talk nonsense’ (Eddington 1927, p. 50). Nine years later, in 1924, Eddington published a paper entitled “On the Relation be- tween the Masses and Luminosities of the Stars” in which he suggested a new test to confirm (or reject) the exceptionally high density of the companion of Sirius: …the question could probably be settled by measuring Einstein shift of the spec- trum… (Eddington 1924, p. -
Hubble's Evidence for the Big Bang
Hubble’s Evidence for the Big Bang | Instructor Guide Students will explore data from real galaxies to assemble evidence for the expansion of the Universe. Prerequisites ● Light spectra, including graphs of intensity vs. wavelength. ● Linear (y vs x) graphs and slope. ● Basic measurement statistics, like mean and standard deviation. Resources for Review ● Doppler Shift Overview ● Students will consider what the velocity vs. distance graph should look like for 3 different types of universes - a static universe, a universe with random motion, and an expanding universe. ● In an online interactive environment, students will collect evidence by: ○ using actual spectral data to calculate the recession velocities of the galaxies ○ using a “standard ruler” approach to estimate distances to the galaxies ● After they have collected the data, students will plot the galaxy velocities and distances to determine what type of model Universe is supported by their data. Grade Level: 9-12 Suggested Time One or two 50-minute class periods Multimedia Resources ● Hubble and the Big Bang WorldWide Telescope Interactive Materials ● Activity sheet - Hubble’s Evidence for the Big Bang Lesson Plan The following represents one manner in which the materials could be organized into a lesson: Focus Question: ● How does characterizing how galaxies move today tell us about the history of our Universe? Learning Objective: ● SWBAT collect and graph velocity and distance data for a set of galaxies, and argue that their data set provides evidence for the Big Bang theory of an expanding Universe. Activity Outline: 1. Engage a. Invite students to share their ideas about these questions: i. Where did the Universe come from? ii. -
Ivanenko. Biography
The People of Physics Faculty Selected papers of the Journal “Soviet Physicist” 1998-2006 Dmitri Ivanenko. Scientific Biography 226 Dmitri Ivanenko (29.07.1904 - 30.12.1994), professor of Moscow State University (since 1943) , was one of the great theoreticians of XX century. He made the fundamental contribution to many areas of nuclear physics, field theory and gravitation theory. His outstanding achievements include: • The Fock - Ivanenko coefficients of parallel displacement of spinors in a curved space-time (1929) 1 . Nobel laureate Abdus Salam called it the first gauge theory. • The Ambartsumian - Ivanenko hypothesis of creation of massive particles which is a corner stone of contemporary quantum field theory (1930) 2 . • The proton-neutron model of atomic nuclei (1932) 3 . • The first shell model of nuclei (in collaboration with E. Gapon) (1932) 4 . • The first model of exchange nuclear forces by means of massive particles (in collaboration with I. Tamm) (1934) 5 . Based on this model, Nobel laureate H. Yukawa developed his meson theory. • The prediction of synchrotron radiation (in collaboration with I. Pomeranchuk) (1944) 6 and its classical theory (in collaboration with A. Sokolov). • Theory of hypernucleus (1956) 7 . • The hypothesis of quark stars (in collaboration with D. Kurdgelaidze) (1965) 8 . • The gauge gravitation theory (in collaboration with G. Sardanashvily), where gravity is treated as a Higgs field responsible for spontaneous breaking of space- 9 time symmetries (1983) . References 1. Fock V., Iwanenko D., Géometrie quantique linéaire et déplacement paralléle, Compt. Rend. Acad Sci. Paris 188 (1929) 1470. 2. Ambarzumian V., Iwanenko D., Les électrons inobservables et les rayons, Compt. -
How Supernovae Became the Basis of Observational Cosmology
Journal of Astronomical History and Heritage, 19(2), 203–215 (2016). HOW SUPERNOVAE BECAME THE BASIS OF OBSERVATIONAL COSMOLOGY Maria Victorovna Pruzhinskaya Laboratoire de Physique Corpusculaire, Université Clermont Auvergne, Université Blaise Pascal, CNRS/IN2P3, Clermont-Ferrand, France; and Sternberg Astronomical Institute of Lomonosov Moscow State University, 119991, Moscow, Universitetsky prospect 13, Russia. Email: [email protected] and Sergey Mikhailovich Lisakov Laboratoire Lagrange, UMR7293, Université Nice Sophia-Antipolis, Observatoire de la Côte d’Azur, Boulevard de l'Observatoire, CS 34229, Nice, France. Email: [email protected] Abstract: This paper is dedicated to the discovery of one of the most important relationships in supernova cosmology—the relation between the peak luminosity of Type Ia supernovae and their luminosity decline rate after maximum light. The history of this relationship is quite long and interesting. The relationship was independently discovered by the American statistician and astronomer Bert Woodard Rust and the Soviet astronomer Yury Pavlovich Pskovskii in the 1970s. Using a limited sample of Type I supernovae they were able to show that the brighter the supernova is, the slower its luminosity declines after maximum. Only with the appearance of CCD cameras could Mark Phillips re-inspect this relationship on a new level of accuracy using a better sample of supernovae. His investigations confirmed the idea proposed earlier by Rust and Pskovskii. Keywords: supernovae, Pskovskii, Rust 1 INTRODUCTION However, from the moment that Albert Einstein (1879–1955; Whittaker, 1955) introduced into the In 1998–1999 astronomers discovered the accel- equations of the General Theory of Relativity a erating expansion of the Universe through the cosmological constant until the discovery of the observations of very far standard candles (for accelerating expansion of the Universe, nearly a review see Lipunov and Chernin, 2012). -
Physics 211A Special Topic Paper Scientist: Yakov Frenkel Paper: on the Transformation of Light Into Heat in Solids I
Physics 211A Special Topic Paper Scientist: Yakov Frenkel Paper: On the Transformation of Light into Heat in Solids I Kelson Kaj, A11478149 11/29/18 Introduction Jakov Frenkel was a Russian born physicist who made multiple contri- butions to fields both within and outside of condensed matter physics. His book Kinetic Theory of Liquids, is a classic text on the subject [1]. He has also made contributions to semiconductor physics, specifically in coming up with the Poole-Frenkel effect [2]. One of his most important contributions was the introduction of Frenkel Excitons, in his paper On the Transforma- tion of Light into Heat in Solids I, although he certainly did not refer to the excitations he studied as "Frenkel Excitons," in the paper [3]. This is the topic that I will present in this report. Frenkel's paper has garnered over 540 citations. Although this is impressive, it doesn't even begin to capture the influence of Frenkel's work. Excitons are bound states made up of an electron and a hole, and have become their own sub-field of condensed matter physics, with some labs devoted completely to their study. The excitons studied in Frenkel's work, Frenkel Excitons, are only one type of exciton. As will be discussed further below, Frenkel Excitons are highly localized excitons, where the hole and electron are less than a lattice constant from each other and are localized to the same atom in the crystal. This is in contrast to other kinds of excitons, such as Wannier Excitons, where the distance between the electron and hole can be larger than a lattice constant, and the electron and hole are not necessarily localized to the same atom on the crystal [4]. -
Reflections December 2020
Surviving the Bobcat Fire By Robert Anderson As recently as December 9, our solar astronomer, Steve Padilla, was taking his evening walk and noticed the smoke of a hotspot flaring up in the canyon just below the Observatory. It was a remnant of the Bobcat Fire, which started nearby on September 6. The local Angeles National Forest firefighters were notified of the flareup, either to monitor it or extinguish it if needed. They have returned many times during the last three months. And we are always glad to see them, especially those individuals who put water to flame here and battled to save the most productive and famous observatory in history. On the sunny Labor Day weekend, when the Bobcat Fire started near Cogswell Reservoir in a canyon east of the Mount Wilson, the Observatory’s maintenance staff went on cautious alert. As the fire spread out of control, it stayed to the east burning north and south of the reservoir for days, threatening communities in the foothills of the San Gabriels. Nevertheless, all non-essential staff and residents were evacuated off the mountain just in case. Under a surreal, smoke-filled September sky, crews David Cendejas, the superintendent of the Observatory, prepare to defend the Observatory. Photo: D. Cendejas and a skeleton crew of CHARA staff, stayed to monitor the situation and to secure the grounds. Routine year- round maintenance of Mount Wilson always includes In this issue . clearing a wide perimeter of combustibles from the buildings, but when a large fire is burning nearby, clearing Surviving the Fire ……………1 Betelgeuse & Baade …………….5 anything that has been missed becomes an urgent priority, News + Notes .….………………2 Thanks to our Supporters! ..….7 along with double-checking all the fire equipment. -
Subrahmanyan Chandrasekhar – Geniaalne Astrofüüsik
Subrahmanyan Chandrasekhar – geniaalne astrofüüsik Sissejuhatus Kuulsin Chandrasekhari nime esimest korda, kui mu sõber ja hilisem kolleeg Tiit Nilson oli saanud veel ülikooliajal – 1962. aastal - oma juhendajaks Juhan Rossi. Tiit näitas mulle Juhani käest saadud vene keelde tõlgitud Chandrasekhari raamatut kiirguslevist, mis oli täis salapäraseid valemeid. Hiljem sai see raamat mullegi väga oluliseks ja 1977. a ostsin selle – inglisekeelsena – Lõuna-California ülikooli raamatupoest Los Angeleses. Sellest ajast on see mu töölauaraamat, ja minuni jõudis arusaamine sellest, et see mees on haruldaselt mitmekülgne suur teadlane. Mingi tõsise probleemi ettevõtnuna avaldas ta terve seeria artikleid probleemi lahenduse kohta ja siis järgnes artikleid kokkuvõttev monograafia. Nii said põhjaliku ülevaate ja lahenduse tähe siseehitus, sh valgete kääbuste ehitus, stellaardünaamika, stohhastilised protsessid, kiirguslevi, negatiivse vesiniku iooni kvantteooria, hüdrodünaamika ja hüdromagnetiline stabiilsus, turbulents, tasakaaluliste objektide tasakaal, üldine relatiivsusteooria, mustade aukude matemaatiline teooria ja põrkuvate gravitatsioonilainete teooria. Lisaks veel Newtoni kuulsa Principia „tõlkimine“ autori geomeetrilisest keelest tänapäevasesse keelde. Mida rohkemat veel ühelt inimeselt nõuda võiks! Lapsepõlv ja perekond Chandrasekhar sündis tolleaegses Briti India (nüüd Pakistani) Punjabi provintsi linnas Lahores 19. oktoobril 1910 Chandrasekhara Subrahmanyan Ayyari (1885-1960) ja tema abikaasa Sitalakshmi (1891-1931) esimese pojana. Kokku -
Zirker J.B. the Magnetic Universe (JHUP, 2009)(ISBN 080189302X
THE MAGNETIC UNIVERSE This page intentionally left blank J. B. ZIRKER THE MAGNETIC THE ELUSIVE TRACES OF AN INVISIBLE FORCE UNIVERSE THE JOHNS HOPKINS UNIVERSITY PRESS BALTIMORE © 2009 The Johns Hopkins University Press All rights reserved. Published 2009 Printed in the United States of America on acid- free paper 2 4 6 8 9 7 5 3 1 The Johns Hopkins University Press 2715 North Charles Street Baltimore, Mary land 21218- 4363 www .press .jhu .edu Library of Congress Cataloging- in- Publication Data Zirker, Jack B. The magnetic universe : the elusive traces of an invisible force / J.B. Zirker. p. cm. Includes bibliographical references and index. ISBN- 13: 978- 0- 8018- 9301- 8 (hardcover : alk. paper) ISBN- 10: 0- 8018- 9301- 1 (hardcover : alk. paper) ISBN- 13: 978- 0- 8018- 9302- 5 (pbk. : alk. paper) ISBN- 10: 0- 8018- 9302- X (pbk. : alk. paper) 1. Magnetic fi elds. 2. Cosmic magnetic fi elds. 3. Magnetism. 4. Magnetosphere. 5. Heliosphere (Ionosphere) 6. Gravity. I. Title. QC754.2.M3Z57 2009 538—dc22 2008054593 A cata log record for this book is available from the British Library. The last printed pages of the book are an extension of this copyright page. Special discounts are available for bulk purchases of this book. For more information, please contact Special Sales at 410- 516- 6936 or [email protected]. The Johns Hopkins University Press uses environmentally friendly book materials, including recycled text paper that is composed of at least 30 percent post- consumer waste, whenever possible. All of our book papers are acid- free, and our jackets and covers are printed on paper with recycled content.