An Elementary Introduction to Cosmology
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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 . -
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 = . -
Subnuclear Physics: Past, Present and Future
Subnuclear Physics: Past, Present and Future International Symposium 30 October - 2 November 2011 – The purpose of the Symposium is to discuss the origin, the status and the future of the new frontier of Physics, the Subnuclear World, whose first two hints were discovered in the middle of the last century: the so-called “Strange Particles” and the “Resonance #++”. It took more than two decades to understand the real meaning of these two great discoveries: the existence of the Subnuclear World with regularities, spontaneously plus directly broken Symmetries, and totally unexpected phenomena including the existence of a new fundamental force of Nature, called Quantum ChromoDynamics. In order to reach this new frontier of our knowledge, new Laboratories were established all over the world, in Europe, in USA and in the former Soviet Union, with thousands of physicists, engineers and specialists in the most advanced technologies, engaged in the implementation of new experiments of ever increasing complexity. At present the most advanced Laboratory in the world is CERN where experiments are being performed with the Large Hadron Collider (LHC), the most powerful collider in the world, which is able to reach the highest energies possible in this satellite of the Sun, called Earth. Understanding the laws governing the Space-time intervals in the range of 10-17 cm and 10-23 sec will allow our form of living matter endowed with Reason to open new horizons in our knowledge. Antonino Zichichi Participants Prof. Werner Arber H.E. Msgr. Marcelo Sánchez Sorondo Prof. Guido Altarelli Prof. Ignatios Antoniadis Prof. Robert Aymar Prof. Rinaldo Baldini Ferroli Prof. -
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. -
Course Syllabus
University of Science and Technology of Hanoi Address: Building 2H, 18 Hoang Quoc Viet, Cau Giay, Hanoi Telephone/ Fax: +84-4 37 91 69 60 Email: [email protected] Website: http://www.usth.edu.vn COURSE SYLLABUS Subject: Intrumentation in Ground and Academic field: Astronomy Space Astrophysics Lecturer: Dr. Pham Ngoc Diep Phone: 01689677899 E-mail: [email protected] Academic year: 2013-2014 COURSE DESCRIPTION Credit points 2 Level Undergraduate Teaching time University of Science and Technology of Hanoi Location Lecture 16 hrs Exercises 8 hrs Time Commitment Practicals 6 hrs Total 30 hrs elementary of waves, classical mechanics, quantum mechanics, nuclear Prerequisites physics and particle physics Recommended Knowledge from Prof. Quynh Lan’s lectures background knowledge This course involves an elementary introduction to astrophysics, cosmology and instrumentation in ground and space astrophysics. The logic is that students should know about the basics of astrophysics and cosmology, the major unanswered questions in the fields. Therefore, they will understand why, what and how we measure astrophysical quantities. Emphases are on understanding the principles of detecting electromagnetic waves at different wavelengths and some different Subject description: particles. It is an exploratory, first course in instrumentation designed primarily for students planning to enrol in the regular-program astrophysics or related field such as space and application courses upon completion of this course. However, it also meets the needs of many students with other interests. Each UNIT is planed to be discussed in 2 hours. With practical work and/or visit to astrophysics labs, students will see in reality how a telescope works, they will have chance to operate it, take data and make some simple data analysis. -
The Big-Bang Theory AST-101, Ast-117, AST-602
AST-101, Ast-117, AST-602 The Big-Bang theory Luis Anchordoqui Thursday, November 21, 19 1 17.1 The Expanding Universe! Last class.... Thursday, November 21, 19 2 Hubbles Law v = Ho × d Velocity of Hubbles Recession Distance Constant (Mpc) (Doppler Shift) (km/sec/Mpc) (km/sec) velocity Implies the Expansion of the Universe! distance Thursday, November 21, 19 3 The redshift of a Galaxy is: A. The rate at which a Galaxy is expanding in size B. How much reader the galaxy appears when observed at large distances C. the speed at which a galaxy is orbiting around the Milky Way D. the relative speed of the redder stars in the galaxy with respect to the blues stars E. The recessional velocity of a galaxy, expressed as a fraction of the speed of light Thursday, November 21, 19 4 The redshift of a Galaxy is: A. The rate at which a Galaxy is expanding in size B. How much reader the galaxy appears when observed at large distances C. the speed at which a galaxy is orbiting around the Milky Way D. the relative speed of the redder stars in the galaxy with respect to the blues stars E. The recessional velocity of a galaxy, expressed as a fraction of the speed of light Thursday, November 21, 19 5 To a first approximation, a rough maximum age of the Universe can be estimated using which of the following? A. the age of the oldest open clusters B. 1/H0 the Hubble time C. the age of the Sun D. -
Finding the W and Z Products, Etc
CERN Courier May 2013 CERN Courier May 2013 Reminiscence Anniversary on precisely the questions that the physicists at CERN would be interested in: the cross-sections for W and Z production; the expected event rates; the angular distribution of the W and Z decay Finding the W and Z products, etc. People would also want to know how uncertain the predictions for the W and Z masses were and why certain theorists (J J Sakurai and James Bjorken among them) were cautioning that the masses could turn out to be different. The writing of the trans- parencies turned out to be time consuming. I had to make frequent revisions, trying to anticipate what questions might be asked. To Thirty years ago, CERN made scientifi c make corrections on the fi lm transparencies, I was using my after- shave lotion, so that the whole room was reeking of perfume. I history with the discoveries of the W and was preparing the lectures on a day-by-day basis, not getting much sleep. To stay awake, I would go to the cafeteria for a coffee shortly Z bosons. Here, we reprint an extract from before it closed. Thereafter I would keep going to the vending the special issue of CERN Courier that machines in the basement for chocolate – until the machines ran out of chocolate or I ran out of coins. commemorated this breakthrough. After the fourth lecture, the room in the dormitory had become such a mess (papers everywhere and the strong smell of after- shave) that I decided to ask the secretariat for an offi ce where I Less than 11 months after Lalit Sehgal’s visit to CERN, Carlo could work. -
The Discovery of the Expansion of the Universe
galaxies Review The Discovery of the Expansion of the Universe Øyvind Grøn Faculty of Technology, Art and Design, Oslo Metropolitan University, PO Box 4 St. Olavs Plass, NO-0130 Oslo, Norway; [email protected]; Tel.: +047-90-94-64-60 Received: 2 November 2018; Accepted: 29 November 2018; Published: 3 December 2018 Abstract: Alexander Friedmann, Carl Wilhelm Wirtz, Vesto Slipher, Knut E. Lundmark, Willem de Sitter, Georges H. Lemaître, and Edwin Hubble all contributed to the discovery of the expansion of the universe. If only two persons are to be ranked as the most important ones for the general acceptance of the expansion of the universe, the historical evidence points at Lemaître and Hubble, and the proper answer to the question, “Who discovered the expansion of the universe?”, is Georges H. Lemaître. Keywords: cosmology history; expansion of the universe; Lemaitre; Hubble 1. Introduction The history of the discovery of the expansion of the universe is fascinating, and it has been thoroughly studied by several historians of science. (See, among others, the contributions to the conference Origins of the expanding universe [1]: 1912–1932). Here, I will present the main points of this important part of the history of the evolution of the modern picture of our world. 2. Einstein’s Static Universe Albert Einstein completed the general theory of relativity in December 1915, and the theory was presented in an impressive article [2] in May 1916. He applied [3] the theory to the construction of a relativistic model of the universe in 1917. At that time, it was commonly thought that the universe was static, since one had not observed any large scale motions of the stars. -
RESEARCH ASSOCIATE in Particle Physics THEORETICAL NUCLEAR PHYSICS
Andrei Dimitrievich Sakharov 1921-1989 People and things Andrei Dimitrievich Sakharov, the quark model, and pioneer talented and versatile scientist, ideas in the quantum theory of fearless activist and staunch gravity. proponent of human rights, fig• He was not able to receive his urehead for Soviet perestroika, Nobel Award in person. From described in the citation for his 1980, during his exile in Gorki, 1975 Nobel Peace Prize as he tried to keep in touch with CERN elections and appointments 'spokesman for the conscience developments in science, receiv• of mankind', died on 14 Decem• ing physics literature, including At its December meetings, CERN ber. the CERN Courier, by registered Council elected C. Lopez, Rector of Beginning research at Lenin• mail. the Autonomous University of Ma• grad's Lebedev Institute in 1945 With the new direction in So• drid, and E. W.J. Mitchell, Chairman under Igor Tamm, he first came viet policy he reemerged as a of the UK Science and Engineering to prominence with his early popular champion in the USSR. Research Council, as Vice-Presi• 1950s contributions to thermo• Last year, accompanied by his dents, and Chris Llewellyn-Smith of nuclear fusion with Tamm, in• wife Elena Bonner, he embarked Oxford as Chairman of the Science cluding the idea to contain plas• on a visit of major world physics Policy Committee. ma in a magnetic 'bottle', later Laboratories. In 1990, the CERN Directorate to become known as the toka- In a message entitled 'The re• consists of Research Directors mak. For his fusion work he be• sponsibility of scientists' to a Pierre Darriulat, Walter Hoogland came an Academician in 1953 1981 New York meeting in his and John Thresher; Gunther Plass at the age of only 32, the youn• honour, he wrote 'scientists are as Director of Accelerators; gest ever to be so honoured. -
Cosmology and Religion — an Outsider's Study
Cosmology and Religion — An Outsider’s Study (Big Bang and Creation) Dezs˝oHorváth [email protected] KFKI Research Institute for Particle and Nuclear Physics (RMKI), Budapest and Institute of Nuclear Research (ATOMKI), Debrecen Dezs˝oHorváth: Cosmology and religion Wien, 10.03.2010 – p. 1/46 Outline Big Bang, Inflation. Lemaître and Einstein. Evolution and Religion. Big Bang and Hinduism, Islam, Christianity. Saint Augustine on Creation. Saint Augustine on Time. John Paul II and Stephen Hawking. Dezs˝oHorváth: Cosmology and religion Wien, 10.03.2010 – p. 2/46 Warning Physics is an exact science (collection of formulae) It is based on precise mathematical formalism. A theory is valid if quantities calculated with it agree with experiment. Real physical terms are measurable quantities, words are just words. Behind the words there are precise mathematics and experimental evidence What and how: Physics Why: philosopy? And theology? Dezs˝oHorváth: Cosmology and religion Wien, 10.03.2010 – p. 3/46 What is Cosmology? Its subject is the Universe as a whole. How did it form? (Not why?) Static, expanding or shrinking? Open or closed? Its substance, composition? Its past and future? Dezs˝oHorváth: Cosmology and religion Wien, 10.03.2010 – p. 4/46 The Story of the Big Bang Theory Red Shift of Distant Galaxies Henrietta S. Leavitt Vesto Slipher Distances to galaxies Red shift of galaxies 1908–1912 1912 Dezs˝oHorváth: Cosmology and religion Wien, 10.03.2010 – p. 5/46 Expanding Universe Cosmological principle: if the expansion linear A. Friedmann v(B/A) = v(C/B) ⇒ v(C/A)=2v(B/A) the Universe is homogeneous, it has no special point. -
Abraham Seiden Santa Cruz Institue for Particle Physics (SCIPP) UC Santa Cruz Department of Physics
Abraham Seiden Santa Cruz Institue for Particle Physics (SCIPP) UC Santa Cruz Department of Physics PROFESSIONAL PREPARATION Columbia University Applied Physics B.S. 1967 California Institute of Technology Physics M.S. 1970 University of California, Santa Cruz Physics Ph.D. 1974 POST DOCTORAL APPOINTMENTS 1975-1976 Postdoctoral Research Scientist, High Energy Physics, University of California, Santa Cruz 1974-1975 Visiting Scientist, CERN APPOINTMENTS 2008-present Distinguished Professor of Physics, University of California, Santa Cruz 1981-2010 Director, Santa Cruz Institute for Particle Physics 1986-2008 Professor of Physics, University of California, Santa Cruz 1985-1986 Visiting Scientist, European Laboratory for Particle Physics (CERN) 1981-1985 Associate Professor of Physics, University of California, Santa Cruz 1978-1981 Assistant Professor of Physics, University of California, Santa Cruz 1976-1978 Assistant Professor of Physics in Residence, University of California, Santa Cruz SELECTED PUBLICATIONS PERTINENT TO THIS PROPOSAL (Primary Author Only) 1. Characteristics of the ATLAS and CMS Detectors. A. Seiden, Phil. Trans. R. Soc., 370 no. 1961, 892 (2012). 2. Comparing radiation tolerant materials and devices for ultra rad-hard tracking detectors. M. Bruzzi, H.F.W. Sadrozinski, A. Seiden, Nucl.Instrum.Meth. A579:754 (2007). 3. Radiation-hard semiconductor detectors for Super LHC. M. Bruzzi et al. Nucl. Instrum. Meth. A 541: 189 (2005). 4. Tracking detectors for the sLHC, the LHC upgrade. H.F.W. Sadrozinski and A. Seiden, Nucl. Instrum. Meth. A 541: 434 (2005) 5. Ionization Damage on Atlas-SCT Front-End Electronics considering Low-Dose-Rate Effects. M. Ullan et al., IEEE Trans. Nucl. Sci. 49:1106, (2002). -
The ISR Legacy
! Subnuclear Physics: Past, Present and Future ! Pontifical Academy of Sciences, Scripta Varia 119, Vatican City 2014 ! www.pas.va/content/dam/accademia/pdf/sv119/sv119-darriulat.pdf ! ! The ISR Legacy P!IERRE D!ARRIULAT ! ! ! VATLY!Astrophysics!Laboratory,!Hanoi,!Vietnam! ! ! 1.!Introduction! It!so!happens!that!the!life!time!of!the!CERN!Intersecting!Storage!Rings!(ISR),! roughly!!speaking!!the!!seventies,!!coincides!!with!!a!!giant!!leap!!in!!our!!understanding!!of! particle!physics:!the!genesis!of!the!Standard!Model.!Those!of!us!who!have!worked!at!the! ISR!remember!these!times!with!the!conviction!that!we!were!not!merely!spectators!of!the! ongoing!progress,!but!also!–!admittedly!modest!–!actors.!While!the!ISR!contribution!to! the!!electroweak!!sector!!is!!indeed!!negligible,!!its!!contribution!!to!!the!!strong!!sector!!is! essential!and!too!often!unjustly!forgotten!in!the!accounts!that!are!commonly!given!of!the! progress!of!particle!physics!during!that!!period.!In!the!present!article,!I!shall!use!three! topics!to!illustrate!how!important!it!has!been:!the!production!of!hadrons,!large!transverse! momentum!final!states!and!the!rising!total!cross-section.! When!!Vicky!!Weisskopf,!!in!!December!!1965,!!in!!his!!last!!Council!!session!!as! Director-General,!obtained!approval!for!the!construction!of!the!ISR,!there!was!no!specific! physics!issue!at!stake,!which!the!machine!was!supposed!to!address;!its!only!justification! was!!to!!explore!!the!terra!!incognita!!of!higher!!centre!of!mass!energy!collisions!(to!!my! knowledge,!!since!!then,!!all!!new!!machines!!have!!been!!proposed!!and!!approved!!with!!a!