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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 . -
The Planck Satellite and the Cosmic Microwave Background
The Cosmic Microwave Background, Dark Matter and Dark Energy Anthony Lasenby, Astrophysics Group, Cavendish Laboratory and Kavli Institute for Cosmology, Cambridge Overview The Cosmic Microwave Background — exciting new results from the Planck Satellite Context of the CMB =) addressing key questions about the Big Bang and the Universe, including Dark Matter and Dark Energy Planck Satellite and planning for its observations have been a long time in preparation — first meetings in 1993! UK has been intimately involved Two instruments — the LFI (Low — e.g. Cambridge is the Frequency Instrument) and the HFI scientific data processing (High Frequency Instrument) centre for the HFI — RAL provided the 4K Cooler The Cosmic Microwave Background (CMB) So what is the CMB? Anywhere in empty space at the moment there is radiation present corresponding to what a blackbody would emit at a temperature of ∼ 2:74 K (‘Blackbody’ being a perfect emitter/absorber — furnace with a small opening is a good example - needs perfect thermodynamic equilibrium) CMB spectrum is incredibly accurately black body — best known in nature! COBE result on this showed CMB better than its own reference b.b. within about 9 minutes of data! Universe History Radiation was emitted in the early universe (hot, dense conditions) Hot means matter was ionised Therefore photons scattered frequently off the free electrons As universe expands it cools — eventually not enough energy to keep the protons and electrons apart — they History of the Universe: superluminal inflation, particle plasma, -
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 = . -
Jul/Aug 2013
I NTERNATIONAL J OURNAL OF H IGH -E NERGY P HYSICS CERNCOURIER WELCOME V OLUME 5 3 N UMBER 6 J ULY /A UGUST 2 0 1 3 CERN Courier – digital edition Welcome to the digital edition of the July/August 2013 issue of CERN Courier. This “double issue” provides plenty to read during what is for many people the holiday season. The feature articles illustrate well the breadth of modern IceCube brings particle physics – from the Standard Model, which is still being tested in the analysis of data from Fermilab’s Tevatron, to the tantalizing hints of news from the deep extraterrestrial neutrinos from the IceCube Observatory at the South Pole. A connection of a different kind between space and particle physics emerges in the interview with the astronaut who started his postgraduate life at CERN, while connections between particle physics and everyday life come into focus in the application of particle detectors to the diagnosis of breast cancer. And if this is not enough, take a look at Summer Bookshelf, with its selection of suggestions for more relaxed reading. To sign up to the new issue alert, please visit: http://cerncourier.com/cws/sign-up. To subscribe to the magazine, the e-mail new-issue alert, please visit: http://cerncourier.com/cws/how-to-subscribe. ISOLDE OUTREACH TEVATRON From new magic LHC tourist trail to the rarest of gets off to a LEGACY EDITOR: CHRISTINE SUTTON, CERN elements great start Results continue DIGITAL EDITION CREATED BY JESSE KARJALAINEN/IOP PUBLISHING, UK p6 p43 to excite p17 CERNCOURIER www. -
The Son of Lamoraal Ulbo De Sitter, a Judge, and Catharine Theodore Wilhelmine Bertling
558 BIOGRAPHIES v.i WiLLEM DE SITTER viT 1872-1934 De Sitter was bom on 6 May 1872 in Sneek (province of Friesland), the son of Lamoraal Ulbo de Sitter, a judge, and Catharine Theodore Wilhelmine Bertling. His father became presiding judge of the court in Arnhem, and that is where De Sitter attended gymna sium. At the University of Groniiigen he first studied mathematics and physics and then switched to astronomy under Jacobus Kapteyn. De Sitter spent two years observing and studying under David Gill at the Cape Obsen'atory, the obseivatory with which Kapteyn was co operating on the Cape Photographic Durchmusterung. De Sitter participated in the program to make precise measurements of the positions of the Galilean moons of Jupiter, using a heliometer. In 1901 he received his doctorate under Kapteyn on a dissertation on Jupiter's satellites: Discussion of Heliometer Observations of Jupiter's Satel lites. De Sitter remained at Groningen as an assistant to Kapteyn in the astronomical laboratory, until 1909, when he was appointed to the chair of astronomy at the University of Leiden. In 1919 he be came director of the Leiden Observatory. He remained in these posts until his death in 1934. De Sitter's work was highly mathematical. With his work on Jupi ter's satellites, De Sitter pursued the new methods of celestial me chanics of Poincare and Tisserand. His earlier heliometer meas urements were later supplemented by photographic measurements made at the Cape, Johannesburg, Pulkowa, Greenwich, and Leiden. De Sitter's final results on this subject were published as 'New Math ematical Theory of Jupiter's Satellites' in 1925. -
A Propensity for Genius: That Something Special About Fritz Zwicky (1898 - 1974)
Swiss American Historical Society Review Volume 42 Number 1 Article 2 2-2006 A Propensity for Genius: That Something Special About Fritz Zwicky (1898 - 1974) John Charles Mannone Follow this and additional works at: https://scholarsarchive.byu.edu/sahs_review Part of the European History Commons, and the European Languages and Societies Commons Recommended Citation Mannone, John Charles (2006) "A Propensity for Genius: That Something Special About Fritz Zwicky (1898 - 1974)," Swiss American Historical Society Review: Vol. 42 : No. 1 , Article 2. Available at: https://scholarsarchive.byu.edu/sahs_review/vol42/iss1/2 This Article is brought to you for free and open access by BYU ScholarsArchive. It has been accepted for inclusion in Swiss American Historical Society Review by an authorized editor of BYU ScholarsArchive. For more information, please contact [email protected], [email protected]. Mannone: A Propensity for Genius A Propensity for Genius: That Something Special About Fritz Zwicky (1898 - 1974) by John Charles Mannone Preface It is difficult to write just a few words about a man who was so great. It is even more difficult to try to capture the nuances of his character, including his propensity for genius as well as his eccentric behavior edging the abrasive as much as the funny, the scope of his contributions, the size of his heart, and the impact on society that the distinguished physicist, Fritz Zwicky (1898- 1974), has made. So I am not going to try to serve that injustice, rather I will construct a collage, which are cameos of his life and accomplishments. In this way, you, the reader, will hopefully be left with a sense of his greatness and a desire to learn more about him. -