DOCSLIB.ORG

Relativity, Gravitation, and Cosmology STATISTICAL, COMPUTATIONAL, and THEORETICAL PHYSICS 12

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Relativity, Gravitation, and Cosmology STATISTICAL, COMPUTATIONAL, and THEORETICAL PHYSICS 12 OXFORD MASTER SERIES IN PARTICLE PHYSICS, ASTROPHYSICS, AND COSMOLOGY OXFORD MASTER SERIES IN PHYSICS The Oxford Master Series is designed for final year undergraduate and beginning graduate students in physics and related disciplines. It has been driven by a perceived gap in the literature today. While basic undergraduate physics texts often show little or no connection with the huge explosion of research over the last two decades, more advanced and specialized texts tend to be rather daunting for students. In this series, all topics and their consequences are treated at a simple level, while pointers to recent developments are provided at various stages. The emphasis is on clear physical principles like symmetry, quantum mechanics, and electromagnetism which underlie the whole of physics. At the same time, the subjects are related to real measurements and to the experimental techniques and devices currently used by physicists in academe and industry. Books in this series are written as course books, and include ample tutorial material, examples, illustrations, revision points, and problem sets. They can likewise be used as preparation for students starting a doctorate in physics and related fields, or for recent graduates starting research in one of these fields in industry. CONDENSED MATTER PHYSICS 1. M. T. Dove: Structure and dynamics: an atomic view of materials 2. J. Singleton: Band theory and electronic properties of solids 3. A. M. Fox: Optical properties of solids 4. S. J. Blundell: Magnetism in condensed matter 5. J. F. Annett: Superconductivity 6. R. A. L. Jones: Soft condensed matter ATOMIC, OPTICAL, AND LASER PHYSICS 7. C. J. Foot: Atomic physics 8. G. A. Brooker: Modern classical optics 9. S. M. Hooker, C. E. Webb: Laser physics PARTICLE PHYSICS, ASTROPHYSICS, AND COSMOLOGY 10. D. H. Perkins: Particle astrophysics 11. T. P. Cheng: Relativity, gravitation, and cosmology STATISTICAL, COMPUTATIONAL, AND THEORETICAL PHYSICS 12. M. Maggiore: A modern introduction to quantum field theory 13. W. Krauth: Statistical mechanics: algorithms and computations 14. J. P. Sethna: Entropy, order parameters, and emergent properties Relativity, Gravitation, and Cosmology A basic introduction TA-PEI CHENG University of Missouri—St. Louis 1 3 Great Clarendon Street, Oxford OX2 6DP Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide in Oxford New York Auckland Cape Town Dar es Salaam Hong Kong Karachi Kuala Lumpur Madrid Melbourne Mexico City Nairobi New Delhi Shanghai Taipei Toronto With offices in Argentina Austria Brazil Chile Czech Republic France Greece Guatemala Hungary Italy Japan Poland Portugal Singapore South Korea Switzerland Thailand Turkey Ukraine Vietnam Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries Published in the United States by Oxford University Press Inc., New York © Oxford University Press, 2005 The moral rights of the author have been asserted Database right Oxford University Press (maker) First published 2005 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this book in any other binding or cover and you must impose the same condition on any acquirer A catalogue record for this title is available from the British Library Library of Congress Cataloging-in-Publication Data Cheng, Ta-Pei. Relativity, gravitation, and cosmology: a basic introduction / Ta-Pei Cheng. p. cm.—(Oxford master series in physics; no. 11) Includes bibliographical references and index. ISBN 0-19-852956-2 (alk. paper)—ISBN 0-19-852957-0 (pbk. : alk. paper) 1. General relativity (Physics)—Textbooks. 2. Space and time. 3. Gravity. 4. Cosmology. I. Title. II. Series: Oxford master series in physics; 11. QC173.6.C4724 2005 530.11—dc22 2004019733 Typeset by Newgen Imaging Systems (P) Ltd., Chennai, India Printed in Great Britain on acid-free paper by Antony Rowe, Chippenham ISBN 0 19 852956 2 (Hbk) ISBN 0 19 852957 0 (Pbk) 10987654321 Preface It seems a reasonable expectation that every student receiving a university degree in physics will have had a course in one of the most important devel- opments in modern physics: Einstein’s general theory of relativity. Also, given the exciting discoveries in astrophysics and cosmology of recent years, it is highly desirable to have an introductory course whereby such subjects can be presented in their proper framework. Again, this is general relativity (GR). Nevertheless, a GR course has not been commonly available to undergradu- ates, or even for that matter, to graduate students who do not specialize in GR or field theory. One of the reasons, in my view, is the insufficient number of suitable textbooks that introduce the subject with an emphasis on physical examples and simple applications without the full tensor apparatus from the very beginning. There are many excellent graduate GR books; there are equally many excellent “popular” books that describe Einstein’s theory of gravitation and cosmology at the qualitative level; and there are not enough books in between. I am hopeful that this book will be a useful addition at this intermediate level. The goal is to provide a textbook that even an instructor who is not a relativist can teach from. It is also intended that other experienced physics readers who have not had a chance to learn GR can use the book to study the subject on their own. As explained below, this book has features that will make such an independent study particularly feasible. Students should have had the usual math preparation at the calculus level, plus some familiarity with matrices, and the physics preparation of courses on mechanics and on electromagnetism where differential equations of Maxwell’s theory are presented. Some exposure to special relativity as part of an intro- ductory modern physics course will also be helpful, even though no prior knowledge of special relativity will be assumed. Part I of this book concen- trates on the metric description of spacetime: first, the flat geometry as in special relativity, and then curved ones for general relativity. Here I discuss the equation of motion in Einstein’s theory, and many of its applications: the three classical tests, black holes, and gravitational lensing, etc. Part II contains three chapters on cosmology. Besides the basic equations describing a homoge- neous and isotropic universe, I present a careful treatment of distance and time in an expanding universe with a space that may be curved. The final chapter on cosmology, Chapter 9 provides an elementary discussion of the inflationary model of the big bang, as well as the recent discovery that the expansion of our universe is accelerating, implying the existence of a “dark energy.” The tensor formulation of relativity is introduced in Part III. After presenting special rela- tivity in a manifestly covariant formalism, we discuss covariant differentiation, parallel transport, and curvature tensor for a curved space. Chapter 12 contains the full tensor formulation of GR, including the Einstein’s field equation and its vi Preface solutions for various simple situations. The subject of gravitational waves can be found in the concluding chapter. The emphasis of the book is pedagogical. The necessary mathematics will be introduced gradually. Tensor calculus is relegated to the last part of the book. Discussion of curved surfaces, especially the familiar example of a spherical surface, precedes that of curved higher dimensional spaces. Parts I and II present the metric description of spacetime. Many applications (including cosmology) can already be discussed at this more accessible level; students can reach these interesting results without having to struggle through the full tensor formulation, which is presented in Part III of the book. A few other pedagogical devices are also deployed: • a bullet list of topical headings at the beginning of each chapter serves as the “chapter abstracts,” giving the reader a foretaste of upcoming material; • matter in marked boxes are calculation details, peripheral topics, historical tit-bits that can be skipped over depending on the reader’s interest; • Review questions at the end of each chapter should help beginning 1We find that the practice of frequent quizzes students to formulate questions on the key elements of the chapter1; brief based on these review questions are an effec- answers to these questions are provided at the back of the book; tive means to make sure that each member is • keeping up with the progress of the class. Solutions to selected problems at the end of the book also contains some extra material that can be studied with techniques already presented in the text. Given this order of presentation, with the more interesting applications coming before the difficult mathematical formalism, it is hoped that the book can be rather versatile in terms of how it can be used. Here are some of the possibilities: 1. Parts I and II should be suitable for an undergraduate course. The tensor formulation in Part III can then be used as extracurricular material for instructors to refer to, and for interested students to explore on their own. Much of the intermediate steps being given and more difficult problems having their solutions provided, this section can, in principle, be used as self-study material by a particularly motivated undergraduate. 2. The whole book can be used for a senior-undergraduate/beginning- graduate course. To fit into a one-semester course, one may have to leave some applications and illustrative examples to students as self-study topics.
Load more

Recommended publications
  • 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.
    [Show full text]
  • Cosmic Age Problem Revisited in the Holographic Dark Energy Model ∗ Jinglei Cui, Xin Zhang
    中国科技论文在线 http://www.paper.edu.cn Physics Letters B 690 (2010) 233–238 Contents lists available at ScienceDirect Physics Letters B www.elsevier.com/locate/physletb Cosmic age problem revisited in the holographic dark energy model ∗ Jinglei Cui, Xin Zhang Department of Physics, College of Sciences, Northeastern University, Shenyang 110004, China article info abstract Article history: Because of an old quasar APM 08279 + 5255 at z = 3.91, some dark energy models face the challenge of Received 18 April 2010 the cosmic age problem. It has been shown by Wei and Zhang [H. Wei, S.N. Zhang, Phys. Rev. D 76 (2007) Received in revised form 18 May 2010 063003, arXiv:0707.2129 [astro-ph]] that the holographic dark energy model is also troubled with such a Accepted 20 May 2010 cosmic age problem. In order to accommodate this old quasar and solve the age problem, we propose in Available online 24 May 2010 this Letter to consider the interacting holographic dark energy in a non-flat universe. We show that the Editor: T. Yanagida cosmic age problem can be eliminated when the interaction and spatial curvature are both involved in Keywords: the holographic dark energy model. Holographic dark energy © 2010 Elsevier B.V. All rights reserved. Cosmic age problem 1. Introduction of quantum gravity could be taken into account. It is commonly believed that the holographic principle [16] is just a fundamental The fact that our universe is undergoing accelerated expansion principle of quantum gravity. Based on the effective quantum field has been confirmed by lots of astronomical observations such as theory, Cohen et al.
    [Show full text]
  • Einstein's Physics
    Einstein’s Physics Albert Einstein at Barnes Foundation in Merion PA, c.1947. Photography by Laura Delano Condax; gift to the author from Vanna Condax. Einstein’s Physics Atoms, Quanta, and Relativity Derived, Explained, and Appraised TA-PEI CHENG University of Missouri–St. Louis Portland State University 3 3 Great Clarendon Street, Oxford, OX2 6DP, United Kingdom Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide. Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries © Ta-Pei Cheng 2013 The moral rights of the author have been asserted Impression: 1 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, by licence or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this work in any other form and you must impose this same condition on any acquirer British Library Cataloguing in Publication Data Data available ISBN 978–0–19–966991–2 Printed and bound by CPI Group (UK) Ltd, Croydon, CR0 4YY Links to third party websites are provided by Oxford in good faith and for information only. Oxford disclaims any responsibility for the materials contained in any third party website referenced in this work.
    [Show full text]
  • Reconciling the Cosmic Age Problem in the Rh = Ct Universe
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Springer - Publisher Connector Eur. Phys. J. C (2014) 74:3090 DOI 10.1140/epjc/s10052-014-3090-1 Regular Article - Theoretical Physics Reconciling the cosmic age problem in the Rh = ct universe H. Yu1,F.Y.Wang1,2,a 1 School of Astronomy and Space Science, Nanjing University, Nanjing 210093, China 2 Key Laboratory of Modern Astronomy and Astrophysics, Nanjing University, Ministry of Education, Nanjing 210093, China Received: 19 April 2014 / Accepted: 19 September 2014 / Published online: 2 October 2014 © The Author(s) 2014. This article is published with open access at Springerlink.com Abstract Many dark energy models fail to pass the cosmic t0 = 13.82 Gyr in the CDM model [6], but it still suf- age test. In this paper, we investigate the cosmic age problem fers from the cosmic age problem [11,12]. The cosmic age associated with nine extremely old Global Clusters (GCs) problem is that some objects are older than the age of the and the old quasar APM 08279+5255 in the Rh = ct uni- universe at its redshift z. In previous literature, many cos- verse. The age data of these oldest GCs in M31 are acquired mological models have been tested by the old quasar APM from the Beijing–Arizona–Taiwan–Connecticut system with 08279+5255 with age 2.1 ± 0.3 Gyr at z = 3.91 [13,14], up-to-date theoretical synthesis models. They have not been such as the CDM [13,15], the (t) model [16], the inter- used to test the cosmic age problem in the Rh = ct uni- acting dark energy models [12], the generalized Chaplygin verse in previous literature.
    [Show full text]
  • Astro-Ph/9812074 3 Dec 1998 1 Ter Calibrations of Cepheid Luminositites, Alues
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server The Cepheid Distance Scale after Hipparcos Frdric Pont Observatoire de Genve, Switzerland Abstract. More than twohundred classical cepheids were measured by the Hip- parcos astrometric satellite, making p ossible a geometrical calibration of the cepheid distance scale. However, the large average distance of even the nearest cepheids measured by Hipparcos implies trigonometric paral- laxes of at most a few mas. Determining unbiased distances and absolute magnitudes from such high relative error parallax data is not a trivial problem. In 1997, Feast & Catchp ole announced that Hipparcos cepheid paral- laxes indicated a Perio d-Luminosity scale 0.2 mag brighter than previous calibrations, with imp ortant consequences on the whole cosmic distance scale. In the wake of this initial study, several authors have reconsid- ered the question, and favour fainter calibrations of cepheid luminositites, compatible with pre-Hipparcos values. All authors used equivalent data sets, and the bulk of the di erence in the results arises from the statistical treatment of the parallax data. Wehave attempted to rep eat the analyses of all these studies and test them with Monte Carlo simulations and synthetic samples. We conclude that the initial Feast & Catchp ole study is sound, and that the subsequent studies are sub jected in several di erentways to biases involved in the treatment of high relative error parallax data. We consider the source of these biases in some detail. We also prop ose a reappraisal of the error budget in the nal Hipparcos cepheid result, leading to a PL relation { adapted from Feast & Catchp ole { of +0 M = 2:81(assumed) log P 1:43 0:16(stat) (syst) V 0:03 astro-ph/9812074 3 Dec 1998 We compare this calibration to recentvalues from cluster cepheids or the surface brightness metho d, and nd that the overall agreement is good within the uncertainties.
    [Show full text]
  • Theoretical Deduction of the Hubble Law Beginning with a Mond Theory in Context of the ΛFRW-Cosmology
    International Journal of Astronomy and Astrophysics, 2014, 4, 551-559 Published Online December 2014 in SciRes. http://www.scirp.org/journal/ijaa http://dx.doi.org/10.4236/ijaa.2014.44051 Theoretical Deduction of the Hubble Law Beginning with a MoND Theory in Context of the ΛFRW-Cosmology Nelson Falcon, Andrés Aguirre Laboratory of Physics of the Atmosphere and the Outer Space, University of Carabobo, Valencia, Venezuela Email: [email protected], [email protected] Received 11 September 2014; revised 8 October 2014; accepted 3 November 2014 Academic Editor: Luigi Maxmilian Caligiuri, University of Calabria, Italy Copyright © 2014 by authors and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/ Abstract We deduced the Hubble law and the age of the Universe, through the introduction of the Inverse Yukawa Field (IYF), as a non-local additive complement of the Newtonian gravitation (Modified Newtonian Dynamics). As a result, we connected the dynamics of astronomical objects at great scale with the Friedmann-Robertson-Walker ΛFRW) model. From the corresponding formalism, the Hubble law can be expressed as v=(4 π[ G] cr) , which was derived by evaluating the IYF force at distances much greater than 50 Mpc, giving a maximum value for the expansion rate of the (max) −−11 universe of H0 86.31 km⋅⋅ s Mpc , consistent with the observational data of 392 astronom- ical objects from NASA/IPAC Extragalactic Database (NED). This additional field (IYF) provides a simple interpretation of dark energy as the action of baryonic matter at large scales.
    [Show full text]
  • No Obvious Change in the Number Density of Galaxies up to Z ≈ 3.5 Yves-Henri Sanejouand
    No obvious change in the number density of galaxies up to z ≈ 3.5 Yves-Henri Sanejouand To cite this version: Yves-Henri Sanejouand. No obvious change in the number density of galaxies up to z ≈ 3.5. 2019. hal-02019920 HAL Id: hal-02019920 https://hal.archives-ouvertes.fr/hal-02019920 Preprint submitted on 14 Feb 2019 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. No obvious change in the number density of galaxies up to z ≈ 3.5 Yves-Henri Sanejouand∗ Facult´edes Sciences et des Techniques, Nantes, France. February 12, 2019 Abstract So, either the methods used for estimating ages of objects like stars or galaxies require significant The analysis of the cumulative count of sources of improvements, or ΛCDM has to be replaced by an- gamma-ray bursts as a function of their redshift other model. strongly suggests that the number density of star- Since ΛCDM is built with still mysterious dom- forming galaxies is roughly constant, up to z ≈ 3.5. inant components like dark energy [13] or non- The analysis of the cumulative count of galaxies baryonic dark matter [14], and since it requires in the Hubble Ultra Deep Field further shows that additional strong assumptions, like an exponential the overall number density of galaxies is constant expansion of space in the early Universe [15, 16], as well, up to z ≈ 2 at least.
    [Show full text]
  • Birth, Age and the Future of the Universe
    INTERNATIONAL SPACE SCIENCE INSTITUTE No 3, May 1999 SPATIUM Published by the Association Pro ISSI Birth,AgeBirth,Age andand thethe FutureFuture ofof thethe UniverseUniverse Recent results of space research tell us a story of unlikely events. Life emanating from the vaste of exploded stars is but one of them. Editorial We are here. There is no doubt Impressum about it.– Research, however, has shown that life, our solar system and all the SPATIUM galaxies interrupting locally the Published by the voidness of space have been caused Association Pro ISSI by tiny unbalances, which seem once or twice a year very unlikely a priori. Recent results of space research tell us a story of unlikely events. INTERNATIONAL SPACE SCIENCE This fascinating history of our INSTITUTE universe was the subject of the key Association Pro ISSI note address by Professor Gustav Hallerstrasse 6,CH-3012 Berne Andreas Tammann,Director of the Phone ++41 31 631 48 96 Institute for Astronomy of the Fax ++41 31 631 48 97 University of Basle on the occa- sion of the third anniversary of President the International Space Science Prof.Hermann Debrunner, Institute on the 27th of November University of Berne 1998. Publisher Dr.Hansjörg Schlaepfer, It is with greatest pleasure that we Contraves Space,Zurich devote this issue to Professor Layout Tammann, who has actively con- Gian-Reto Roth, tributed to the understanding of Contraves Space,Zurich our universe over the past 40 years. Printing Drucklade AG,CH-8008 Zurich Hansjörg Schlaepfer Berne,May 1999 Front cover Rings of glowing gas encircling the supernova 1987A.
    [Show full text]
  • Modern Cosmology – Nearly Perfect but Incomplete
    INTERNATIONAL SPACE SCIENCE INSTITUTE SPATIUM Published by the Association Pro ISSI No. 47, May 2021 Modern Cosmology – nearly perfect but incomplete 2101267_[211415]_Spatium_47_2021_(001_016).indd 1 27.04.21 13:58 Editorial ”Cosmologists are often in error, of the computer age allowing the but never in doubt”. This aphorism simulation of more and more com- Impressum by Lev Davidovich Landau (1908- plex cosmological as well as astro- 1968) may have been applied to physical models. This is why dis- cosmology before the discovery of criminating the “traditional” from ISSN 2297–5888 (Print) the cosmic microwave background the “modern” cosmology is justi- ISSN 2297–590X (Online) (CMB), predicted in 1933 by Er- fied. Moreover, modern cosmol- ich Regener, vaguely indicated by ogy is built on physical, astrophys- Spatium Andrew McKellar in 1940/41, pos- ical, and cosmological concepts Published by the tulated in the 1940s by George and parameters which are con- Association Pro ISSI Gamow, Ralph Alpher and Rob- firmed by experiments and meas- ert Herman, and definitely de- urements to a high degree of tected in 1964 by Arno Penzias and precision. Robert Woodrow Wilson. Cos- The content of this issue resulted mology was a rather theoretical and from the talk “Cosmology Today” Association Pro ISSI perhaps highly speculative branch by Prof. Dr. Bruno Leibundgut Hallerstrasse 6, CH-3012 Bern of astrophysics at the time. Several held on October 14, 2020, in the Phone +41 (0)31 631 48 96 cosmological models were dis- Pro ISSI seminar series. In his pre- see cussed based on and resulting from sentation Prof.
    [Show full text]
  • Cosmological Implications of Different Baryon Acoustic Oscillation Data
    Cosmological implications of different baryon acoustic oscillation data Shuang Wang,1, ∗ Yazhou Hu,2 and Miao Li1 1School of Physics and Astronomy, Sun Yat-Sen University, Zhuhai 519082, P. R. China 2Kavli Institute of Theoretical Physics China, Chinese Academy of Scienses, Beijing 100190, P. R. China In this work, we explore the cosmological implications of different baryon acoustic oscillation (BAO) data, including the BAO data extracted by using the spherically averaged one-dimensional galaxy clustering (GC) statistics (hereafter BAO1) and the BAO data obtained by using the anisotropic two-dimensional GC statistics (hereafter BAO2). To make a comparison, we also take into account the case without BAO data (hereafter NO BAO). Firstly, making use of these BAO data, as well as the SNLS3 type Ia supernovae sample and the Planck distance priors data, we give the cosmological constraints of the ΛCDM, the wCDM, and the Chevallier-Polarski-Linder (CPL) model. Then, we discuss the impacts of different BAO data on cosmological consquences, includ- ing its effects on parameter space, equation of state (EoS), figure of merit (FoM), deceleration- acceleration transition redshift, Hubble parameter H(z), deceleration parameter q(z), statefinder (1) (1) hierarchy S3 (z), S4 (z) and cosmic age t(z). We find that: (1) NO BAO data always give a small- est fractional matter density Ωm0, a largest fractional curvature density Ωk0 and a largest Hubble constant h; in contrast, BAO1 data always give a largest Ωm0, a smallest Ωk0 and a smallest h. (2) For the wCDM and the CPL model, NO BAO data always give a largest EoS w; in contrast, BAO2 data always give a smallest w.
    [Show full text]
  • The End of the Age Problem, and the Case for a Cosmological Constant Revisited
    CWRU-P6-97 CERN-TH-97/122 astro-ph/9706227 THE END OF THE AGE PROBLEM, AND THE CASE FOR A COSMOLOGICAL CONSTANT REVISITED Lawrence M. Krauss1,2 1Theory Division, CERN, CH-1211, Geneva 23, Switzerland 2Departments of Physics and Astronomy Case Western Reserve University Cleveland, OH 44106-7079 (submitted to Science) Abstract The lower limit on the age of the universe derived from globular cluster dating tech- niques, which previously strongly motivated a non-zero cosmological constant, has now been dramatically reduced, allowing consistency for a flat matter dominated universe −1 −1 with a Hubble Constant, H0 ≤ 66kms Mpc . The case for an open universe versus a flat universe with non-zero cosmological constant is reanalyzed in this context, incor- porating not only the new age data, but also updates on baryon abundance constraints, and large scale structure arguments. For the first time, the allowed parameter space for the density of non-relativistic matter appears larger for an open universe than for a flat universe with cosmological constant, while a flat universe with zero cosmological constant remains strongly disfavored. Several other preliminary observations suggest a non-zero cosmological constant, but a definitive determination awaits refined mea- surements of q0, and small scale anisotropies of the Cosmic Microwave background. I argue that fundamental theoretical arguments favor a non-zero cosmological constant over an open universe. However, if either case is confirmed, the challenges posed for fundamental particle physics will be great. The cosmological model perhaps most strongly favored by the data over the past few years has involved a proposal which is heretical from an elementary particle physics per- spective.
    [Show full text]
  • Arxiv:1301.2737V1 [Gr-Qc] 13 Jan 2013
    Modified holographic Ricci dark energy coupled to interacting dark matter and a non interacting baryonic component Luis P. Chimento,1, a M´onica Forte,2, b and Mart´ınG. Richarte1, c 1Departamento de F´ısica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and IFIBA, CONICET, Ciudad Universitaria, Pabell´on I, 1428, Buenos Aires , Argentina. 2Departamento de F´ısica, Facultad de ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabell´on I, 1428, Buenos Aires , Argentina. (Dated: January 15, 2013) We examine a Friedmann-Robertson-Walker universe filled with interacting dark matter, modified holographic Ricci dark energy (MHRDE), and a decoupled baryonic component.The estimations of the cosmic parameters with Hubble data lead to an age of the universe of 13.17 Gyr and show that the MHRDE is free from the cosmic-age problem at low redshift (0 ≤ z ≤ 2) in contrast to holographic Ricci dark energy (HRDE) case. We constrain the parameters with the Union2 data set and contrast with the Hubble data. We also study the behavior of dark energy at early times by taking into account the severe bounds found at recombination era and/or at big bang nucleosynthesis. The inclusion of a non interacting baryonic matter forces that the amount of dark energy at zt ∼ O(1) changes abruptly implying that Ωx(z ≃ 1100) = 0.03, so the bounds reported by the forecast of Planck and CMBPol experiments are more favored for the MHRDE model than in the case of HRDE cutoff. For the former model, we also obtain that at high redshift the fraction of dark energy varies from 0.006 to 0.002, then the amount of Ωx at the big bang nucleosynthesis era does not disturb the observed Helium abundance in the universe provided that the bound 10 Ωx(z ≃ 10 ) < 0.21 is hold.
    [Show full text]