DOCSLIB.ORG

Cosmological Aspects of Unified Theories

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

University of Patras School of Natural Sciences Department of Physics Division of Theoretical and Mathematical Physics, Astronomy and Astrophysics Cosmological aspects of Unified Theories Andreas Lymperis Supervisor: Prof. Smaragda Lola Thesis submitted to the University of Patras for the Degree of Doctor of Philosophy February 2021 2 Three-member advisory committee (in alphabetical order): 1. Smaragda Lola (Supervisor) - Professor, Physics Department, University of Patras 2. Leandros Perivolaropoulos - Professor, Physics Department, University of Ioannina 3. Andreas Terzis - Professor, Physics Department, University of Patras Seven-member PhD thesis examination committee (in alphabetical order): 1. Spyros Basilakos - Director Of Research, Institute for Astronomy, Astrophysics, Space Applications and Remote Sensing, National Observatory of Athens 2. Panagiota Kanti - Professor, Physics Department, University of Ioannina 3. Smaragda Lola (Supervisor) - Professor, Physics Department, University of Patras 4. Leandros Perivolaropoulos - Professor, Physics Department, University of Ioannina 5. Emmanuel Saridakis - Principal Researcher, Institute for Astronomy, Astrophysics, Space Applications and Remote Sensing, National Observatory of Athens 6. Vassilis Spanos - Associate Professor, Department of Physics, University of Athens 7. Andreas Terzis - Professor, Physics Department, University of Patras 3 Abstract In this thesis, we study cosmological aspects of some well-known dark energy models, and extending our investigation into Unified Theories. We explore the existence of geodesi- cally complete singularities in quintessence and scalar-tensor quintessence models using analytical expressions for the scale factor and the scalar field. We show that close to the 2 q singularity the scale factor is of the form a(t) = as +b(ts t)+c(ts t) +d(ts t) where − − − as; b; c; d are constants which are obtained from the dynamical equations and ts is the time of the singularity. In the case of quintessence we find q = n + 2 (i.e. 2 < q < 3), while in the case of scalar-tensor quintessence we have a stronger singularity with q = n + 1 (1 < q < 2). We verify these analytical results numerically and extend them to the case where a perfect fluid, with a constant equation of state w = p/ρ, is present. We find that the strength of the singularity (value of q) remains unaffected by the presence of a perfect fluid. The linear and quadratic terms in (ts t) that appear in the expansion of the scale − factor around ts are subdominant for the diverging derivatives close to the singularity, but can play an important role in the estimation of the Hubble parameter. Using the an- alytically derived relations between these terms, we derive relations involving the Hubble parameter close to the singularity, which may be used as observational signatures of such singularities in this class of models. For quintessence with matter fluid, we find that close _ 3 3 2 to the singularity H = Ω0m(1 + zs) 3H . These terms should be taken into account 2 − when searching in cosmological data for such future or past time singularities. Next, using the Tsallis entropy and applying the first law of thermodynamics we construct several cosmological scenarios. We show that the universe exhibits the usual thermal history, with the sequence of matter and dark-energy eras, and according to the value of δ the dark-energy equation-of-state parameter can be quintessence-like, phantom-like, or experience the phantom-divide crossing during evolution. Even in the case where the explicit cosmological constant is absent, the scenario at hand can very efficiently mimic ΛCDM cosmology, and is in excellent agreement with Supernovae type Ia observational data. Finally, we revisit inflation with non-canonical scalar fields by applying deformed steepness exponential potentials. We show that the resulting scenario can lead to infla- tionary observables and in particular to scalar spectral index and tensor-to-scalar ratio in remarkable agreement with observations. Additionally, a significant advantage of the 4 scenario is that parameters, such as the non-canonicality exponent and scale, as well as the potential exponent and scale, do not need to acquire unnatural values and hence can accept a theoretical justification. Hence, we obtain a significant improvement with respect to alternative schemes, and we present distinct correlations between the model parameters that better fit the data, which can be tested in future probes. This combina- tion of observational efficiency and theoretical justification makes the scenario at hand a good candidate for the description of inflation. 5 To my wife Alexandra 6 Whatever tomorrow wants from me At least I'm here, at least I'm free Free to choose to see the signs ....and this is my line. \Poets Of The Fall" 7 Acknowledgements I would like to warmly thank all those that helped, supported, collaborated and believed in me throughout the preparation of this thesis. Without them, it could not have taken its present form. Moreover, during these years, I was given the opportunity to associate with world class scientists and give oral presentations in well-known international conferences, workshops and summer schools. First and foremost, I thank my thesis supervisor Professor S. Lola, for this great opportunity to get involved with physics research. Professor Lola offered me full support, insight into scientific and research subjects and assistance with projects, helping me take my first steps in this unique and beautiful world of physics. She offered me full financial support to travel, meet people and have stimulating and fruitful conversations about several subjects in physics. Above all, she was at my side in difficult times, throughout these years and that makes for more than a typical supervisor - student relationship. Without her assistance and dedicated involvement in every step of the way, this thesis would have never been completed. Even from the first years of my PhD studies I had the luck to meet and collaborate with two outstanding people and scientists, Prof. Leandros Perivolaropoulos and Principal Researcher Emmanuel Saridakis. At the very last, I owe them my gratitude and many thanks for their patience, their trust and for sharing with me their vast knowledge across a broad range of cosmology topics. At this point I would like to also express my gratitude to the other honorable members of my PhD thesis committee, Prof. Andreas Terzis, Prof. Panagiota Kanti, Director of Research Spyros Basilakos and Assistant Prof. Vassilis Spanos. I must also thank my friend and colleague Kostas Blekos, without his help this thesis would not have taken its present form. My words are bound and this acknowledgement would be limited without men- tioning the most basic source of my life, my family. I owe a lot to my wife Alexandra who is my shelter and inspiration all these years and my parents Nickos and Argyroula who encouraged and helped me at every stage of my personal and academic life and longed to see this achievement come true. In addition, I would like to express my gratitude to all the Department faculty mem- 8 bers, for their help and support throughout my years of studying. Lastly, I offer my sincere thanks to all those who directly or indirectly have given me support in this undertaking. Contents 1 Introduction 12 2 The Standard Model of Cosmology 18 2.1 A Brief History Of The Universe . 20 2.2 The ΛCDM Model . 23 2.2.1 The Expanding Universe . 23 2.2.2 Friedmann-Lema^ıtre-Robertson-Walker Metric . 24 2.2.3 Einstein Field Equations . 28 2.2.4 Solutions To Einstein Equations - Friedmann Equations . 29 2.2.5 Problems of the Big-Bang Theory . 33 3 Cosmic Inflation 37 3.1 Canonical Inflationary Dynamics . 38 3.2 Slow-roll Approximation . 40 3.3 Inflationary Observables . 43 3.3.1 Scalar-Tensor Power Spectra . 43 3.3.2 Some Examples Of Canonical Inflationary Models . 46 3.4 Non-canonical Inflationary Dynamics . 49 3.4.1 Non-Canonical Scalar Dynamics . 51 3.4.2 Inflationary Parameters - Observables . 54 3.4.3 Some Examples Of Non-Canonical Inflationary Models . 55 4 Dark Matter 59 4.1 Extensions of the Standard Model . 59 4.2 Evidence For Dark Matter . 60 9 CONTENTS 10 4.2.1 Galaxy Rotation Curves . 60 4.2.2 Gravitational Lensing . 61 4.2.3 CMB Radiation . 62 4.3 Constraints On Dark Matter . 65 4.4 Dark Matter Candidates . 65 5 Dark Energy 68 5.1 Evidence For Dark energy . 68 5.1.1 Luminosity Distance . 68 5.1.2 High-Redshift Supernovae Ia . 70 5.1.3 The Age Of The Universe . 71 5.1.4 CMB and Large-Scale Structure (LSS) . 72 5.2 Dark Energy Candidates . 72 5.2.1 Cosmological Constant . 72 5.2.2 Dark Energy Scalar-Field Models . 74 5.2.3 Quintessence . 74 5.2.4 K-essence . 75 5.2.5 Tachyon field . 75 5.2.6 Phantom field . 76 5.2.7 Chaplygin gas . 76 5.3 The Fate Of The Universe - Future Time Singularities . 77 5.4 Thermodynamical Approach To Dark Energy . 80 5.4.1 Friedmann equations as the first law of thermodynamics . 81 5.5 Modified Gravity . 83 5.5.1 f(R) Gravity . 84 5.5.2 Scalar-Tensor Theories . 85 5.5.3 Gauss-Bonnet Gravity . 86 6 Sudden Future Singularities in Quintessence and Scalar-Tensor Quintessence Models 90 6.1 Sudden Future Singularities in Quintessence Models . 90 6.1.1 Evolution without perfect fluid . 90 CONTENTS 11 6.1.2 Numerical analysis . 99 6.1.3 Evolution with a perfect fluid . 101 6.2 Sudden Future Singularities in Scalar-Tensor Quintessence Models . 105 6.2.1 Evolution without a perfect fluid . 105 6.2.2 Numerical analysis . 108 6.2.3 Evolution with a perfect fluid . 112 7 Modified Cosmology through non-extensive horizon Thermodynamics 117 7.1 Tsallis entropy .
Recommended publications
  • Expanding Space, Quasars and St. Augustine's Fireworks

    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.
  • Cosmic Age Problem Revisited in the Holographic Dark Energy Model ∗ Jinglei Cui, Xin Zhang

    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.
  • An Introduction to Effective Field Theory

    An Introduction to Effective Field Theory

    An Introduction to Effective Field Theory Thinking Effectively About Hierarchies of Scale c C.P. BURGESS i Preface It is an everyday fact of life that Nature comes to us with a variety of scales: from quarks, nuclei and atoms through planets, stars and galaxies up to the overall Universal large-scale structure. Science progresses because we can understand each of these on its own terms, and need not understand all scales at once. This is possible because of a basic fact of Nature: most of the details of small distance physics are irrelevant for the description of longer-distance phenomena. Our description of Nature’s laws use quantum field theories, which share this property that short distances mostly decouple from larger ones. E↵ective Field Theories (EFTs) are the tools developed over the years to show why it does. These tools have immense practical value: knowing which scales are important and why the rest decouple allows hierarchies of scale to be used to simplify the description of many systems. This book provides an introduction to these tools, and to emphasize their great generality illustrates them using applications from many parts of physics: relativistic and nonrelativistic; few- body and many-body. The book is broadly appropriate for an introductory graduate course, though some topics could be done in an upper-level course for advanced undergraduates. It should interest physicists interested in learning these techniques for practical purposes as well as those who enjoy the beauty of the unified picture of physics that emerges. It is to emphasize this unity that a broad selection of applications is examined, although this also means no one topic is explored in as much depth as it deserves.
  • Einstein's Physics

    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.
  • Soft Gravitons and the Flat Space Limit of Anti-Desitter Space

    Soft Gravitons and the Flat Space Limit of Anti-Desitter Space

    RUNHETC-2016-15, UTTG-18-16 Soft Gravitons and the Flat Space Limit of Anti-deSitter Space Tom Banks Department of Physics and NHETC Rutgers University, Piscataway, NJ 08854 E-mail: [email protected] Willy Fischler Department of Physics and Texas Cosmology Center University of Texas, Austin, TX 78712 E-mail: fi[email protected] Abstract We argue that flat space amplitudes for the process 2 n gravitons at center of mass → energies √s much less than the Planck scale, will coincide approximately with amplitudes calculated from correlators of a boundary CFT for AdS space of radius R LP , only ≫ when n < R/LP . For larger values of n in AdS space, insisting that all the incoming energy enters “the arena”[20] , implies the production of black holes, whereas there is no black hole production in the flat space amplitudes. We also argue, from unitarity, that flat space amplitudes for all n are necessary to reconstruct the complicated singularity arXiv:1611.05906v3 [hep-th] 8 Apr 2017 at zero momentum in the 2 2 amplitude, which can therefore not be reproduced as → the limit of an AdS calculation. Applying similar reasoning to amplitudes for real black hole production in flat space, we argue that unitarity of the flat space S-matrix cannot be assessed or inferred from properties of CFT correlators. 1 Introduction The study of the flat space limit of correlation functions in AdS/CFT was initiated by the work of Polchinski and Susskind[20] and continued in a host of other papers. Most of those papers agree with the contention, that the limit of Witten diagrams for CFT correlators smeared with appropriate test functions, for operators carrying vanishing angular momentum on the compact 1 space,1 converge to flat space S-matrix elements between states in Fock space.
  • Reconciling the Cosmic Age Problem in the Rh = Ct Universe

    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.
  • Collective Coordinates for D-Branes 1 Introduction

    Collective Coordinates for D-Branes 1 Introduction

    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server UTTG-01-96 Collective Co ordinates for D-branes Willy Fischler, Sonia Paban and Moshe Rozali Theory Group, Department of Physics University of Texas, Austin, Texas 78712 Abstract We develop a formalism for the scattering o D-branes that includes collective co- ordinates. This allows a systematic expansion in the string coupling constant for such pro cesses, including a worldsheet calculation for the D-brane's mass. 1 Intro duction In the recent developments of string theory, solitons play a central role. For example, in the case of duality among various string theories, solitons of a weakly coupled string theory b ecome elementary excitations of the dual theory [1]. Another example, among many others, is the role of solitons in resolving singularities in compacti ed geometries, as they b ecome light[2]. In order to gain more insight in the various asp ects of these recent developments, it is imp ortant to understand the dynamics of solitons in the context of string theory.In this quest one of the to ols at our disp osal is the use of scattering involving these solitons. This includes the scattering of elementary string states o these solitons as well as the scattering among solitons. An imp ortant class of solitons that have emerged are D-branes [4]. In an in uential pap er [3]itwas shown that these D-branes carry R R charges, and are therefore a central ingredient in the aforementioned dualities.
  • King's Research Portal

    King's Research Portal

    King’s Research Portal DOI: 10.1088/1742-6596/631/1/012089 Document Version Publisher's PDF, also known as Version of record Link to publication record in King's Research Portal Citation for published version (APA): Sarkar, S. (2015). String theory backgrounds with torsion in the presence of fermions and implications for leptogenesis. Journal of Physics: Conference Series, 631(1), [012089]. 10.1088/1742-6596/631/1/012089 Citing this paper Please note that where the full-text provided on King's Research Portal is the Author Accepted Manuscript or Post-Print version this may differ from the final Published version. If citing, it is advised that you check and use the publisher's definitive version for pagination, volume/issue, and date of publication details. And where the final published version is provided on the Research Portal, if citing you are again advised to check the publisher's website for any subsequent corrections. General rights Copyright and moral rights for the publications made accessible in the Research Portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognize and abide by the legal requirements associated with these rights. •Users may download and print one copy of any publication from the Research Portal for the purpose of private study or research. •You may not further distribute the material or use it for any profit-making activity or commercial gain •You may freely distribute the URL identifying the publication in the Research Portal Take down policy If you believe that this document breaches copyright please contact [email protected] providing details, and we will remove access to the work immediately and investigate your claim.
  • Astro-Ph/9812074 3 Dec 1998 1 Ter Calibrations of Cepheid Luminositites, Alues

    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.
  • Theoretical Deduction of the Hubble Law Beginning with a Mond Theory in Context of the ΛFRW-Cosmology

    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.
  • Collective Coordinates for D-Branes

    Collective Coordinates for D-Branes

    UTTG-01-96 Collective Coordinates for D-branes Willy Fischler, Sonia Paban and Moshe Rozali∗ Theory Group, Department of Physics University of Texas, Austin, Texas 78712 Abstract We develop a formalism for the scattering off D-branes that includes collective co- ordinates. This allows a systematic expansion in the string coupling constant for such processes, including a worldsheet calculation for the D-brane’s mass. 1 Introduction In the recent developments of string theory, solitons play a central role. For example, in the case of duality among various string theories, solitons of a weakly coupled string theory become elementary excitations of the dual theory [1]. Another example, among many others, is the role of solitons in resolving singularities in compactified geometries, as they become light [2]. In order to gain more insight in the various aspects of these recent developments, it is important to understand the dynamics of solitons in the context of string theory. In this quest one of the tools at our disposal is the use of scattering involving these solitons. This includes the scattering of elementary string states off these solitons as well as the arXiv:hep-th/9604014v2 11 Apr 1996 scattering among solitons. An important class of solitons that have emerged are D-branes [4]. In an influential paper [3] it was shown that these D-branes carry R R charges, − and are therefore a central ingredient in the aforementioned dualities. These objects are described by simple conformal field theories, which makes them particularly suited for explicit calculations. In this paper we use some of the preliminary ideas about collective coordinates de- veloped in a previous paper [5], to describe the scattering of elementary string states off D-branes.
  • 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

    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.