Dark Matter and the Universe
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The Hubble Constant H0 --- Describing How Fast the Universe Is Expanding A˙ (T) H(T) = , A(T) = the Cosmic Scale Factor A(T)
Determining H0 and q0 from Supernova Data LA-UR-11-03930 Mian Wang Henan Normal University, P.R. China Baolian Cheng Los Alamos National Laboratory PANIC11, 25 July, 2011,MIT, Cambridge, MA Abstract Since 1929 when Edwin Hubble showed that the Universe is expanding, extensive observations of redshifts and relative distances of galaxies have established the form of expansion law. Mapping the kinematics of the expanding universe requires sets of measurements of the relative size and age of the universe at different epochs of its history. There has been decades effort to get precise measurements of two parameters that provide a crucial test for cosmology models. The two key parameters are the rate of expansion, i.e., the Hubble constant (H0) and the deceleration in expansion (q0). These two parameters have been studied from the exceedingly distant clusters where redshift is large. It is indicated that the universe is made up by roughly 73% of dark energy, 23% of dark matter, and 4% of normal luminous matter; and the universe is currently accelerating. Recently, however, the unexpected faintness of the Type Ia supernovae (SNe) at low redshifts (z<1) provides unique information to the study of the expansion behavior of the universe and the determination of the Hubble constant. In this work, We present a method based upon the distance modulus redshift relation and use the recent supernova Ia data to determine the parameters H0 and q0 simultaneously. Preliminary results will be presented and some intriguing questions to current theories are also raised. Outline 1. Introduction 2. Model and data analysis 3. -
The State of the Multiverse: the String Landscape, the Cosmological Constant, and the Arrow of Time
The State of the Multiverse: The String Landscape, the Cosmological Constant, and the Arrow of Time Raphael Bousso Center for Theoretical Physics University of California, Berkeley Stephen Hawking: 70th Birthday Conference Cambridge, 6 January 2011 RB & Polchinski, hep-th/0004134; RB, arXiv:1112.3341 The Cosmological Constant Problem The Landscape of String Theory Cosmology: Eternal inflation and the Multiverse The Observed Arrow of Time The Arrow of Time in Monovacuous Theories A Landscape with Two Vacua A Landscape with Four Vacua The String Landscape Magnitude of contributions to the vacuum energy graviton (a) (b) I Vacuum fluctuations: SUSY cutoff: ! 10−64; Planck scale cutoff: ! 1 I Effective potentials for scalars: Electroweak symmetry breaking lowers Λ by approximately (200 GeV)4 ≈ 10−67. The cosmological constant problem −121 I Each known contribution is much larger than 10 (the observational upper bound on jΛj known for decades) I Different contributions can cancel against each other or against ΛEinstein. I But why would they do so to a precision better than 10−121? Why is the vacuum energy so small? 6= 0 Why is the energy of the vacuum so small, and why is it comparable to the matter density in the present era? Recent observations Supernovae/CMB/ Large Scale Structure: Λ ≈ 0:4 × 10−121 Recent observations Supernovae/CMB/ Large Scale Structure: Λ ≈ 0:4 × 10−121 6= 0 Why is the energy of the vacuum so small, and why is it comparable to the matter density in the present era? The Cosmological Constant Problem The Landscape of String Theory Cosmology: Eternal inflation and the Multiverse The Observed Arrow of Time The Arrow of Time in Monovacuous Theories A Landscape with Two Vacua A Landscape with Four Vacua The String Landscape Many ways to make empty space Topology and combinatorics RB & Polchinski (2000) I A six-dimensional manifold contains hundreds of topological cycles. -
The Multiverse: Conjecture, Proof, and Science
The multiverse: conjecture, proof, and science George Ellis Talk at Nicolai Fest Golm 2012 Does the Multiverse Really Exist ? Scientific American: July 2011 1 The idea The idea of a multiverse -- an ensemble of universes or of universe domains – has received increasing attention in cosmology - separate places [Vilenkin, Linde, Guth] - separate times [Smolin, cyclic universes] - the Everett quantum multi-universe: other branches of the wavefunction [Deutsch] - the cosmic landscape of string theory, imbedded in a chaotic cosmology [Susskind] - totally disjoint [Sciama, Tegmark] 2 Our Cosmic Habitat Martin Rees Rees explores the notion that our universe is just a part of a vast ''multiverse,'' or ensemble of universes, in which most of the other universes are lifeless. What we call the laws of nature would then be no more than local bylaws, imposed in the aftermath of our own Big Bang. In this scenario, our cosmic habitat would be a special, possibly unique universe where the prevailing laws of physics allowed life to emerge. 3 Scientific American May 2003 issue COSMOLOGY “Parallel Universes: Not just a staple of science fiction, other universes are a direct implication of cosmological observations” By Max Tegmark 4 Brian Greene: The Hidden Reality Parallel Universes and The Deep Laws of the Cosmos 5 Varieties of Multiverse Brian Greene (The Hidden Reality) advocates nine different types of multiverse: 1. Invisible parts of our universe 2. Chaotic inflation 3. Brane worlds 4. Cyclic universes 5. Landscape of string theory 6. Branches of the Quantum mechanics wave function 7. Holographic projections 8. Computer simulations 9. All that can exist must exist – “grandest of all multiverses” They can’t all be true! – they conflict with each other. -
Modified Standard Einstein's Field Equations and the Cosmological
Issue 1 (January) PROGRESS IN PHYSICS Volume 14 (2018) Modified Standard Einstein’s Field Equations and the Cosmological Constant Faisal A. Y. Abdelmohssin IMAM, University of Gezira, P.O. BOX: 526, Wad-Medani, Gezira State, Sudan Sudan Institute for Natural Sciences, P.O. BOX: 3045, Khartoum, Sudan E-mail: [email protected] The standard Einstein’s field equations have been modified by introducing a general function that depends on Ricci’s scalar without a prior assumption of the mathemat- ical form of the function. By demanding that the covariant derivative of the energy- momentum tensor should vanish and with application of Bianchi’s identity a first order ordinary differential equation in the Ricci scalar has emerged. A constant resulting from integrating the differential equation is interpreted as the cosmological constant introduced by Einstein. The form of the function on Ricci’s scalar and the cosmologi- cal constant corresponds to the form of Einstein-Hilbert’s Lagrangian appearing in the gravitational action. On the other hand, when energy-momentum is not conserved, a new modified field equations emerged, one type of these field equations are Rastall’s gravity equations. 1 Introduction term in his standard field equations to represent a kind of “anti ff In the early development of the general theory of relativity, gravity” to balance the e ect of gravitational attractions of Einstein proposed a tensor equation to mathematically de- matter in it. scribe the mutual interaction between matter-energy and Einstein modified his standard equations by introducing spacetime as [13] a term to his standard field equations including a constant which is called the cosmological constant Λ, [7] to become Rab = κTab (1.1) where κ is the Einstein constant, Tab is the energy-momen- 1 Rab − gabR + gabΛ = κTab (1.6) tum, and Rab is the Ricci curvature tensor which represents 2 geometry of the spacetime in presence of energy-momentum. -
Copyrighted Material
ftoc.qrk 5/24/04 1:46 PM Page iii Contents Timeline v de Sitter,Willem 72 Dukas, Helen 74 Introduction 1 E = mc2 76 Eddington, Sir Arthur 79 Absentmindedness 3 Education 82 Anti-Semitism 4 Ehrenfest, Paul 85 Arms Race 8 Einstein, Elsa Löwenthal 88 Atomic Bomb 9 Einstein, Mileva Maric 93 Awards 16 Einstein Field Equations 100 Beauty and Equations 17 Einstein-Podolsky-Rosen Besso, Michele 18 Argument 101 Black Holes 21 Einstein Ring 106 Bohr, Niels Henrik David 25 Einstein Tower 107 Books about Einstein 30 Einsteinium 108 Born, Max 33 Electrodynamics 108 Bose-Einstein Condensate 34 Ether 110 Brain 36 FBI 113 Brownian Motion 39 Freud, Sigmund 116 Career 41 Friedmann, Alexander 117 Causality 44 Germany 119 Childhood 46 God 124 Children 49 Gravitation 126 Clothes 58 Gravitational Waves 128 CommunismCOPYRIGHTED 59 Grossmann, MATERIAL Marcel 129 Correspondence 62 Hair 131 Cosmological Constant 63 Heisenberg, Werner Karl 132 Cosmology 65 Hidden Variables 137 Curie, Marie 68 Hilbert, David 138 Death 70 Hitler, Adolf 141 iii ftoc.qrk 5/24/04 1:46 PM Page iv iv Contents Inventions 142 Poincaré, Henri 220 Israel 144 Popular Works 222 Japan 146 Positivism 223 Jokes about Einstein 148 Princeton 226 Judaism 149 Quantum Mechanics 230 Kaluza-Klein Theory 151 Reference Frames 237 League of Nations 153 Relativity, General Lemaître, Georges 154 Theory of 239 Lenard, Philipp 156 Relativity, Special Lorentz, Hendrik 158 Theory of 247 Mach, Ernst 161 Religion 255 Mathematics 164 Roosevelt, Franklin D. 258 McCarthyism 166 Russell-Einstein Manifesto 260 Michelson-Morley Experiment 167 Schroedinger, Erwin 261 Millikan, Robert 171 Solvay Conferences 265 Miracle Year 174 Space-Time 267 Monroe, Marilyn 179 Spinoza, Baruch (Benedictus) 268 Mysticism 179 Stark, Johannes 270 Myths and Switzerland 272 Misconceptions 181 Thought Experiments 274 Nazism 184 Time Travel 276 Newton, Isaac 188 Twin Paradox 279 Nobel Prize in Physics 190 Uncertainty Principle 280 Olympia Academy 195 Unified Theory 282 Oppenheimer, J. -
Measuring Dark Energy and Primordial Non-Gaussianity: Things to (Or Not To?) Worry About!
Measuring Dark Energy and Primordial Non-Gaussianity: Things To (or Not To?) Worry About! Devdeep Sarkar Center for Cosmology, UC Irvine in collaboration with: Scott Sullivan (UCI/UCLA), Shahab Joudaki (UCI), Alexandre Amblard (UCI), Paolo Serra (UCI), Daniel Holz (Chicago/LANL), and Asantha Cooray (UCI) UC Berkeley-LBNL Cosmology Group Seminar September 16, 2008 Outline Outline Start With... Dark Energy Why Pursue Dark Energy? DE Equation of State (EOS) DE from SNe Ia ++ Beware of Systematics Two Population Model Gravitational Lensing Outline Start With... And Then... Dark Energy CMB Bispectrum Why Pursue Dark Energy? Why Non-Gaussianity? DE Equation of State (EOS) Why in CMB Bispectrum? DE from SNe Ia ++ The fNL Beware of Systematics WL of CMB Bispectrum Two Population Model Analytic Sketch Gravitational Lensing Numerical Results Outline Start With... And Then... Dark Energy CMB Bispectrum Why Pursue Dark Energy? Why Non-Gaussianity? DE Equation of State (EOS) Why in CMB Bispectrum? DE from SNe Ia ++ The fNL Beware of Systematics WL of CMB Bispectrum Two Population Model Analytical Sketch Gravitational Lensing Numerical Results Credit: NASA/WMAP Science Team Credit: NASA/WMAP Science Team Credit: NASA/WMAP Science Team THE ASTRONOMICAL JOURNAL, 116:1009È1038, 1998 September ( 1998. The American Astronomical Society. All rights reserved. Printed in U.S.A. OBSERVATIONAL EVIDENCE FROM SUPERNOVAE FOR AN ACCELERATING UNIVERSE AND A COSMOLOGICAL CONSTANT ADAM G. RIESS,1 ALEXEI V. FILIPPENKO,1 PETER CHALLIS,2 ALEJANDRO CLOCCHIATTI,3 ALAN DIERCKS,4 PETER M. GARNAVICH,2 RON L. GILLILAND,5 CRAIG J. HOGAN,4 SAURABH JHA,2 ROBERT P. KIRSHNER,2 B. LEIBUNDGUT,6 M. -
Cosmic Microwave Background
1 29. Cosmic Microwave Background 29. Cosmic Microwave Background Revised August 2019 by D. Scott (U. of British Columbia) and G.F. Smoot (HKUST; Paris U.; UC Berkeley; LBNL). 29.1 Introduction The energy content in electromagnetic radiation from beyond our Galaxy is dominated by the cosmic microwave background (CMB), discovered in 1965 [1]. The spectrum of the CMB is well described by a blackbody function with T = 2.7255 K. This spectral form is a main supporting pillar of the hot Big Bang model for the Universe. The lack of any observed deviations from a 7 blackbody spectrum constrains physical processes over cosmic history at redshifts z ∼< 10 (see earlier versions of this review). Currently the key CMB observable is the angular variation in temperature (or intensity) corre- lations, and to a growing extent polarization [2–4]. Since the first detection of these anisotropies by the Cosmic Background Explorer (COBE) satellite [5], there has been intense activity to map the sky at increasing levels of sensitivity and angular resolution by ground-based and balloon-borne measurements. These were joined in 2003 by the first results from NASA’s Wilkinson Microwave Anisotropy Probe (WMAP)[6], which were improved upon by analyses of data added every 2 years, culminating in the 9-year results [7]. In 2013 we had the first results [8] from the third generation CMB satellite, ESA’s Planck mission [9,10], which were enhanced by results from the 2015 Planck data release [11, 12], and then the final 2018 Planck data release [13, 14]. Additionally, CMB an- isotropies have been extended to smaller angular scales by ground-based experiments, particularly the Atacama Cosmology Telescope (ACT) [15] and the South Pole Telescope (SPT) [16]. -
Arxiv:Astro-Ph/9805201V1 15 May 1998 Hitpe Stubbs Christopher .Phillips M
Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant To Appear in the Astronomical Journal Adam G. Riess1, Alexei V. Filippenko1, Peter Challis2, Alejandro Clocchiatti3, Alan Diercks4, Peter M. Garnavich2, Ron L. Gilliland5, Craig J. Hogan4,SaurabhJha2,RobertP.Kirshner2, B. Leibundgut6,M. M. Phillips7, David Reiss4, Brian P. Schmidt89, Robert A. Schommer7,R.ChrisSmith710, J. Spyromilio6, Christopher Stubbs4, Nicholas B. Suntzeff7, John Tonry11 ABSTRACT We present spectral and photometric observations of 10 type Ia supernovae (SNe Ia) in the redshift range 0.16 ≤ z ≤ 0.62. The luminosity distances of these objects are determined by methods that employ relations between SN Ia luminosity and light curve shape. Combined with previous data from our High-Z Supernova Search Team (Garnavich et al. 1998; Schmidt et al. 1998) and Riess et al. (1998a), this expanded set of 16 high-redshift supernovae and a set of 34 nearby supernovae are used to place constraints on the following cosmological parameters: the Hubble constant (H0), the mass density (ΩM ), the cosmological constant (i.e., the vacuum energy density, ΩΛ), the deceleration parameter (q0), and the dynamical age of the Universe (t0). The distances of the high-redshift SNe Ia are, on average, 10% to 15% farther than expected in a low mass density (ΩM =0.2) Universe without a cosmological constant. Different light curve fitting methods, SN Ia subsamples, and prior constraints unanimously favor eternally expanding models with positive cosmological constant -
ASTRON 329/429, Fall 2015 – Problem Set 3
ASTRON 329/429, Fall 2015 { Problem Set 3 Due on Tuesday Nov. 3, in class. All students must complete all problems. 1. More on the deceleration parameter. In problem set 2, we defined the deceleration parameter q0 (see also eq. 6.14 in Liddle's textbook). Show that for a universe containing only pressureless matter with a cosmological constant Ω q = 0 − Ω (t ); (1) 0 2 Λ 0 where Ω0 ≡ Ωm(t0) and t0 is the present time. Assuming further that the universe is spatially flat, express q0 in terms of Ω0 only (2 points). 2. No Big Bang? Observations of the cosmic microwave background and measurements of the abundances of light elements such as lithium believed to have been synthesized when the uni- verse was extremely hot and dense (Big Bang nucleosynthesis) provide strong evidence that the scale factor a ! 0 in the past, i.e. of a \Big Bang." The existence of a Big Bang puts constraints on the allowed combinations of cosmological parameters such Ωm and ΩΛ. Consider for example a fictitious universe that contains only a cosmological constant with ΩΛ > 1 but no matter or radiation (Ωm = Ωrad = 0). Suppose that this universe has a positive Hubble constant H0 at the present time. Show that such a universe did not experience a Big Bang in the past and so violates the \Big Bang" constraint (2 points). 3. Can neutrinos be the dark matter? Thermal equilibrium in the early universe predicts that the number density of neutrinos for each neutrino flavor in the cosmic neutrino background, nν, is related to the number density of photons in the cosmic microwave background, nγ, through nν + nν¯ = (3=11)nγ. -
The Cosmological Constant Problem Philippe Brax
The Cosmological constant problem Philippe Brax To cite this version: Philippe Brax. The Cosmological constant problem. Contemporary Physics, Taylor & Francis, 2004, 45, pp.227-236. 10.1080/00107510410001662286. hal-00165345 HAL Id: hal-00165345 https://hal.archives-ouvertes.fr/hal-00165345 Submitted on 25 Jul 2007 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. The Cosmological Constant Problem Ph. Brax1a a Service de Physique Th´eorique CEA/DSM/SPhT, Unit´e de recherche associ´ee au CNRS, CEA-Saclay F-91191 Gif/Yvette cedex, France Abstract Observational evidence seems to indicate that the expansion of the universe is currently accelerating. Such an acceleration strongly suggests that the content of the universe is dominated by a non{clustered form of matter, the so{called dark energy. The cosmological constant, introduced by Einstein to reconcile General Relativity with a closed and static Universe, is the most likely candidate for dark energy although other options such as a weakly interacting field, also known as quintessence, have been proposed. The fact that the dark energy density is some one hundred and twenty orders of magnitude lower than the energy scales present in the early universe constitutes the cosmological constant problem. -
Cosmological Consequences of a Parametrized Equation of State
S S symmetry Article Cosmological Consequences of a Parametrized Equation of State Abdul Jawad 1 , Shamaila Rani 1, Sidra Saleem 1, Kazuharu Bamba 2,* and Riffat Jabeen 3 1 Department of Mathematics, COMSATS University Islamabad Lahore-Campus, Lahore-54000, Pakistan 2 Division of Human Support System, Faculty of Symbiotic Systems Science, Fukushima University, Fukushima 960-1296, Japan 3 Department of Statistics, COMSATS University Islamabad, Lahore-Campus, Lahore-54000, Pakistan * Correspondence: [email protected] Received: 24 May 2019; Accepted: 16 July 2019; Published: 5 August 2019 Abstract: We explore the cosmic evolution of the accelerating universe in the framework of dynamical Chern–Simons modified gravity in an interacting scenario by taking the flat homogeneous and isotropic model. For this purpose, we take some parametrizations of the equation of state parameter. This parametrization may be a Taylor series extension in the redshift, a Taylor series extension in the scale factor or any other general parametrization of w. We analyze the interaction term which calculates the action of interaction between dark matter and dark energy. We explore various cosmological parameters such as deceleration parameter, squared speed of sound, Om-diagnostic and statefinder via graphical behavior. Keywords: dynamical Chern–Simons modified gravity; parametrizations; cosmological parameters PACS: 95.36.+d; 98.80.-k 1. Introduction It is believed that in present day cosmology, one of the most important discoveries is the acceleration of the cosmic expansion [1–10]. It is observed that the universe expands with repulsive force and is not slowing down under normal gravity. This unknown force, called dark energy (DE), and is responsible for current cosmic acceleration. -
From Cosmic Deceleration to Acceleration: New Constraints from SN Ia and BAO/CMB
Journal-ref: JCAP03(2012)027 From cosmic deceleration to acceleration: new constraints from SN Ia and BAO/CMB R. Giostri, M.Vargas dos Santos, I. Waga, R. R. R. Reis, M. O. Calv~ao,and B. L. Lago Instituto de F´ısica,Universidade Federal do Rio de Janeiro C. P. 68528, CEP 21941-972, Rio de Janeiro, RJ, Brazil E-mail: [email protected], [email protected], [email protected], [email protected], [email protected], [email protected] Abstract. We use type Ia supernovae (SN Ia) data in combination with recent baryonic acoustic oscillations (BAO) and cosmic microwave background (CMB) observations to con- strain a kink-like parametrization of the deceleration parameter (q). This q-parametrization can be written in terms of the initial (qi) and present (q0) values of the deceleration pa- rameter, the redshift of the cosmic transition from deceleration to acceleration (zt) and the redshift width of such transition (τ). By assuming a flat space geometry, qi = 1=2 and adopt- ing a likelihood approach to deal with the SN Ia data we obtain, at the 68% confidence level +0:13 +0:16 +0:11 (C.L.), that: zt = 0:56−0:10, τ = 0:47−0:20 and q0 = −0:31−0:11 when we combine BAO/CMB observations with SN Ia data processed with the MLCS2k2 light-curve fitter. When in +0:13 this combination we use the SALT2 fitter we get instead, at the same C.L.: zt = 0:64−0:07, +0:11 +0:17 τ = 0:36−0:17 and q0 = −0:53−0:13.