DOCSLIB.ORG

Scale Factor - Expansion of the Universe Age of the Universe Lookback Time Cosmology the Origin and Evolution of the Universe

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Scale Factor - Expansion of the Universe Age of the Universe Lookback Time Cosmology the Origin and Evolution of the Universe Clusters are Very Large Magnets U NM December 1, 2009 Carilli & Taylor 2002 (ARA&A) B ~ 10 µG Hydra A Faraday Rotaon Measures B ~ 30 µG Coma X-ray + radio 6 Results B0 = 4.6 +/- 0.7 µG scale lengths between 2 and 30 kpc average B ~ 2 µG Bonafede et al. 2009 7 Astronomy 422 Lecture 19: Newtonian Cosmology Key concepts: Scale factor - expansion of the universe Age of the universe Lookback time Cosmology The origin and evolution of the Universe. Recall two concepts: Olbers's paradox and the Cosmological Principle. • Olbers's paradox: Why is the sky dark at night? If the Universe is – spatially infinite – infinitely old and not evolving then the night sky should be bright. • Solution: The Universe has finite age, so the light from most stars have not had time to reach us yet. The Cosmological Principle • Modern cosmology based on the assumption that the Universe is – Homogeneous – Isotropic These assumptions are the cosmological principle. These tenets seem to hold on large scales (>100 Mpc), but definitely not on small scales Hubble's law a natural outcome of this? Definition of redshift, given from spectra. The Hubble constant Luminosity distance In observational astronomy, the term recessional velocity, V is used. At lowz: NB: To determine the distance d to a quasar with z>1, it is NOT correct to use the Doppler formula and then Hubble's Law relating the recessional velocity V to d. V is not really the radial velocity of the quasar, it is the expansion velocity of space time. A cosmological model is required to relate z to d. The Doppler shift is a linear effect due to the relative motion of two objects The cosmological redshift is due to stretching of the photon wavelength due to the expansion of the Universe. At small redshifts, these agree, but not at high redshifts (not Euclidean any longer!) Recessional velocity depends on the scale factor (more later). So at z = 3, R(t0)/R(tem) = 4, universe was ¼ of the size it is today Naïve interpretation: age of the Universe • The most naïve interpretation is that there is an explosion at a single point with us at the center, and no acceleration of deceleration. • It t is the time passed between moment of Big Bang and now, then r=vt is the distance of any object traveling at speed v. – Hubble's Law if t=1/H • Thus, this simple interpretation gives current age of the Universe as t=1/H0 = 14Gyrs. Problems with this interpretation • Needs us to be at the center of explosion • What happens at large r, when Hubble's Law predict v>c? • Deceleration produced by gravitation of all the matter contained in galaxies? • Adequate resolution of these difficulties requires GR combined with the cosmological principle. Cosmological principle illustrated as a raisin cake. On average the universe is isotropic and homogeneous when viewed at any instant by any observer in a typical galaxy. Newtonian Cosmology • Birkhoff's rule: For a homogeneous density distribution ρ(t) the effect of gravitation on a galaxy m at a small distance r from an observer in any other galaxy can be computed by Newtonian physics considering only the mass Mr within radius dr. r Anticipating GR, we will write k is a constant with units length-2, related to curvature of space in GR. = constant, describing the shell radius at current time t0, = r(t0) k will determine the fate of the Universe, basically three cases. Expansion will stop, the Universe is bound. Expansion continues forever, the Universe is unbound. Expansion stops at t=∞. Now let us introduce the scale factor, R(t). Recall r(t) is the coordinate distance. Same for all shells = constant as shell expands, called the comoving coordinate. Now, R(t0)=1. During the expansion, Mr = constant: = present density Relating R(t) to the Hubble Law: Now use the expressions for r(t) and v(t) into the expression for the total energy: Expansion Law of the Universe Critical Density Dividing line between expansion and eventual contraction. Unbound: E>0 Critical: E=0 Bound: E<0 Set k=0 in the equation for the total energy: \e\\'tonian Cosmology 1153 Comments on actual density and critical density A=1 • The critical density is ~29 orders of magnitude smaller than the density of water - but 20-25 times larger than the density of luminous matter if this matter was spread out uniformly throughout space. a 1oo I • For the Universe to be critical, there has to be a lot of unseen matter or energy I Rich clusters (med) a Morgan groups (med) (dark matter/dark energy?) LI Hickson groups (med) Q CFA groups (med) A x-ruy group, jf The Local Group *M101, M31, MilkyWay • Empirical evidence for dark matter * Spirals(med) 0 Ellipticals (med) concentrated in halos of galaxies appears 0 Cor Bor supercluster I Shapley supercluster in rotation curves of spiral galaxies. X Cosmic virial theorem I Least action method f Virgo inlall (range) : Bulk flows (range) 0.01 0.1 1 10 Characteristicsize (Mpc) |E29,4 Themass-tolightratioasafunctionofthecharacteristicsizeofavarietyofsystems. rakento be 100 km s-r Mpc-t for this figure pdor to publication of the WMAP results.(Figure I tiom Dodelson,Modern Cosmology, AcademicPress, New York, 2003, with permissionfrom r. Datafrom Bahcallet al.,Ap. J.,541,1, 2000.) Density parameter At present: Using the definitions we have for the Expansion Law gives: Useful later in GR: A flat universe (no acceleration case). Flatness problem: Behavior of Ω with redshift: Ω = 1 + (Ω0 -1)/(1+ Ω0z) This presents us with the flatness problem. Ω has to be “tuned” very close to 1 in the early universe so that we can observe it close to 1 now. Age for a critical universe R vs. t, for Use Expansion law: Integrate to get R: Use and to get: age of universe k > 0: R oscillates between 0 and Rmax k < 0: R increases forever C&O give the expressions for R. Verify that they are solutions to expansion law! Redshift and scale factor As the universe expands, the photon wavelength grows: True for any Age of universe observed at redshift z For k=0 - see C&O for k>0 and k<0. for example: z=1: t=0.24th = 3 Gyr z=6: t=0.035th= 500 Myr z= 50: t=0.002th= 26 Myr Note also Ned Wright’s cosmology calculator at: http://www.astro.ucla.edu/~wright/CosmoCalc.html Lookback time How far back in time are we looking? For k=0, plugging in for t0, t(z): C&O show, for any k, that at large z: expansion law same, regardless of k. Difficulties with Newtonian Cosmology • Arbitrary nature of Birkhoff's rule (in context of Newtonian theory) to account for 'local' effects of gravitation. • Globally we cannot avoid the issue of galaxies separating from each other at very high speeds. • E=0, the critical case, is preferred. Otherwise, we would need to explain from where the energy of the expansion came? – Then, the age of the Universe is 9Gyr, shorter than the age of oldest stars in the Milky Way. • We will need relativistic cosmology (next time). Next time: Chapter 29.2-4.
Load more

Recommended publications
  • AST 541 Lecture Notes: Classical Cosmology Sep, 2018
    ClassicalCosmology | 1 AST 541 Lecture Notes: Classical Cosmology Sep, 2018 In the next two weeks, we will cover the basic classic cosmology. The material is covered in Longair Chap 5 - 8. We will start with discussions on the first basic assumptions of cosmology, that our universe obeys cosmological principles and is expanding. We will introduce the R-W metric, which describes how to measure distance in cosmology, and from there discuss the meaning of measurements in cosmology, such as redshift, size, distance, look-back time, etc. Then we will introduce the second basic assumption in cosmology, that the gravity in the universe is described by Einstein's GR. We will not discuss GR in any detail in this class. Instead, we will use a simple analogy to introduce the basic dynamical equation in cosmology, the Friedmann equations. We will look at the solutions of Friedmann equations, which will lead us to the definition of our basic cosmological parameters, the density parameters, Hubble constant, etc., and how are they related to each other. Finally, we will spend sometime discussing the measurements of these cosmological param- eters, how to arrive at our current so-called concordance cosmology, which is described as being geometrically flat, with low matter density and a dominant cosmological parameter term that gives the universe an acceleration in its expansion. These next few lectures are the foundations of our class. You might have learned some of it in your undergraduate astronomy class; now we are dealing with it in more detail and more rigorously. 1 Cosmological Principles The crucial principles guiding cosmology theory are homogeneity and expansion.
    [Show full text]
  • Lecture 8: the Big Bang and Early Universe
    Astr 323: Extragalactic Astronomy and Cosmology Spring Quarter 2014, University of Washington, Zeljkoˇ Ivezi´c Lecture 8: The Big Bang and Early Universe 1 Observational Cosmology Key observations that support the Big Bang Theory • Expansion: the Hubble law • Cosmic Microwave Background • The light element abundance • Recent advances: baryon oscillations, integrated Sachs-Wolfe effect, etc. 2 Expansion of the Universe • Discovered as a linear law (v = HD) by Hubble in 1929. • With distant SNe, today we can measure the deviations from linearity in the Hubble law due to cosmological effects • The curves in the top panel show a closed Universe (Ω = 2) in red, the crit- ical density Universe (Ω = 1) in black, the empty Universe (Ω = 0) in green, the steady state model in blue, and the WMAP based concordance model with Ωm = 0:27 and ΩΛ = 0:73 in purple. • The data imply an accelerating Universe at low to moderate redshifts but a de- celerating Universe at higher redshifts, consistent with a model having both a cosmological constant and a significant amount of dark matter. 3 Cosmic Microwave Background (CMB) • The CMB was discovered by Penzias & Wil- son in 1965 (although there was an older mea- surement of the \sky" temperature by McKel- lar using interstellar molecules in 1940, whose significance was not recognized) • This is the best black-body spectrum ever mea- sured, with T = 2:73 K. It is also remark- ably uniform accross the sky (to one part in ∼ 10−5), after dipole induced by the solar mo- tion is corrected for. • The existance of CMB was predicted by Gamow in 1946.
    [Show full text]
  • Large Scale Structure Signals of Neutrino Decay
    Large Scale Structure Signals of Neutrino Decay Peizhi Du University of Maryland Phenomenology 2019 University of Pittsburgh based on the work with Zackaria Chacko, Abhish Dev, Vivian Poulin, Yuhsin Tsai (to appear) Motivation SM neutrinos: We have detected neutrinos 50 years ago Least known particles in the SM 1 Motivation SM neutrinos: We have detected neutrinos 50 years ago Least known particles in the SM What we don’t know: • Origin of mass • Majorana or Dirac • Mass ordering • Total mass 1 Motivation SM neutrinos: We have detected neutrinos 50 years ago Least known particles in the SM What we don’t know: • Origin of mass • Majorana or Dirac • Mass ordering D1 • Total mass ⌫ • Lifetime …… D2 1 Motivation SM neutrinos: We have detected neutrinos 50 years ago Least known particles in the SM What we don’t know: • Origin of mass • Majorana or Dirac probe them in cosmology • Mass ordering D1 • Total mass ⌫ • Lifetime …… D2 1 Why cosmology? Best constraints on (m⌫ , ⌧⌫ ) CMB LSS Planck SDSS Huge number of neutrinos Neutrinos are non-relativistic Cosmological time/length 2 Why cosmology? Best constraints on (m⌫ , ⌧⌫ ) Near future is exciting! CMB LSS CMB LSS Planck SDSS CMB-S4 Euclid Huge number of neutrinos Passing the threshold: Neutrinos are non-relativistic σ( m⌫ ) . 0.02 eV < 0.06 eV “Guaranteed”X evidence for ( m , ⌧ ) Cosmological time/length ⌫ ⌫ or new physics 2 Massive neutrinos in structure formation δ ⇢ /⇢ cdm ⌘ cdm cdm 1 ∆t H− ⇠ Dark matter/baryon 3 Massive neutrinos in structure formation δ ⇢ /⇢ cdm ⌘ cdm cdm 1 ∆t H− ⇠ Dark matter/baryon
    [Show full text]
  • Arxiv:Hep-Ph/9912247V1 6 Dec 1999 MGNTV COSMOLOGY IMAGINATIVE Abstract
    IMAGINATIVE COSMOLOGY ROBERT H. BRANDENBERGER Physics Department, Brown University Providence, RI, 02912, USA AND JOAO˜ MAGUEIJO Theoretical Physics, The Blackett Laboratory, Imperial College Prince Consort Road, London SW7 2BZ, UK Abstract. We review1 a few off-the-beaten-track ideas in cosmology. They solve a variety of fundamental problems; also they are fun. We start with a description of non-singular dilaton cosmology. In these scenarios gravity is modified so that the Universe does not have a singular birth. We then present a variety of ideas mixing string theory and cosmology. These solve the cosmological problems usually solved by inflation, and furthermore shed light upon the issue of the number of dimensions of our Universe. We finally review several aspects of the varying speed of light theory. We show how the horizon, flatness, and cosmological constant problems may be solved in this scenario. We finally present a possible experimental test for a realization of this theory: a test in which the Supernovae results are to be combined with recent evidence for redshift dependence in the fine structure constant. arXiv:hep-ph/9912247v1 6 Dec 1999 1. Introduction In spite of their unprecedented success at providing causal theories for the origin of structure, our current models of the very early Universe, in partic- ular models of inflation and cosmic defect theories, leave several important issues unresolved and face crucial problems (see [1] for a more detailed dis- cussion). The purpose of this chapter is to present some imaginative and 1Brown preprint BROWN-HET-1198, invited lectures at the International School on Cosmology, Kish Island, Iran, Jan.
    [Show full text]
  • Homework 2: Classical Cosmology
    Homework 2: Classical Cosmology Due Mon Jan 21 2013 You may find Hogg astro-ph/9905116 a useful reference for what follows. Ignore radiation energy density in all problems. Problem 1. Distances. a) Compute and plot for at least three sets of cosmological parameters of your choice the fol- lowing quantities as a function of redshift (up to z=10): age of the universe in Gyrs; angular size distance in Gpc; luminosity distance in Gpc; angular size in arcseconds of a galaxy of 5kpc in intrin- sic size. Choose one of them to be the so-called concordance cosmology (Ωm, ΩΛ, h) = (0.3, 0.7, 0.7), one of them to have non-zero curvature and one of them such that the angular diameter distance becomes negative. What does it mean to have negative angular diameter distance? [10 pts] b) Consider a set of flat cosmologies and find the redshift at which the apparent size of an object of given intrinsic size is minimum as a function of ΩΛ. [10 pts] 2. The horizon and flatness problems 1) Compute the age of the universe tCMB at the time of the last scattering surface of the cosmic microwave background (approximately z = 1000), in concordance cosmology. Approximate the horizon size as ctCMB and get an estimate of the angular size of the horizon on the sky. Patches of the CMB larger than this angular scale should not have been in causal contact, but nonetheless the CMB is observed to be smooth across the entire sky. This is the famous ”horizon problem”.
    [Show full text]
  • Measuring the Velocity Field from Type Ia Supernovae in an LSST-Like Sky
    Prepared for submission to JCAP Measuring the velocity field from type Ia supernovae in an LSST-like sky survey Io Odderskov,a Steen Hannestada aDepartment of Physics and Astronomy University of Aarhus, Ny Munkegade, Aarhus C, Denmark E-mail: [email protected], [email protected] Abstract. In a few years, the Large Synoptic Survey Telescope will vastly increase the number of type Ia supernovae observed in the local universe. This will allow for a precise mapping of the velocity field and, since the source of peculiar velocities is variations in the density field, cosmological parameters related to the matter distribution can subsequently be extracted from the velocity power spectrum. One way to quantify this is through the angular power spectrum of radial peculiar velocities on spheres at different redshifts. We investigate how well this observable can be measured, despite the problems caused by areas with no information. To obtain a realistic distribution of supernovae, we create mock supernova catalogs by using a semi-analytical code for galaxy formation on the merger trees extracted from N-body simulations. We measure the cosmic variance in the velocity power spectrum by repeating the procedure many times for differently located observers, and vary several aspects of the analysis, such as the observer environment, to see how this affects the measurements. Our results confirm the findings from earlier studies regarding the precision with which the angular velocity power spectrum can be determined in the near future. This level of precision has been found to imply, that the angular velocity power spectrum from type Ia supernovae is competitive in its potential to measure parameters such as σ8.
    [Show full text]
  • AST4220: Cosmology I
    AST4220: Cosmology I Øystein Elgarøy 2 Contents 1 Cosmological models 1 1.1 Special relativity: space and time as a unity . 1 1.2 Curvedspacetime......................... 3 1.3 Curved spaces: the surface of a sphere . 4 1.4 The Robertson-Walker line element . 6 1.5 Redshifts and cosmological distances . 9 1.5.1 Thecosmicredshift . 9 1.5.2 Properdistance. 11 1.5.3 The luminosity distance . 13 1.5.4 The angular diameter distance . 14 1.5.5 The comoving coordinate r ............... 15 1.6 TheFriedmannequations . 15 1.6.1 Timetomemorize! . 20 1.7 Equationsofstate ........................ 21 1.7.1 Dust: non-relativistic matter . 21 1.7.2 Radiation: relativistic matter . 22 1.8 The evolution of the energy density . 22 1.9 The cosmological constant . 24 1.10 Some classic cosmological models . 26 1.10.1 Spatially flat, dust- or radiation-only models . 27 1.10.2 Spatially flat, empty universe with a cosmological con- stant............................ 29 1.10.3 Open and closed dust models with no cosmological constant.......................... 31 1.10.4 Models with more than one component . 34 1.10.5 Models with matter and radiation . 35 1.10.6 TheflatΛCDMmodel. 37 1.10.7 Models with matter, curvature and a cosmological con- stant............................ 40 1.11Horizons.............................. 42 1.11.1 Theeventhorizon . 44 1.11.2 Theparticlehorizon . 45 1.11.3 Examples ......................... 46 I II CONTENTS 1.12 The Steady State model . 48 1.13 Some observable quantities and how to calculate them . 50 1.14 Closingcomments . 52 1.15Exercises ............................. 53 2 The early, hot universe 61 2.1 Radiation temperature in the early universe .
    [Show full text]
  • Arxiv:0910.5224V1 [Astro-Ph.CO] 27 Oct 2009
    Baryon Acoustic Oscillations Bruce A. Bassett 1,2,a & Ren´ee Hlozek1,2,3,b 1 South African Astronomical Observatory, Observatory, Cape Town, South Africa 7700 2 Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch, Cape Town, South Africa 7700 3 Department of Astrophysics, University of Oxford Keble Road, Oxford, OX1 3RH, UK a [email protected] b [email protected] Abstract Baryon Acoustic Oscillations (BAO) are frozen relics left over from the pre-decoupling universe. They are the standard rulers of choice for 21st century cosmology, provid- ing distance estimates that are, for the first time, firmly rooted in well-understood, linear physics. This review synthesises current understanding regarding all aspects of BAO cosmology, from the theoretical and statistical to the observational, and includes a map of the future landscape of BAO surveys, both spectroscopic and photometric . † 1.1 Introduction Whilst often phrased in terms of the quest to uncover the nature of dark energy, a more general rubric for cosmology in the early part of the 21st century might also be the “the distance revolution”. With new knowledge of the extra-galactic distance arXiv:0910.5224v1 [astro-ph.CO] 27 Oct 2009 ladder we are, for the first time, beginning to accurately probe the cosmic expansion history beyond the local universe. While standard candles – most notably Type Ia supernovae (SNIa) – kicked off the revolution, it is clear that Statistical Standard Rulers, and the Baryon Acoustic Oscillations (BAO) in particular, will play an increasingly important role. In this review we cover the theoretical, observational and statistical aspects of the BAO as standard rulers and examine the impact BAO will have on our understand- † This review is an extended version of a chapter in the book Dark Energy Ed.
    [Show full text]
  • A Model-Independent Approach to Reconstruct the Expansion History of the Universe with Type Ia Supernovae
    A Model-Independent Approach to Reconstruct the Expansion History of the Universe with Type Ia Supernovae Dissertation submitted to the Technical University of Munich by Sandra Ben´ıtezHerrera Max Planck Institute for Astrophysics October 2013 TECHNISHCE UNIVERSITAT¨ MUNCHEN¨ Max-Planck Institute f¨urAstrophysik A Model-Independent Approach to Reconstruct the Expansion History of the Universe with Type Ia Supernovae Sandra Ben´ıtezHerrera Vollst¨andigerAbdruck der von der Fakult¨atf¨urPhysik der Technischen Uni- versitt M¨unchen zur Erlangung des akademischen Grades eines Doktors der Naturwissenschaften (Dr. rer. nat.) genehmigten Dissertation. Vorsitzende(r): Univ.-Prof. Dr. Lothar Oberauer Pr¨uferder Dissertation: 1. Hon.-Prof. Dr. Wolfgang Hillebrandt 2. Univ.-Prof. Dr. Shawn Bishop Die Dissertation wurde am 23.10.2013 bei der Technischen Universit¨atM¨unchen eingereicht und durch die Fakult¨atf¨urPhysik am 21.11.2013 angenommen. \Our imagination is stretched to the utmost, not, as in fiction, to imagine things which are not really there, but just to comprehend those things which are there." Richard Feynman \It is impossible to be a mathematician without being a poet in soul." Sofia Kovalevskaya 6 Contents 1 Introduction 11 2 From General Relativity to Cosmology 15 2.1 The Robertson-Walker Metric . 15 2.2 Einstein Gravitational Equations . 17 2.3 The Cosmological Constant . 19 2.4 The Expanding Universe . 21 2.5 The Scale Factor and the Redshift . 22 2.6 Distances in the Universe . 23 2.6.1 Standard Candles and Standard Rulers . 26 2.7 Cosmological Probes for Acceleration . 27 2.7.1 Type Ia Supernovae as Cosmological Test .
    [Show full text]
  • Arxiv:2002.11464V1 [Physics.Gen-Ph] 13 Feb 2020 a Function of the Angles Θ and Φ in the Sky Is Shown in Fig
    Flat Space, Dark Energy, and the Cosmic Microwave Background Kevin Cahill Department of Physics and Astronomy University of New Mexico Albuquerque, New Mexico 87106 (Dated: February 27, 2020) This paper reviews some of the results of the Planck collaboration and shows how to compute the distance from the surface of last scattering, the distance from the farthest object that will ever be observed, and the maximum radius of a density fluctuation in the plasma of the CMB. It then explains how these distances together with well-known astronomical facts imply that space is flat or nearly flat and that dark energy is 69% of the energy of the universe. I. COSMIC MICROWAVE BACKGROUND RADIATION The cosmic microwave background (CMB) was predicted by Gamow in 1948 [1], estimated to be at a temperature of 5 K by Alpher and Herman in 1950 [2], and discovered by Penzias and Wilson in 1965 [3]. It has been observed in increasing detail by Roll and Wilkinson in 1966 [4], by the Cosmic Background Explorer (COBE) collaboration in 1989{1993 [5, 6], by the Wilkinson Microwave Anisotropy Probe (WMAP) collaboration in 2001{2013 [7, 8], and by the Planck collaboration in 2009{2019 [9{12]. The Planck collaboration measured CMB radiation at nine frequencies from 30 to 857 6 GHz by using a satellite at the Lagrange point L2 in the Earth's shadow some 1.5 10 km × farther from the Sun [11, 12]. Their plot of the temperature T (θ; φ) of the CMB radiation as arXiv:2002.11464v1 [physics.gen-ph] 13 Feb 2020 a function of the angles θ and φ in the sky is shown in Fig.
    [Show full text]
  • New Varying Speed of Light Theories
    New varying speed of light theories Jo˜ao Magueijo The Blackett Laboratory,Imperial College of Science, Technology and Medicine South Kensington, London SW7 2BZ, UK ABSTRACT We review recent work on the possibility of a varying speed of light (VSL). We start by discussing the physical meaning of a varying c, dispelling the myth that the constancy of c is a matter of logical consistency. We then summarize the main VSL mechanisms proposed so far: hard breaking of Lorentz invariance; bimetric theories (where the speeds of gravity and light are not the same); locally Lorentz invariant VSL theories; theories exhibiting a color dependent speed of light; varying c induced by extra dimensions (e.g. in the brane-world scenario); and field theories where VSL results from vacuum polarization or CPT violation. We show how VSL scenarios may solve the cosmological problems usually tackled by inflation, and also how they may produce a scale-invariant spectrum of Gaussian fluctuations, capable of explaining the WMAP data. We then review the connection between VSL and theories of quantum gravity, showing how “doubly special” relativity has emerged as a VSL effective model of quantum space-time, with observational implications for ultra high energy cosmic rays and gamma ray bursts. Some recent work on the physics of “black” holes and other compact objects in VSL theories is also described, highlighting phenomena associated with spatial (as opposed to temporal) variations in c. Finally we describe the observational status of the theory. The evidence is slim – redshift dependence in alpha, ultra high energy cosmic rays, and (to a much lesser extent) the acceleration of the universe and the WMAP data.
    [Show full text]
  • “The Constancy, Or Otherwise, of the Speed of Light”
    “Theconstancy,orotherwise,ofthespeedoflight” DanielJ.Farrell&J.Dunning-Davies, DepartmentofPhysics, UniversityofHull, HullHU67RX, England. [email protected] Abstract. Newvaryingspeedoflight(VSL)theoriesasalternativestotheinflationary model of the universe are discussed and evidence for a varying speed of light reviewed.WorklinkedwithVSLbutprimarilyconcernedwithderivingPlanck’s black body energy distribution for a gas-like aether using Maxwell statistics is consideredalso.DoublySpecialRelativity,amodificationofspecialrelativityto accountforobserverdependentquantumeffectsatthePlanckscale,isintroduced and it is found that a varying speed of light above a threshold frequency is a necessityforthistheory. 1 1. Introduction. SincetheSpecialTheoryofRelativitywasexpoundedandaccepted,ithasseemedalmost tantamount to sacrilege to even suggest that the speed of light be anything other than a constant.ThisissomewhatsurprisingsinceevenEinsteinhimselfsuggestedinapaperof1911 [1] that the speed of light might vary with the gravitational potential. Interestingly, this suggestion that gravity might affect the motion of light also surfaced in Michell’s paper of 1784[2],wherehefirstderivedtheexpressionfortheratioofthemasstotheradiusofastar whose escape speed equalled the speed of light. However, in the face of sometimes fierce opposition, the suggestion has been made and, in recent years, appears to have become an accepted topic for discussion and research. Much of this stems from problems faced by the ‘standardbigbang’modelforthebeginningoftheuniverse.Problemswiththismodelhave
    [Show full text]