DOCSLIB.ORG

Thermodynamics of Cosmological Matter Creation I

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Thermodynamics of Cosmological Matter Creation I Proc. Nati. Acad. Sci. USA Vol. 85, pp. 7428-7432, October 1988 Physics Thermodynamics of cosmological matter creation I. PRIGOGINE*t, J. GEHENIAUt, E. GUNZIGt, AND P. NARDONEt *Center for Statistical Mechanics, University of Texas, Austin, TX 78712; and tFree University of Brussels, Brussels, Belgium Contributed by I. Prigogine, June 3, 1988 ABSTRACT A type of cosmological history that includes ergy of these produced particles is then extracted from that large-scale entropy production is proposed. These cosmologies of the (classical) gravitational field (1-4). But these semiclas- are based on reinterpretation of the matter-energy stress ten- sical Einstein equations are adiabatic and reversible as well, sor in Einstein's equations. This modifies the usual adiabatic and consequently they are unable to provide the entropy energy conservation laws, thereby including irreversible mat- burst accompanying the production of matter. Moreover, the ter creation. This creation corresponds to an irreversible ener- quantum nature of these equations renders the various re- gy flow from the gravitational field to the created matter con- sults highly sensitive to quantum subtleties in curved space- stituents. This point of view results from consideration of the times such as the inevitable subtraction procedures. thermodynamics ofopen systems in the framework ofcosmolo- The aim of the present work is to overcome these prob- gy. It is shown that the second law of thermodynamics requires lems and present a phenomenological model of the origin of that space-time transforms into matter, while the inverse the instability leading from the Minkowskian vacuum to the transformation is forbidden. It appears that the usual initial present universe. We propose a phenomenological macro- singularity associated with the big bang is structurally unsta- scopic approach that allows for both particles and entropy ble with respect to irreversible matter creation. The corre- production in the early universe. We shall indeed show that sponding cosmological history therefore starts from an insta- the thermodynamics of open systems (5, 6*), as applied to bility of the vacuum rather than from a singularity. This is cosmology, leads naturally to a reinterpretation, in Ein- exemplified in the framework of a simple phenomenological stein's equations, of the matter stress-energy tensor (7, 8), model that leads to a three-stage cosmology: the first drives the which then takes into account matter creation on a macro- cosmological system from the initial instability to a de Sitter scopic level. To do this, we extend the concept of adiabatic regime, and the last connects with the usual matter-radiation transformation from closed to open systems. This will then Robertson-Walker universe. Matter as well as entropy cre- apply to systems in which matter-creation occurs. ation occurs during the first two stages, while the third in- These considerations lead to an extension of thermody- volves the traditional cosmological evolution. A remarkable namics as associated with cosmology. Traditionally, in addi- fact is that the de Sitter stage appears to be an attractor inde- tion to the geometrical state ofthe universe, the two physical pendent of the initial fluctuation. This is also the case for all variables describing the cosmological fluid are the energy- the physical predictions involving the present Robertson- density p and the pressure p. Einstein's equations are then Walker universe. Most results obtained previously, in the solved assuming an equation of state p = p(p). In our case, framework of quantum field theory, can now be obtained on a however, a supplementary variable, the particle density n, macroscopic basis. It is shown that this description leads quite enters naturally into the description. This leads to an en- naturally to the introduction of primeval black holes as the largement of traditional cosmology, which we shall develop intermediate stage between the Minkowski vacuum and the in Section 3. An important conclusion is that, in these cir- present matter-radiation universe. The instability at the ori- cumstances, creation of matter can occur only as an irrevers- gin of the universe is the result of fluctuations of the vacuum in ible process, corresponding to an irreversible transfer of en- which black holes act as membranes that stabilize these fluctu- ergy from the gravitational field to the created matter. More ations. In short, black holes will be produced by an "inverse" precisely, the transition from traditional cosmology (involv- Hawking radiation process and, once formed, will decompose ing only adiabatic transformations for closed systems) to adi- into "real" matter through the usual Hawking radiation. In abatic transformations for open systems, leads to modifica- this way, the irreversible transformation of space-time into tion of the expression for energy conservation (Section 2). matter can be described as a phase separation between matter As a result, a supplementary effective pressure Pc, related to and gravitation in which black holes play the role of "critical particle creation, appears. This pressure is always negative nuclei." or zero, according to the second law.§ Moreover, it is shown that the big bang singularity, pres- ent in traditional cosmology, is structurally unstable with re- Section I. Introduction spect to irreversible matter creation. Such a cosmology starts from an instability (10-12) of the Minkowski vacuum Very few physical theories are in such a paradoxical situa- and not from a singularity. We specify these properties in tion as cosmology. On the one hand, our universe is charac- Section 3, in the framework of a simple phenomenological terized by a considerable entropy content, mainly in the model of irreversible particle production. This model pro- form of black body radiation. On the other hand, Einstein's vides a cosmological history that evolves in three stages equations are adiabatic and reversible, and consequently (Section 4): (i) A creation period that drives the cosmologi- they cannot provide, by themselves, an explanation of the cal system from an initial fluctuation of the vacuum to a de origin of cosmological entropy. Sitter space; (ii) the de Sitter space exists during the decay As is well known, matter may be produced quantum me- chanically in the framework of Einstein's equations. The en- tRecently, two of us (J.G. and I.P.) have considered the problem of a redefinition of matter-density and pressure in the stress tensor. To some extent, the work reported here continues this attempt. The publication costs of this article were defrayed in part by page charge §It should be emphasized that our approach differs from that used payment. This article must therefore be hereby marked "advertisement" by Hoyle to take into account matter creation with a "C-field" in accordance with 18 U.S.C. §1734 solely to indicate this fact. (see, for example, ref. 9). 7428 Downloaded by guest on September 28, 2021 Physics: Prigogine et aL Proc. NatL Acadl ScL USA 85 (1988) 7429 time of its constituents; and (iii) a phase transition turns the start from the total differential of the entropy de Sitter space into the usual Robertson-Walker universe, Td(sV) = d(pV) + p dV - d(nV), [2-7] which extends to the present. 1L A fundamental fact is that the de Sitter regime appears as where At is the chemical potential an attractor whose properties are independent of the initial fluctuation. This implies, in turn, that all the physical param- s = S/V pn = h-Ts with A .O,2 s 2 O. [2-8] eters characterizing the present Robertson-Walker stage are For closed systems and adiabatic transformation, relation 2- independent of this initial fluctuation. In particular, the spe- 7 leads to cific entropy per baryon S = ny/nb depends only on two characteristic times of the theory: the creation period time rc dS = 0 and diS = 0. [2-9] and the de Sitter decay time Td, which are obtained in Sec- Let us consider the effect of matter creation. We consider tion 4. expect that we still into homogeneous systems and we therefore Our model takes the second law of thermodynamics have dS = 0. In contrast, matter creation contributes to the account from the beginning. Indeed, the energy transfer entropy production. We have therefore from space-time curvature to matter is treated as an irre- versible process, leading to a burst of entropy associated T djS = T dS = (h/n)d(nV) - ,u d(nV) of matter. Therefore, the distinction be- with the creation = . 0. [2-10] tween space-time and matter is provided by entropy cre- T(s/n)d(nV) ation. The latter occurs only during the two first cosmologi- This inequality, in the cosmological context developed in cal stages while, as is well known, the Robertson-Walker Section 3, implies that space-time can produce matter, universe evolves adiabatically on the cosmological scale. while the reverse process is thermodynamically forbidden. It is interesting that "mini black holes" seem to play an The relation between space-time and matter ceases to be essential role in these fluctuations that lead from the Min- symmetrical, since particle production, occurring at the ex- kowski vacuum to the present universe. It is tempting to re- pense of gravitational energy, appears to be an irreversible late this to the fact that black holes play the role of mem- process. A situation somewhat similar corresponds to sys- branes stabilizing the vacuum fluctuations. In this way, the tems in which macroscopic kinetic energy can be trans- primeval stage corresponding to the formation of the uni- formed into internal energy. This kinetic energy then ap- verse can be viewed as a phase separation between gravita- pears as a source term in the entropy balance equation (5, 6). tion and matter. A few remarks concerning this mechanism The microscopic interpretation of this process in which are presented in Section 5.
Load more

Recommended publications
  • Arxiv:1904.10313V3 [Gr-Qc] 22 Oct 2020 PACS Numbers: Keywords: Entropy, Holographic Principle and CCDM Models
    Thermodynamic constraints on matter creation models R. Valentim∗ Departamento de F´ısica, Instituto de Ci^enciasAmbientais, Qu´ımicas e Farmac^euticas - ICAQF, Universidade Federal de S~aoPaulo (UNIFESP) Unidade Jos´eAlencar, Rua S~aoNicolau No. 210, 09913-030 { Diadema, SP, Brazil J. F. Jesusy Universidade Estadual Paulista (UNESP), C^ampusExperimental de Itapeva Rua Geraldo Alckmin 519, 18409-010, Vila N. Sra. de F´atima,Itapeva, SP, Brazil and Universidade Estadual Paulista (UNESP), Faculdade de Engenharia de Guaratinguet´a Departamento de F´ısica e Qu´ımica, Av. Dr. Ariberto Pereira da Cunha 333, 12516-410 - Guaratinguet´a,SP, Brazil Abstract Entropy is a fundamental concept from Thermodynamics and it can be used to study models on context of Creation Cold Dark Matter (CCDM). From conditions on the first (S_ 0)1 and ≥ second order (S¨ < 0) time derivatives of total entropy in the initial expansion of Sitter through the radiation and matter eras until the end of Sitter expansion, it is possible to estimate the intervals of parameters. The total entropy (St) is calculated as sum of the entropy at all eras (Sγ and Sm) plus the entropy of the event horizon (Sh). This term derives from the Holographic Principle where it suggests that all information is contained on the observable horizon. The main feature of this method for these models are that thermodynamic equilibrium is reached in a final de Sitter era. Total entropy of the universe is calculated with three terms: apparent horizon (Sh), entropy of matter (Sm) and entropy of radiation (Sγ). This analysis allows to estimate intervals of parameters of CCDM models.
    [Show full text]
  • Birth of De Sitter Universe from a Time Crystal Universe
    PHYSICAL REVIEW D 100, 123531 (2019) Birth of de Sitter universe from a time crystal universe † Daisuke Yoshida * and Jiro Soda Department of Physics, Kobe University, Kobe 657-8501, Japan (Received 30 September 2019; published 18 December 2019) We show that a simple subclass of Horndeski theory can describe a time crystal universe. The time crystal universe can be regarded as a baby universe nucleated from a flat space, which is mediated by an extension of Giddings-Strominger instanton in a 2-form theory dual to the Horndeski theory. Remarkably, when a cosmological constant is included, de Sitter universe can be created by tunneling from the time crystal universe. It gives rise to a past completion of an inflationary universe. DOI: 10.1103/PhysRevD.100.123531 I. INTRODUCTION Euler-Lagrange equations of motion contain up to second order derivatives. Actually, bouncing cosmology in the Inflation has succeeded in explaining current observa- Horndeski theory has been intensively investigated so far tions of the large scale structure of the Universe [1,2]. [23–29]. These analyses show the presence of gradient However, inflation has a past boundary [3], which could be instability [30,31] and finally no-go theorem for stable a true initial singularity or just a coordinate singularity bouncing cosmology in Horndeski theory was found for the depending on how much the Universe deviates from the spatially flat universe [32]. However, it was shown that the exact de Sitter [4], or depending on the topology of the no-go theorem does not hold when the spatial curvature is Universe [5].
    [Show full text]
  • 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]
  • European Astroparticle Physics Strategy 2017-2026 Astroparticle Physics European Consortium
    European Astroparticle Physics Strategy 2017-2026 Astroparticle Physics European Consortium August 2017 European Astroparticle Physics Strategy 2017-2026 www.appec.org Executive Summary Astroparticle physics is the fascinating field of research long-standing mysteries such as the true nature of Dark at the intersection of astronomy, particle physics and Matter and Dark Energy, the intricacies of neutrinos cosmology. It simultaneously addresses challenging and the occurrence (or non-occurrence) of proton questions relating to the micro-cosmos (the world decay. of elementary particles and their fundamental interactions) and the macro-cosmos (the world of The field of astroparticle physics has quickly celestial objects and their evolution) and, as a result, established itself as an extremely successful endeavour. is well-placed to advance our understanding of the Since 2001 four Nobel Prizes (2002, 2006, 2011 and Universe beyond the Standard Model of particle physics 2015) have been awarded to astroparticle physics and and the Big Bang Model of cosmology. the recent – revolutionary – first direct detections of gravitational waves is literally opening an entirely new One of its paths is targeted at a better understanding and exhilarating window onto our Universe. We look of cataclysmic events such as: supernovas – the titanic forward to an equally exciting and productive future. explosions marking the final evolutionary stage of massive stars; mergers of multi-solar-mass black-hole Many of the next generation of astroparticle physics or neutron-star binaries; and, most compelling of all, research infrastructures require substantial capital the violent birth and subsequent evolution of our infant investment and, for Europe to remain competitive Universe.
    [Show full text]
  • On Asymptotically De Sitter Space: Entropy & Moduli Dynamics
    On Asymptotically de Sitter Space: Entropy & Moduli Dynamics To Appear... [1206.nnnn] Mahdi Torabian International Centre for Theoretical Physics, Trieste String Phenomenology Workshop 2012 Isaac Newton Institute , CAMBRIDGE 1 Tuesday, June 26, 12 WMAP 7-year Cosmological Interpretation 3 TABLE 1 The state of Summarythe ofart the cosmological of Observational parameters of ΛCDM modela Cosmology b c Class Parameter WMAP 7-year ML WMAP+BAO+H0 ML WMAP 7-year Mean WMAP+BAO+H0 Mean 2 +0.056 Primary 100Ωbh 2.227 2.253 2.249−0.057 2.255 ± 0.054 2 Ωch 0.1116 0.1122 0.1120 ± 0.0056 0.1126 ± 0.0036 +0.030 ΩΛ 0.729 0.728 0.727−0.029 0.725 ± 0.016 ns 0.966 0.967 0.967 ± 0.014 0.968 ± 0.012 τ 0.085 0.085 0.088 ± 0.015 0.088 ± 0.014 2 d −9 −9 −9 −9 ∆R(k0) 2.42 × 10 2.42 × 10 (2.43 ± 0.11) × 10 (2.430 ± 0.091) × 10 +0.030 Derived σ8 0.809 0.810 0.811−0.031 0.816 ± 0.024 H0 70.3km/s/Mpc 70.4km/s/Mpc 70.4 ± 2.5km/s/Mpc 70.2 ± 1.4km/s/Mpc Ωb 0.0451 0.0455 0.0455 ± 0.0028 0.0458 ± 0.0016 Ωc 0.226 0.226 0.228 ± 0.027 0.229 ± 0.015 2 +0.0056 Ωmh 0.1338 0.1347 0.1345−0.0055 0.1352 ± 0.0036 e zreion 10.4 10.3 10.6 ± 1.210.6 ± 1.2 f t0 13.79 Gyr 13.76 Gyr 13.77 ± 0.13 Gyr 13.76 ± 0.11 Gyr a The parameters listed here are derived using the RECFAST 1.5 and version 4.1 of the WMAP[WMAP-7likelihood 1001.4538] code.
    [Show full text]
  • FRW Type Cosmologies with Adiabatic Matter Creation
    Brown-HET-991 March 1995 FRW Type Cosmologies with Adiabatic Matter Creation J. A. S. Lima1,2, A. S. M. Germano2 and L. R. W. Abramo1 1 Physics Department, Brown University, Providence, RI 02912,USA. 2 Departamento de F´ısica Te´orica e Experimental, Universidade Federal do Rio Grande do Norte, 59072 - 970, Natal, RN, Brazil. Abstract Some properties of cosmological models with matter creation are inves- tigated in the framework of the Friedman-Robertson-Walker (FRW) line element. For adiabatic matter creation, as developed by Prigogine arXiv:gr-qc/9511006v1 2 Nov 1995 and coworkers, we derive a simple expression relating the particle num- ber density n and energy density ρ which holds regardless of the mat- ter creation rate. The conditions to generate inflation are discussed and by considering the natural phenomenological matter creation rate ψ = 3βnH, where β is a pure number of the order of unity and H is the Hubble parameter, a minimally modified hot big-bang model is proposed. The dynamic properties of such models can be deduced from the standard ones simply by replacing the adiabatic index γ of the equation of state by an effective parameter γ∗ = γ(1 β). The − thermodynamic behavior is determined and it is also shown that ages large enough to agree with observations are obtained even given the high values of H suggested by recent measurements. 1 Introduction The origin of the material content (matter plus radiation) filling the presently observed universe remains one of the most fascinating unsolved mysteries in cosmology even though many authors worked out to understand the matter creation process and its effects on the evolution of the universe [1-27].
    [Show full text]
  • Universe Model Multicomponent
    We can’t solve problems by using the same kind of thinking we used when we created them. Albert Einstein WORLD – UNIVERSE MODEL MULTICOMPONENT DARK MATTER COSMIC GAMMA-RAY BACKGROUND Vladimir S. Netchitailo Biolase Inc., 4 Cromwell, Irvine CA 92618, USA. [email protected] ABSTRACT World – Universe Model is based on two fundamental parameters in various rational exponents: Fine-structure constant α, and dimensionless quantity Q. While α is constant, Q increases with time, and is in fact a measure of the size and the age of the World. The Model makes predictions pertaining to masses of dark matter (DM) particles and explains the diffuse cosmic gamma-ray background radiation as the sum of contributions of multicomponent self-interacting dark matter annihilation. The signatures of DM particles annihilation with predicted masses of 1.3 TeV, 9.6 GeV, 70 MeV, 340 keV, and 3.7 keV, which are calculated independently of astrophysical uncertainties, are found in spectra of the diffuse gamma-ray background and the emission of various macroobjects in the World. The correlation between different emission lines in spectra of macroobjects is connected to their structure, which depends on the composition of the core and surrounding shells made up of DM particles. Thus the diversity of Very High Energy (VHE) gamma-ray sources in the World has a clear explanation. 1 1. INTRODUCTION In 1937, Paul Dirac proposed a new basis for cosmology: the hypothesis of a time varying gravitational “constant” [1]. In 1974, Dirac added a mechanism of continuous creation of matter in the World [2]: One might assume that nucleons are created uniformly throughout space, and thus mainly in intergalactic space.
    [Show full text]
  • Galaxy Formation Within the Classical Big Bang Cosmology
    Galaxy formation within the classical Big Bang Cosmology Bernd Vollmer CDS, Observatoire astronomique de Strasbourg Outline • some basics of astronomy small structure • galaxies, AGNs, and quasars • from galaxies to the large scale structure of the universe large • the theory of cosmology structure • measuring cosmological parameters • structure formation • galaxy formation in the cosmological framework • open questions small structure The architecture of the universe • Earth (~10-9 ly) • solar system (~6 10-4 ly) • nearby stars (> 5 ly) • Milky Way (~6 104 ly) • Galaxies (>2 106 ly) • large scale structure (> 50 106 ly) How can we investigate the universe Astronomical objects emit elctromagnetic waves which we can use to study them. BUT The earth’s atmosphere blocks a part of the electromagnetic spectrum. need for satellites Back body radiation • Opaque isolated body at a constant temperature Wien’s law: sun/star (5500 K): 0.5 µm visible human being (310 K): 9 µm infrared molecular cloud (15 K): 200 µm radio The structure of an atom Components: nucleus (protons, neutrons) + electrons Bohr’s model: the electrons orbit around the nucleus, the orbits are discrete Bohr’s model is too simplistic quantum mechanical description The emission of an astronomical object has 2 components: (i) continuum emission + (ii) line emission Stellar spectra Observing in colors Usage of filters (Johnson): U (UV), B (blue), V (visible), R (red), I (infrared) The Doppler effect • Is the apparent change in frequency and wavelength of a wave which is emitted by
    [Show full text]
  • Searches for Leptophilic Dark Matter with Astrophysical Experiments
    . Searches for leptophilic dark matter with astrophysical experiments . Von der Fakult¨atf¨urMathematik, Informatik und Naturwissenschaften der RWTH Aachen University zur Erlangung des akademischen Grades einer Doktorin der Naturwissenschaften genehmigte Dissertation vorgelegt von M. Sc. Leila Ali Cavasonza aus Finale Ligure, Savona, Italien Berichter: Universit¨atsprofessorDr. rer. nat. Michael Kr¨amer Universit¨atsprofessorDr. rer. nat. Stefan Schael Tag der m¨undlichen Pr¨ufung: 13.05.16 Diese Dissertation ist auf den Internetseiten der Universit¨atsbibliothekonline verf¨ugbar RWTH Aachen University Leila Ali Cavasonza Institut f¨urTheoretische Teilchenphysik und Kosmologie Searches for leptophilic dark matter with astrophysical experiments PhD Thesis February 2016 Supervisors: Prof. Dr. Michael Kr¨amer Prof. Dr. Stefan Schael Zusammenfassung Suche nach leptophilischer dunkler Materie mit astrophysikalischen Experimenten Die Natur der dunklen Materie (DM) zu verstehen ist eines der wichtigsten Ziele der Teilchen- und Astroteilchenphysik. Große experimentelle Anstrengungen werden un- ternommen, um die dunkle Materie nachzuweisen, in der Annahme, dass sie neben der Gravitationswechselwirkung eine weitere Wechselwirkung mit gew¨ohnlicher Materie hat. Die dunkle Materie in unserer Galaxie k¨onnte gew¨ohnliche Teilchen durch An- nihilationsprozesse erzeugen und der kosmischen Strahlung einen zus¨atzlichen Beitrag hinzuf¨ugen.Deswegen sind pr¨aziseMessungen der Fl¨ussekosmischer Strahlung ¨außerst wichtig. Das AMS-02 Experiment misst die
    [Show full text]
  • FRW Cosmology
    17/11/2016 Cosmology 13.8 Gyrs of Big Bang History Gravity Ruler of the Universe 1 17/11/2016 Strong Nuclear Force Responsible for holding particles together inside the nucleus. The nuclear strong force carrier particle is called the gluon. The nuclear strong interaction has a range of 10‐15 m (diameter of a proton). Electromagnetic Force Responsible for electric and magnetic interactions, and determines structure of atoms and molecules. The electromagnetic force carrier particle is the photon (quantum of light) The electromagnetic interaction range is infinite. Weak Force Responsible for (beta) radioactivity. The weak force carrier particles are called weak gauge bosons (Z,W+,W‐). The nuclear weak interaction has a range of 10‐17 m (1% of proton diameter). Gravity Responsible for the attraction between masses. Although the gravitational force carrier The hypothetical (carrier) particle is the graviton. The gravitational interaction range is infinite. By far the weakest force of nature. 2 17/11/2016 The weakest force, by far, rules the Universe … Gravity has dominated its evolution, and determines its fate … Grand Unified Theories (GUT) Grand Unified Theories * describe how ∑ Strong ∑ Weak ∑ Electromagnetic Forces are manifestations of the same underlying GUT force … * This implies the strength of the forces to diverge from their uniform GUT strength * Interesting to see whether gravity at some very early instant unifies with these forces ??? 3 17/11/2016 Newton’s Static Universe ∑ In two thousand years of astronomy, no one ever guessed that the universe might be expanding. ∑ To ancient Greek astronomers and philosophers, the universe was seen as the embodiment of perfection, the heavens were truly heavenly: – unchanging, permanent, and geometrically perfect.
    [Show full text]
  • “De Sitter Effect” in the Rise of Modern Relativistic Cosmology
    The role played by the “de Sitter effect” in the rise of modern relativistic cosmology ● Matteo Realdi ● Department of Astronomy, Padova ● Sait 2009. Pisa, 7-5-2009 Table of contents ● Introduction ● 1917: Einstein, de Sitter and the universes of General Relativity ● 1920's: the debates on the “de Sitter effect”. The connection between theory and observation and the rise of scientific cosmology ● 1930: the expanding universe and the decline of the interest in the de Sitter effect ● Conclusion 1 - Introduction ● Modern cosmology: study of the origin, structure and evolution of the universe as a whole, based on the interpretation of astronomical observations at different wave- lengths through the laws of physics ● The early years: 1917-1930. Extremely relevant period, characterized by new ideas, discoveries, controversies, in the light of the first comparison of theoretical world-models with observations at the turning point of relativity revolution ● Particular attention on the interest in the so-called “de Sitter effect”, a theoretical redshift-distance relation which is predicted through the line element of the empty universe of de Sitter ● The de Sitter effect: fundamental influence in contributions that scientists as de Sitter, Eddington, Weyl, Lanczos, Lemaître, Robertson, Tolman, Silberstein, Wirtz, Lundmark, Stromberg, Hubble offered during the 1920's both in theoretical and in observational cosmology (emergence of the modern approach of cosmologists) ➔ Predictions and confirmations of an appropriate redshift- distance relation marked the tortuous process towards the change of viewpoint from the 1917 paradigm of a static universe to the 1930 picture of an expanding universe evolving both in space and in time 2 - 1917: the Universes of General Relativity ● General relativity: a suitable theory in order to describe the whole of space, time and gravitation? ● Two different metrics, i.e.
    [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]