DOCSLIB.ORG

Constraining the Hubble Parameter Using Distance Modulus-Redshift

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Constraining the Hubble Parameter Using Distance Modulus-Redshift id3621125 pdfMachine by Broadgun Software - a great PDF writer! - a great PDF creator! - http://www.pdfmachine.com http://www.broadgun.com Mehtapress 2013 Print-ISSN: 2320-6756 Online-ISSN: 2320-6764 J.Phy.Ast. Journal of FulPl hpaypseircs & Astronomy Full Paper WWW.MEHTAPRESS.COM C.C.Onuchukwu1*, A.C.Ezeribe2 Constraining the Hubble parameter using dis- 1Department of Industrial Physics, tance modulus – Redshift relation Anambra State University, Uli, (NIGE- RIA) Abstract 2Department of Physics/Industrial Phys- ics, Nnamdi Azikiwe University, Awka, Using the relation between distance modulus (m – M), redshift (z) and deceleration parameter (NIGERIA) (q ), obtained using Friedman-Robertson-Walker (FRW) metric, we constrain the Hubble 0 E-mail: [email protected] parameter (h). Using the mean and the median values of our data obtained from NASA Extragalactic Database (NED), the value of Hubble parameter we estimated is 0.66 0.11 Received: September 26, 2013 and 0.84 0.11 for q = –1 and q = 0 respectively. In general, using the minimum and the 0 0 Accepted: November 10, 2013 maximum values of the parameter in our data, the value of Hubble parameter we estimated lies in the range 0.6 0.2 h 2.2 0.7, with an average value of h = 0.67 0.22 – 0.96 0.29, giving an average age for the universe as 11.4 2.4 – 14.3 2.2 Gyr. *Corresponding author’s Name & Address Key Words C.C.Onuchukwu Cosmology - Miscellaneous; Astronomical database - Miscellaneous; Method - Statistical; Data Department of Industrial Physics, Analysis. Anambra State University, Uli, (NIGE- RIA) E-mail: [email protected] INTRODUCTION the evolution of the universe, the Big Bang Theory is pres- ently the most acceptable model that described most of The universe is all of space, time, matter and energy the observational features in the evolution of the universe. that exist. The ultimate fate of the universe is determined, It explained the universe to have started from an extremely through its gravity, thus, the amount of matter/energy in hot dense phase called the Planck epoch (all fundamental the universe is therefore a considerable importance in cos- forces are unified – the period of Theory Of Everything mology. The Wilkinson Microwave Anisotropy Probe (TOE)) at the end of which gravitational force separated (WMAP) in collaboration with National Aeronautics and from gauge forces, and passed through the Grand Unifi- Space Admiration (NASA) in one of their mission esti- cation Epoch and Inflationary Epoch (at the end of which mated that the universe comprises of about 4.6% of vis- strong forces separated from electroweak force) and the ible matter, 24% of matter with gravity but do not emit Electroweak Epoch (unification of electromagnetism and observable light (the dark matter) and about 71.4% was weak nuclear interaction). Other phases include – attributed to dark energy (possibly anti-gravity) that may Baryogenesis, Hadron Epoch, Lepton Era, Nucleosyn- be responsible for driving the acceleration of the observed thesis, Photon Era, Recombination Epoch and presently expansion of the universe[20]. The universe has been ob- Matter Dominated Era[7,14,23-25]. served to be expanding, first suggested by Einstein in his The generally acceptable mathematical theory for study- general theory of relativity and observed by ing the evolution of the universe is general relativity[9]. Hubble[17,21,29,30]. General relativity is the theory of gravitation, in which Amongst the different models proposed to explain gravitational effects between masses results from warping Full Paper JOPA, 2(4) 2013 of space-time by the masses. In a uniform universe, gen- deceleration parameter (q ) of the universe to constrain 0 eral relativity has a simple solution for the evolution of the the Hubble constant for a large database obtained from geometry of the universe (contraction or expansion) which NED and possibly trace the evolution of the Hubble pa- depends on its content and past history[29]. In the presence rameter as a function of redshift (H(z)). of enough matter, the expansion will slow or even be- come a contraction. On the other hand, the dark energy THEORETICAL RELATIONSHIPS (cosmological constant ()) drives the universe towards increasing expansion[29]. The current rate of expansion is The evolutionary trend of the universe has been mod- usually expressed as Hubble constant (H ) with an esti- eled by using the density parameter (), determine by the 0 mated value of H = 100h kms-1 Mpc-1, with the Hubble density of the universe, the deceleration parameter (q ) 0 0 parameter (h) having values of h = 0.5 – 1.0[24,25]. and the Hubble constant (H ). The Hubble constant is an 0 One of the fundamental goals of cosmology is to important parameter in cosmology as it not only deter- determine the expansion rate of the universe. Various mines its expansion rate, it also set limit to the possible methods that have been applied include: age, critical density and size of the observable universe. (1) The use of distant Type 1a supernovae (SN 1a) as The velocity (v) of the expansion of the universe has been standard candles[22,2,8,31]. The apparent peak magnitude defined by Hubble[16] as of these supernovae yields a relative luminosity dis- v(t) = H (t)d (1) tance d as a function of redshift from which the 0 L where d is the radius of the expanding universe. The size Hubble constant is estimated[27,28,32]. of the universe is unknown, yet it undergoes expansion or (2) Large galaxy surveys for mapping of cosmic distances contraction, thus, the evolution of the universe can be ex- and expansion, by using the large scale clustering pat- press in terms of cosmic scale factor (a(t)) as tern of galaxies which contains the signature of Baryon Acoustic Oscillation (BAOs). BAO refers to the regu- (2) lar periodic fluctuations in the density of the visible In terms of the cosmic expansion factor (R ), at the baryonic matter of the universe, caused by acoustic 0 time (t ), the Hubble constant is given by (e.g.[24]) waves which existed in the early universe. By looking 0 at large scale clustering of galaxies, a preferred length- scale which was imprinted in the distribution of pho- (3) tons and baryons propagated by the sound waves in where is the first time derivative of R . The cosmic the relativistic plasma of the early universe, can be 0 scale factor affect all distances, thus, the wavelength ( ) calibrated by the observation of Cosmic Background e of a photon emitted at time of emission (t ) and observed Microwave Radiation (CMBR) and applied as cos- e [24] [1,5,19] at another time (t ), will be (e.g. ) mological standard rod (e.g. ). 0 (3) Other test include the redshift-angular size test, galaxy cluster gas mass fraction, strong gravitational lensing (4) test and structure formation test, these test generally where is the wavelength of the observed photon at 0 constrain cosmological parameters as a function of time (t ). The cosmological redshift (z) is usually given by [26] 0 redshift (see review by Samushia & Rastra ). (e.g.[24]) Several decades have passed since Hubble published the correlation between distances to galaxies and their ex- (5) pansion velocities, but establishing an accurate cosmologi- cal distance scale and value for the Hubble constant (H ) where d is radius of the universe centered on the observer 0 at time t , and c is the speed of photons. Allowing for have proved challenging. The value of H has evolved 0 0 from H = 500 kms-1 Mps-1 recorded by Hubble[17] to a some form of time evolution of the expansion factor 0 [24] well-known range of range of H = 50 - 100 kms-1 Mps- (R(t)), we expand it using Taylor series. Following Roos 0 1[3]. The Hubble Space Telescope (HST) gave a more spe- we can for t in general write cific value of H = 70 - 80 10%[11], while the WAMP 0 (6) data give H = 72 5 kms-1 Mps-1, = 0.3, and = 0 m 0.7[30], where is relative matter density (both luminous Making use of the definition of equation (3), equa- m and dark matter) and is the relative dark energy den- tion (6) implies that to a second order expansion, the cos- sity. mic scale factor can be written as In this article, we which to use the dependence of observed distance modulus (m – M) on redshift (z) and FP 141 JOPA, 2(4) 2013 . Full Paper (e.g.[24]) (7) (16) From equation (3), we can write For an expanding universe parameterized by the cos- (8) mic scale factor (a(t)), in which photons are redshifted and The deceleration parameter (q) which measure the rate suffer from energy effect, if the apparent brightness of a galaxy is B , then its proper distance is given by (e.g.[24]) of slowing down of the expansion factor is defined a (e.g.[24]) by (17) Equating B = B , implies that d = (1 + z)d . Thus, the a o L p (9) luminosity distance in terms of redshift is given by Makin use of equations (3), (4), (7) and (9) in equation (5), the cosmological redshift can be expressed as (18) In terms of distance modulus (m – M), the luminosity (10) distance to a source is given by (e.g.[15]) making use of the series expansion , equation (10) can be approxi- (19) mated to Substituting equation (18) into equation (19), we have (20) (11) where , and H = In obtaining equation (11), we made use of terms 0 only to the second order in t.
Load more

Recommended publications
  • The Matter – Antimatter Asymmetry of the Universe and Baryogenesis
    The matter – antimatter asymmetry of the universe and baryogenesis Andrew Long Lecture for KICP Cosmology Class Feb 16, 2017 Baryogenesis Reviews in General • Kolb & Wolfram’s Baryon Number Genera.on in the Early Universe (1979) • Rio5o's Theories of Baryogenesis [hep-ph/9807454]} (emphasis on GUT-BG and EW-BG) • Rio5o & Trodden's Recent Progress in Baryogenesis [hep-ph/9901362] (touches on EWBG, GUTBG, and ADBG) • Dine & Kusenko The Origin of the Ma?er-An.ma?er Asymmetry [hep-ph/ 0303065] (emphasis on Affleck-Dine BG) • Cline's Baryogenesis [hep-ph/0609145] (emphasis on EW-BG; cartoons!) Leptogenesis Reviews • Buchmuller, Di Bari, & Plumacher’s Leptogenesis for PeDestrians, [hep-ph/ 0401240] • Buchmulcer, Peccei, & Yanagida's Leptogenesis as the Origin of Ma?er, [hep-ph/ 0502169] Electroweak Baryogenesis Reviews • Cohen, Kaplan, & Nelson's Progress in Electroweak Baryogenesis, [hep-ph/ 9302210] • Trodden's Electroweak Baryogenesis, [hep-ph/9803479] • Petropoulos's Baryogenesis at the Electroweak Phase Transi.on, [hep-ph/ 0304275] • Morrissey & Ramsey-Musolf Electroweak Baryogenesis, [hep-ph/1206.2942] • Konstandin's Quantum Transport anD Electroweak Baryogenesis, [hep-ph/ 1302.6713] Constituents of the Universe formaon of large scale structure (galaxy clusters) stars, planets, dust, people late ame accelerated expansion Image stolen from the Planck website What does “ordinary matter” refer to? Let’s break it down to elementary particles & compare number densities … electron equal, universe is neutral proton x10 billion 3⇣(3) 3 3 n =3 T 168 cm− neutron x7 ⌫ ⇥ 4⇡2 ⌫ ' matter neutrinos photon positron =0 2⇣(3) 3 3 n = T 413 cm− γ ⇡2 CMB ' anti-proton =0 3⇣(3) 3 3 anti-neutron =0 n =3 T 168 cm− ⌫¯ ⇥ 4⇡2 ⌫ ' anti-neutrinos antimatter What is antimatter? First predicted by Dirac (1928).
    [Show full text]
  • Scalar Correlation Functions in De Sitter Space from the Stochastic Spectral Expansion
    IMPERIAL/TP/2019/TM/03 Scalar correlation functions in de Sitter space from the stochastic spectral expansion Tommi Markkanena;b , Arttu Rajantiea , Stephen Stopyrac and Tommi Tenkanend aDepartment of Physics, Imperial College London, Blackett Laboratory, London, SW7 2AZ, United Kingdom bLaboratory of High Energy and Computational Physics, National Institute of Chemical Physics and Biophysics, R¨avala pst. 10, Tallinn, 10143, Estonia cDepartment of Physics and Astronomy, UCL, Gower Street, London WC1E 6BT, United Kingdom dDepartment of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218, United States of America E-mail: [email protected], tommi.markkanen@kbfi.ee, [email protected], [email protected], [email protected] Abstract. We consider light scalar fields during inflation and show how the stochastic spec- tral expansion method can be used to calculate two-point correlation functions of an arbitrary local function of the field in de Sitter space. In particular, we use this approach for a massive scalar field with quartic self-interactions to calculate the fluctuation spectrum of the density contrast and compare it to other approximations. We find that neither Gaussian nor linear arXiv:1904.11917v2 [gr-qc] 1 Aug 2019 approximations accurately reproduce the power spectrum, and in fact always overestimate it. For example, for a scalar field with only a quartic term in the potential, V = λφ4=4, we find a blue spectrum with spectral index n 1 = 0:579pλ. − Contents 1 Introduction1 2 The stochastic approach2 2.1
    [Show full text]
  • Outline of Lecture 2 Baryon Asymmetry of the Universe. What's
    Outline of Lecture 2 Baryon asymmetry of the Universe. What’s the problem? Electroweak baryogenesis. Electroweak baryon number violation Electroweak transition What can make electroweak mechanism work? Dark energy Baryon asymmetry of the Universe There is matter and no antimatter in the present Universe. Baryon-to-photon ratio, almost constant in time: nB 10 ηB = 6 10− ≡ nγ · Baryon-to-entropy, constant in time: n /s = 0.9 10 10 B · − What’s the problem? Early Universe (T > 1012 K = 100 MeV): creation and annihilation of quark-antiquark pairs ⇒ n ,n n q q¯ ≈ γ Hence nq nq¯ 9 − 10− nq + nq¯ ∼ How was this excess generated in the course of the cosmological evolution? Sakharov conditions To generate baryon asymmetry, three necessary conditions should be met at the same cosmological epoch: B-violation C-andCP-violation Thermal inequilibrium NB. Reservation: L-violation with B-conservation at T 100 GeV would do as well = Leptogenesis. & ⇒ Can baryon asymmetry be due to electroweak physics? Baryon number is violated in electroweak interactions. Non-perturbative effect Hint: triangle anomaly in baryonic current Bµ : 2 µ 1 gW µνλρ a a ∂ B = 3colors 3generations ε F F µ 3 · · · 32π2 µν λρ ! "Bq a Fµν: SU(2)W field strength; gW : SU(2)W coupling Likewise, each leptonic current (n = e, µ,τ) g2 ∂ Lµ = W ε µνλρFa Fa µ n 32π2 · µν λρ a 1 Large field fluctuations, Fµν ∝ gW− may have g2 Q d3xdt W ε µνλρFa Fa = 0 ≡ 32 2 · µν λρ ' # π Then B B = d3xdt ∂ Bµ =3Q fin− in µ # Likewise L L =Q n, fin− n, in B is violated, B L is not.
    [Show full text]
  • What Did the Early Universe Look Like? Key Stage 5
    1 What did the early Universe look like? Key Stage 5 Topics covered: Cosmic Microwave Background Radiation, Wien’s displacement law, Doppler Effect Watch the video “What makes the Universe colourful?” https://vimeo.com/213990458 Scientists theorise that the Universe began with the Big Bang around 13.8 billion years ago. Space has been expanding ever since and the initial Big Bang energy has spread out. As a result the temperature of the Universe has fallen and the wavelength of light has stretched out. The history of the Universe can be split into different epochs – see the handout ‘TIMELINE OF THE UNIVERSE’. If we treat the Universe as a black body* then we can work out the peak wavelength of light travelling through the Universe at different epochs by using Wien’s law: 2.898 × 10−3 휆 = 푚푎푥 푇 휆푚푎푥 – peak wavelength emitted by the black body (m - metres) 푇 – temperature of the black body (K – Kelvin) * A black body is an ideal case of an object or system which perfectly absorbs and emits radiation and light and does not reflect any of it. 2 1. Use the ‘TIMELINE OF THE UNIVERSE’ handout to help. For each of the following epochs: 350,000 years (t1 - near the end of the photon epoch) 380,000 years (t2 - at recombination) 13.8 billion years (t3 - present day) a) Complete the table below to work out the peak wavelength (휆푚푎푥) of light that would be travelling through the Universe at that time. epoch Temperature Peak wavelength t1 350,000 years t2 380,000 years t3 13.8 billion years b) Mark these three wavelengths (as vertical lines / arrows) on the diagram below as t1, t2 and t3.
    [Show full text]
  • Cosmology and Dark Matter Lecture 3
    1 Cosmology and Dark Matter V.A. Rubakov Lecture 3 2 Outline of Lecture 3 Baryon asymmetry of the Universe Generalities. Electroweak baryon number non-conservation What can make electroweak mechanism work? Leptogenesis and neutrino masses Before the hot epoch 3 Baryon asymmetry of the Universe There is matter and no antimatter in the present Universe. Baryon-to-photon ratio, almost constant in time: nB 10 ηB = 6 10− ≡ nγ · 10 Baryon-to-entropy, constant in time: nB/s = 0.9 10 · − What’s the problem? Early Universe (T > 1012 K = 100 MeV): creation and annihilation of quark-antiquark pairs nq,nq¯ nγ Hence ⇒ ≈ nq nq¯ 9 − 10− nq + nq¯ ∼ Very unlikely that this excess is initial condition. Certainly not, if inflation. How was this excess generated in the course of the cosmological evolution? Sakharov’67, Kuzmin’70 4 Sakharov conditions To generate baryon asymmetry from symmetric initial state, three necessary conditions should be met at the same cosmological epoch: B-violation C- and CP-violation Thermal inequilibrium NB. Reservation: L-violation with B-conservation at T 100 GeV would do as well = Leptogenesis. ≫ ⇒ Can baryon asymmetry be due to 5 electroweak physics? Baryon number is violated in electroweak interactions. “Sphalerons”. Non-perturbative effect Hint: triangle anomaly in baryonic current Bµ : 2 µ 1 gW µνλρ a a ∂µ B = 3 3 ε Fµν F 3 colors generations 32π2 λρ Bq · · · a Fµν : SU(2)W field strength; gW : SU(2)W coupling Likewise, each leptonic current (n = e, µ,τ) 2 µ gW µνλρ a a ∂µ L = ε Fµν Fλρ n 32π2 · B is violated, B L B Le Lµ Lτ is not.
    [Show full text]
  • Hot Big Bang Model: Early Universe and History of Matter Initial „Soup“ with Elementary Particles and Radiation in Thermal Equilibrium
    Hot Big Bang model: early Universe and history of matter Initial „soup“ with elementary particles and radiation in thermal equilibrium. Radiation dominated era (recall energy density grows faster than matter density going back in time (~ a-4 rather than a-3). Thermal equilbrium maintained by electroweak interactions between individual particle species and between them and radiation field --- interaction rate G=n<vs>, where n is the number density of a type of particles, s the cross section and v the relative velocity (s depends on v in general). Key concepts: (1) At any given time particles can be created if their rest mass energy is such that kBT >> mc2, where T is the temperature of radiation. As the Universe expands T ~ a-1 (radiation dominated) so only increasingly lighter particles can be created. Important example: pair production from g + g < - -> e- + e+ (requires T > 5.8 x 109 K), which Immediately thermalize with electrons via Compton scattering and produce electronic - neutrinos via e- + e+ < --> ne + n e , also in thermal equilibrium with radiation. (2) As the Universe expands G decreases because n and v decrease -! when G < H(t) particle species decouples from photon fluid and n „freezes-out“ to the value at first decoupling(subsequently diluted only by expansion of Universe if particle stable). Present-day elementary particles are „thermal relics“ that have decoupled from photon 2 fluid at different times, some when they were still relativistic („hot relics“, kBT >> mc , T 2 is temperature of radiation field), some when they were non-relativistic (kBT <<mc ,“cold relics“) In the early Universe the very high temperatures (T ~ 1010 K a t ~ 1 s) guarantee that all elementary particles are relativistic and in thermal equilibrium with radiation.
    [Show full text]
  • Primordial Backgrounds of Relic Gravitons Arxiv:1912.07065V2 [Astro-Ph.CO] 19 Mar 2020
    Primordial backgrounds of relic gravitons Massimo Giovannini∗ Department of Physics, CERN, 1211 Geneva 23, Switzerland INFN, Section of Milan-Bicocca, 20126 Milan, Italy Abstract The diffuse backgrounds of relic gravitons with frequencies ranging between the aHz band and the GHz region encode the ultimate information on the primeval evolution of the plasma and on the underlying theory of gravity well before the electroweak epoch. While the temperature and polarization anisotropies of the microwave background radiation probe the low-frequency tail of the graviton spectra, during the next score year the pulsar timing arrays and the wide-band interferometers (both terrestrial and hopefully space-borne) will explore a much larger frequency window encompassing the nHz domain and the audio band. The salient theoretical aspects of the relic gravitons are reviewed in a cross-disciplinary perspective touching upon various unsettled questions of particle physics, cosmology and astrophysics. CERN-TH-2019-166 arXiv:1912.07065v2 [astro-ph.CO] 19 Mar 2020 ∗Electronic address: [email protected] 1 Contents 1 The cosmic spectrum of relic gravitons 4 1.1 Typical frequencies of the relic gravitons . 4 1.1.1 Low-frequencies . 5 1.1.2 Intermediate frequencies . 6 1.1.3 High-frequencies . 7 1.2 The concordance paradigm . 8 1.3 Cosmic photons versus cosmic gravitons . 9 1.4 Relic gravitons and large-scale inhomogeneities . 13 1.4.1 Quantum origin of cosmological inhomogeneities . 13 1.4.2 Weyl invariance and relic gravitons . 13 1.4.3 Inflation, concordance paradigm and beyond . 14 1.5 Notations, units and summary . 14 2 The tensor modes of the geometry 17 2.1 The tensor modes in flat space-time .
    [Show full text]
  • Quiz 4 Study Guide Astronomy 1143 – Spring 2014 (This Includes Many Concepts That Will Be on Quiz 4; No Guarantee That It Includes All of Them)
    Quiz 4 Study Guide Astronomy 1143 – Spring 2014 (This includes many concepts that will be on Quiz 4; no guarantee that it includes all of them) Forces Did the forces always have different strengths? Why does fusion require high speeds=high temperatures to happen? The Nature of Normal Matter, Dark Matter and Anti-matter What is the difference between hot and cold dark matter? What is an example of a hot dark matter candidate? What is an example of a cold dark matter candidate? How do we know that the Universe has cold dark matter and not hot dark matter? How do we know that the dark matter is not baryonic? What is the leading candidate for the dark matter particle? What observations are being made to try and detect the dark matter particle? Why are astronomers looking for the results of dark matter annihilation towards the centers of the Milky Way and nearby dwarf galaxies? Why does the probability of annihilation between two dark matter particles have to be small (R)? What is the difference between weak lensing and strong lensing (R)? How does weak lensing let us test dark matter models (R)? How do observations of the Bullet Cluster show that dark matter is a better explanation than Modified Gravity? Curvature of Space and Destiny of Universe What is the fate of our Universe? Can you have a flat Universe that is decelerating? Can you have a positively curved Universe that is accelerating? How can ΩM and ΩΛ tell you about the fate of a universe? What does our Universe look like (Flat? Negatively curved? Positively curved?) How can we calculate
    [Show full text]
  • Primordial Black Holes from the QCD Epoch: Linking Dark Matter
    Primordial black holes from the QCD epoch: Linking dark matter, baryogenesis and anthropic selection 0,1 2 3 Bernard Carr , Sebastien Clesse , Juan García-Bellido ∗ 0School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London E1 4NS, UK 1Research Center for the Early Universe, University of Tokyo, Tokyo 113-0033, Japan 2Service de Physique Théorique, Université Libre de Bruxelles (ULB), Boulevard du Triomphe, CP225, 1050 Brussels, Belgium and 3Instituto de Física Teórica UAM-CSIC, Universidad Autonóma de Madrid, Cantoblanco, 28049 Madrid, Spain (Dated: December 16, 2020) arXiv:1904.02129v2 [astro-ph.CO] 15 Dec 2020 1 Abstract If primordial black holes (PBHs) formed at the quark-hadron epoch, their mass must be close to the Chandrasekhar limit, this also being the characteristic mass of stars. If they provide the dark matter (DM), the collapse fraction must be of order the cosmological baryon-to-photon ratio 10 9, which suggests a ∼ − scenario in which a baryon asymmetry is produced efficiently in the outgoing shock around each PBH and then propagates to the rest of the Universe. We suggest that the temperature increase in the shock provides the ingredients for hot spot electroweak baryogenesis. This also explains why baryons and DM have comparable densities, the precise ratio depending on the size of the PBH relative to the cosmological horizon at formation. The observed value of the collapse fraction and baryon asymmetry depends on the amplitude of the curvature fluctuations which generate the PBHs and may be explained by an anthropic selection effect associated with the existence of galaxies.
    [Show full text]
  • Early Universe Thermodynamics and Evolution in Nonviscous and Viscous Strong and Electroweak Epochs: Possible Analytical Solutions
    entropy Article Early Universe Thermodynamics and Evolution in Nonviscous and Viscous Strong and Electroweak Epochs: Possible Analytical Solutions Abdel Nasser Tawfik 1,2,* and Carsten Greiner 2 1 Egyptian Center for Theoretical Physics, Juhayna Square off 26th-July-Corridor, Giza 12588, Egypt 2 Institute for Theoretical Physics (ITP), Goethe University Frankfurt, Max-von-Laue-Str. 1, D-60438 Frankfurt am Main, Germany; [email protected] * Correspondence: tawfi[email protected] Simple Summary: In the early Universe, both QCD and EW eras play an essential role in laying seeds for nucleosynthesis and even dictating the cosmological large-scale structure. Taking advantage of recent developments in ultrarelativistic nuclear experiments and nonperturbative and perturbative lattice simulations, various thermodynamic quantities including pressure, energy density, bulk viscosity, relaxation time, and temperature have been calculated up to the TeV-scale, in which the possible influence of finite bulk viscosity is characterized for the first time and the analytical dependence of Hubble parameter on the scale factor is also introduced. Abstract: Based on recent perturbative and non-perturbative lattice calculations with almost quark flavors and the thermal contributions from photons, neutrinos, leptons, electroweak particles, and scalar Higgs bosons, various thermodynamic quantities, at vanishing net-baryon densities, such as pressure, energy density, bulk viscosity, relaxation time, and temperature have been calculated Citation: Tawfik, A.N.; Greine, C. up to the TeV-scale, i.e., covering hadron, QGP, and electroweak (EW) phases in the early Universe. Early Universe Thermodynamics and This remarkable progress motivated the present study to determine the possible influence of the Evolution in Nonviscous and Viscous bulk viscosity in the early Universe and to understand how this would vary from epoch to epoch.
    [Show full text]
  • Lecture 17 : the Early Universe I
    Lecture 17 : The Early Universe I ªCosmic radiation and matter densities ªThe hot big bang ªFundamental particles and forces ªStages of evolution in the early Universe This week: read Chapter 12 in textbook 11/4/19 1 Cosmic evolution ª From Hubble’s observations, we know the Universe is expanding ª This can be understood theoretically in terms of solutions of GR equations ª Earlier in time, all the matter must have been squeezed more tightly together ª If crushed together at high enough density, the galaxies, stars, etc could not exist as we see them now -- everything must have been different! ª What was the Universe like long, long ago? ª What were the original contents? ª What were the early conditions like? ª What physical processes occurred under those conditions? ª How did changes over time result in the contents and structure we see today? 11/4/19 2 Quiz ªWhat is the modification in the modified Friedmann equation? A. Dividing by the critical density to get Ω B. Including the curvature k C. Adding the Cosmological Constant Λ D. Adding the Big Bang 11/4/19 3 Quiz ªWhat is the modification in the modified Friedmann equation? A. Dividing by the critical density to get Ω B. Including the curvature k C. Adding the Cosmological Constant Λ D. Adding the Big Bang 11/4/19 4 Quiz ªWhen is Dark Energy important? A. When the Universe is small B. When the Universe is big C. When the Universe is young D. When the Universe is old 11/4/19 5 Quiz ªWhen is Dark Energy important? A.
    [Show full text]
  • 16Th the Very Early Universe
    Re-cap from last lecture Discovery of the CMB- logic From Hubbles observations, we know the Universe is expanding This can be understood theoretically in terms of solutions of GR equations Earlier in time, all the matter must have been squeezed more tightly together and a lot hotter AT R=0 have the Big Bang the CMB is the 'relic' of the Big Bang Its extremely uniform and can be well fit by a black body spectrum of T=2.7k 4/9/15 34 Re-cap from last lecture The energy density of the universe in the form of radiation and matter density change differently with redshift 3 3 ρmatter∝(R0/R(t)) =(1+z) (R /R(t))4=(1+z)4 ρradiation∝ 0 Strong connection between temperature of the CMB and the scale factor of the universe T~1/R Energy density of background radiation increases as cosmic scale factor R(t) decreases at earlier time t: 4/9/15 35 How Does the Temperature Change with Redshift Remember from eq 10.10 in the book that Rnow/Rthen=1+z where z is the redshift of objects at observed when the universe had scale factor Rthen Putting this into eq 12.2 one gets T(z)=T0(1+z) where the book has conveniently relabeled variables R0=Rnow 4/9/15 36 ! At a given temperature, each particle or photon has the same average energy: 3 E = k T 2 B ! kB is called Boltzmanns constant (has the value of -23 kB=1.38×10 J/K) ------------------------------------------------------------------ ! In early Universe, the average energy per particle or photon increases enormously ! In early Universe, temperature was high enough that electrons had energies too high to remain bound in atoms ! In very early Universe, energies were too high for protons and neutrons to remain bound in nuclei ! In addition, photon energies were high enough that matter- anti matter particle pairs could be created 4/9/15 37 Particle production ! Suppose two very early Universe photons collide ! If they have sufficient combined energy, a particle/anti-particle pair can be formed.
    [Show full text]