Big Bang Nucleosynthesis Finally, Relative Abundances Are Sensitive to Density of Normal (Baryonic Matter)
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Inflation and the Theory of Cosmological Perturbations
Inflation and the Theory of Cosmological Perturbations A. Riotto INFN, Sezione di Padova, via Marzolo 8, I-35131, Padova, Italy. Abstract These lectures provide a pedagogical introduction to inflation and the theory of cosmological per- turbations generated during inflation which are thought to be the origin of structure in the universe. Lectures given at the: Summer School on arXiv:hep-ph/0210162v2 30 Jan 2017 Astroparticle Physics and Cosmology Trieste, 17 June - 5 July 2002 1 Notation A few words on the metric notation. We will be using the convention (−; +; +; +), even though we might switch time to time to the other option (+; −; −; −). This might happen for our convenience, but also for pedagogical reasons. Students should not be shielded too much against the phenomenon of changes of convention and notation in books and articles. Units We will adopt natural, or high energy physics, units. There is only one fundamental dimension, energy, after setting ~ = c = kb = 1, [Energy] = [Mass] = [Temperature] = [Length]−1 = [Time]−1 : The most common conversion factors and quantities we will make use of are 1 GeV−1 = 1:97 × 10−14 cm=6:59 × 10−25 sec, 1 Mpc= 3.08×1024 cm=1.56×1038 GeV−1, 19 MPl = 1:22 × 10 GeV, −1 −1 −42 H0= 100 h Km sec Mpc =2.1 h × 10 GeV, 2 −29 −3 2 4 −3 2 −47 4 ρc = 1:87h · 10 g cm = 1:05h · 10 eV cm = 8:1h × 10 GeV , −13 T0 = 2:75 K=2.3×10 GeV, 2 Teq = 5:5(Ω0h ) eV, Tls = 0:26 (T0=2:75 K) eV. -
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. -
Inflationary Cosmology: from Theory to Observations
Inflationary Cosmology: From Theory to Observations J. Alberto V´azquez1, 2, Luis, E. Padilla2, and Tonatiuh Matos2 1Instituto de Ciencias F´ısicas,Universidad Nacional Aut´onomade Mexico, Apdo. Postal 48-3, 62251 Cuernavaca, Morelos, M´exico. 2Departamento de F´ısica,Centro de Investigaci´ony de Estudios Avanzados del IPN, M´exico. February 10, 2020 Abstract The main aim of this paper is to provide a qualitative introduction to the cosmological inflation theory and its relationship with current cosmological observations. The inflationary model solves many of the fundamental problems that challenge the Standard Big Bang cosmology, such as the Flatness, Horizon, and the magnetic Monopole problems. Additionally, it provides an explanation for the initial conditions observed throughout the Large-Scale Structure of the Universe, such as galaxies. In this review, we describe general solutions to the problems in the Big Bang cosmology carry out by a single scalar field. Then, with the use of current surveys, we show the constraints imposed on the inflationary parameters (ns; r), which allow us to make the connection between theoretical and observational cosmology. In this way, with the latest results, it is possible to select, or at least to constrain, the right inflationary model, parameterized by a single scalar field potential V (φ). Abstract El objetivo principal de este art´ıculoes ofrecer una introducci´oncualitativa a la teor´ıade la inflaci´onc´osmica y su relaci´oncon observaciones actuales. El modelo inflacionario resuelve algunos problemas fundamentales que desaf´ıanal modelo est´andarcosmol´ogico,denominado modelo del Big Bang caliente, como el problema de la Planicidad, el Horizonte y la inexistencia de Monopolos magn´eticos.Adicionalmente, provee una explicaci´onal origen de la estructura a gran escala del Universo, como son las galaxias. -
Evolution of the Cosmological Horizons in a Concordance Universe
Evolution of the Cosmological Horizons in a Concordance Universe Berta Margalef–Bentabol 1 Juan Margalef–Bentabol 2;3 Jordi Cepa 1;4 [email protected] [email protected] [email protected] 1Departamento de Astrofísica, Universidad de la Laguna, E-38205 La Laguna, Tenerife, Spain: 2Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, E-28040 Madrid, Spain. 3Facultad de Ciencias Físicas, Universidad Complutense de Madrid, E-28040 Madrid, Spain. 4Instituto de Astrofísica de Canarias, E-38205 La Laguna, Tenerife, Spain. Abstract The particle and event horizons are widely known and studied concepts, but the study of their properties, in particular their evolution, have only been done so far considering a single state equation in a deceler- ating universe. This paper is the first of two where we study this problem from a general point of view. Specifically, this paper is devoted to the study of the evolution of these cosmological horizons in an accel- erated universe with two state equations, cosmological constant and dust. We have obtained closed-form expressions for the horizons, which have allowed us to compute their velocities in terms of their respective recession velocities that generalize the previous results for one state equation only. With the equations of state considered, it is proved that both velocities remain always positive. Keywords: Physics of the early universe – Dark energy theory – Cosmological simulations This is an author-created, un-copyedited version of an article accepted for publication in Journal of Cosmology and Astroparticle Physics. IOP Publishing Ltd/SISSA Medialab srl is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. -
Or Causality Problem) the Flatness Problem (Or Fine Tuning Problem
4/28/19 The Horizon Problem (or causality problem) Antipodal points in the CMB are separated by ~ 1.96 rhorizon. Why then is the temperature of the CMB constant to ~ 10-5 K? The Flatness Problem (or fine tuning problem) W0 ~ 1 today coupled with expansion of the Universe implies that |1 – W| < 10-14 when BB nucleosynthesis occurred. Our existence depends on a very close match to the critical density in the early Universe 1 4/28/19 Theory of Cosmic Inflation Universe undergoes brief period of exponential expansion How Inflation Solves the Flatness Problem 2 4/28/19 Cosmic Inflation Summary Standard Big Bang theory has problems with tuning and causality Inflation (exponential expansion) solves these problems: - Causality solved by observable Universe having grown rapidly from a small region that was in causal contact before inflation - Fine tuning problems solved by the diluting effect of inflation Inflation naturally explains origin of large scale structure: - Early Universe has quantum fluctuations both in space-time itself and in the density of fields in space. Inflation expands these fluctuation in size, moving them out of causal contact with each other. Thus, large scale anisotropies are “frozen in” from which structure can form. Some kind of inflation appears to be required but the exact inflationary model not decided yet… 3 4/28/19 BAO: Baryonic Acoustic Oscillations Predict an overdensity in baryons (traced by galaxies) ~ 150 Mpc at the scale set by the distance that the baryon-photon acoustic wave could have traveled before CMB recombination 4 4/28/19 Curves are different models of Wm A measure of clustering of SDSS Galaxies of clustering A measure Eisenstein et al. -
Phy306 Introduction to Cosmology Homework 3 Notes
PHY306 INTRODUCTION TO COSMOLOGY HOMEWORK 3 NOTES 1. Show that, for a universe which is not flat, 1 − Ω 1 − Ω = , where Ω = Ω r + Ω m + Ω Λ and the subscript 0 refers to the present time. [2] This was generally quite well done, although rather lacking in explanation. You should really define the Ωs, and you need to explain that you divide the expression for t by that for t0. 2. Suppose that inflation takes place around 10 −35 s after the Big Bang. Assume the following simplified properties of the universe: ● it is matter dominated from the end of inflation to the present day; ● at the present day 0.9 ≤ Ω ≤ 1.1; ● the universe is currently 10 10 years old; ● inflation is driven by a cosmological constant. Using these assumptions, calculate the minimum amount of inflation needed to resolve the flatness problem, and hence determine the value of the cosmological constant required if the inflation period ends at t = 10 −34 s. [4] This was not well done at all, although it is not really a complicated calculation. I think the principal problem was that people simply did not think it through—not only do you not explain what you’re doing to the marker, you frequently don’t explain it to yourself! Some people therefore got hopelessly confused between the two time periods involved—the matter-dominated epoch from 10 −34 s to 10 10 years, and the inflationary period from 10 −35 to 10 −34 s. The most common error—in fact, considerably more common than the right answer—was simply assuming that during the post-inflationary epoch 1 − . -
The High Redshift Universe: Galaxies and the Intergalactic Medium
The High Redshift Universe: Galaxies and the Intergalactic Medium Koki Kakiichi M¨unchen2016 The High Redshift Universe: Galaxies and the Intergalactic Medium Koki Kakiichi Dissertation an der Fakult¨atf¨urPhysik der Ludwig{Maximilians{Universit¨at M¨unchen vorgelegt von Koki Kakiichi aus Komono, Mie, Japan M¨unchen, den 15 Juni 2016 Erstgutachter: Prof. Dr. Simon White Zweitgutachter: Prof. Dr. Jochen Weller Tag der m¨undlichen Pr¨ufung:Juli 2016 Contents Summary xiii 1 Extragalactic Astrophysics and Cosmology 1 1.1 Prologue . 1 1.2 Briefly Story about Reionization . 3 1.3 Foundation of Observational Cosmology . 3 1.4 Hierarchical Structure Formation . 5 1.5 Cosmological probes . 8 1.5.1 H0 measurement and the extragalactic distance scale . 8 1.5.2 Cosmic Microwave Background (CMB) . 10 1.5.3 Large-Scale Structure: galaxy surveys and Lyα forests . 11 1.6 Astrophysics of Galaxies and the IGM . 13 1.6.1 Physical processes in galaxies . 14 1.6.2 Physical processes in the IGM . 17 1.6.3 Radiation Hydrodynamics of Galaxies and the IGM . 20 1.7 Bridging theory and observations . 23 1.8 Observations of the High-Redshift Universe . 23 1.8.1 General demographics of galaxies . 23 1.8.2 Lyman-break galaxies, Lyα emitters, Lyα emitting galaxies . 26 1.8.3 Luminosity functions of LBGs and LAEs . 26 1.8.4 Lyα emission and absorption in LBGs: the physical state of high-z star forming galaxies . 27 1.8.5 Clustering properties of LBGs and LAEs: host dark matter haloes and galaxy environment . 30 1.8.6 Circum-/intergalactic gas environment of LBGs and LAEs . -
Anisotropy of the Cosmic Background Radiation Implies the Violation Of
YITP-97-3, gr-qc/9707043 Anisotropy of the Cosmic Background Radiation implies the Violation of the Strong Energy Condition in Bianchi type I Universe Takeshi Chiba, Shinji Mukohyama, and Takashi Nakamura Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-01, Japan (January 1, 2018) Abstract We consider the horizon problem in a homogeneous but anisotropic universe (Bianchi type I). We show that the problem cannot be solved if (1) the matter obeys the strong energy condition with the positive energy density and (2) the Einstein equations hold. The strong energy condition is violated during cosmological inflation. PACS numbers: 98.80.Hw arXiv:gr-qc/9707043v1 18 Jul 1997 Typeset using REVTEX 1 I. INTRODUCTION The discovery of the cosmic microwave background (CMB) [1] verified the hot big bang cosmology. The high degree of its isotropy [2], however, gave rise to the horizon problem: Why could causally disconnected regions be isotropized? The inflationary universe scenario [3] may solve the problem because inflation made it possible for the universe to expand enormously up to the presently observable scale in a very short time. However inflation is the sufficient condition even if the cosmic no hair conjecture [4] is proved. Here, a problem again arises: Is inflation the unique solution to the horizon problem? What is the general requirement for the solution of the horizon problem? Recently, Liddle showed that in FRW universe the horizon problem cannot be solved without violating the strong energy condition if gravity can be treated classically [5]. Actu- ally the strong energy condition is violated during inflation. -
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 . -
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. -
The Rh = Ct Universe Without Inflation
A&A 553, A76 (2013) Astronomy DOI: 10.1051/0004-6361/201220447 & c ESO 2013 Astrophysics The Rh = ct universe without inflation F. Melia Department of Physics, The Applied Math Program, and Department of Astronomy, The University of Arizona, Tucson, AZ 85721, USA e-mail: [email protected] Received 26 September 2012 / Accepted 3 April 2013 ABSTRACT Context. The horizon problem in the standard model of cosmology (ΛDCM) arises from the observed uniformity of the cosmic microwave background radiation, which has the same temperature everywhere (except for tiny, stochastic fluctuations), even in regions on opposite sides of the sky, which appear to lie outside of each other’s causal horizon. Since no physical process propagating at or below lightspeed could have brought them into thermal equilibrium, it appears that the universe in its infancy required highly improbable initial conditions. Aims. In this paper, we demonstrate that the horizon problem only emerges for a subset of Friedmann-Robertson-Walker (FRW) cosmologies, such as ΛCDM, that include an early phase of rapid deceleration. Methods. The origin of the problem is examined by considering photon propagation through a FRW spacetime at a more fundamental level than has been attempted before. Results. We show that the horizon problem is nonexistent for the recently introduced Rh = ct universe, obviating the principal motivation for the inclusion of inflation. We demonstrate through direct calculation that, in this cosmology, even opposite sides of the cosmos have remained causally connected to us – and to each other – from the very first moments in the universe’s expansion. −35 −32 Therefore, within the context of the Rh = ct universe, the hypothesized inflationary epoch from t = 10 sto10 s was not needed to fix this particular “problem”, though it may still provide benefits to cosmology for other reasons. -
A New Scale of Particle Mass in a Fractal Universe with A
A new scale of particle mass in a fractal universe with a cosmological constant Scott Funkhouser(1) and Nicola Pugno(2) (1)Dept of Physics, the Citadel, 171 Moultrie St. Charleston, SC, 29409 (2)Department of Structural Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy ABSTRACT Considerations of the total action of a fractal universe with a cosmological constant lead to a new microscopic mass scale that is a function of the fractal dimension and fundamental parameters. For a universe with a fractal dimension D=2 the model predicts a mass that is of order near the nucleon mass. A scaling law between the cosmological constant and the mass of the nucleon follows that is identical to a known scaling law originating with Zel’dovich. This analysis also provides new limitations on the possible nature of dark matter in a fractal universe with a cosmological constant. 1. A new scale of mass Consider a system that is well represented by a fractal structure with dimension D. Let the total mass M of the system be dominated by some number N of a certain species of particle whose mass is m, so that N≈M/m. The total action A of the fractal system must be related to the Planck quantum of action h by [1,2] M ( D +1)/ D A ≈ hN (D +1)/ D ≈ h . (1) m Certain prominent features of the universe exhibit strong signatures of a fractal structure. Insomuch as the universe may be represented by a fractal, (1) should relate the total cosmic action to the parameters of the dominant species of massive particles in the universe [2].