CCOSMOLOGICAL MODELS ================= John Pazmino NYSkies Astronomu Inc nyskies@nyskies.org www.nyskies.org 1994 July 27 initial 2020 July 12 current Recent Astronomy Seminar ---------------------- The Recent Astronomy Seminar was a twice-monthly discussion group of astronomers in the New York area. It was conducted by the Amateur Astronomers Association in Yorkville, Manhattan, thruout the year, rain or shine. Topics were drawn from the current litterature and experiences of the members. Many sessions feature handouts, slides and videos, and computer demonstrations and simulations. In January 2005 the Seminar was converted to a 'members-only' function. These meetings were no longer announced thru NYC Events, NYSkies yahooogroup or other public medium. 1By summer 2005 the seminar skipped posting sessions for the coming fall season. and was terminated as an Association function. NYSkies Astronomy Seminar ---------------------- In March 2005 NYSkies began its own series of astronomy meetings for local astronomers. It is free and open to the public, the NYSkies Astronomy Seminar. The sessions convened in Chelsea, Manhattan, on the first and third Thursdays of each month. Topics are drawn from the current litterature and experiences of the members. Sessions may feature handouts, topical talks, slides and other visuals, and demonstrations and simulations. Notices of the meetings are in NYC Events, the NYSkies monthly roster of astronomy and related activities in New York, This was at first issued in the NYSkies yahoogroup and several astronomy Internet newsgroups. NYC Events, with the Seminar announcements, shifted to the NYSkies web on October 2007 but remained in the newsgroups until about 2010. With the global attraction of the web, the newsgroup posting of NYC Events was ended. The Seminar now meets, on first and third Fridays of every month, on 14th Street bordering Chelsea and Greenwich Village, Manhattan. Details about the NYSkies Astronomy Seminar are at www.nyskies.org/seminar.htm In addition to NYC Events, meeting notices are sent to astronomers thru a separate mailing list several days before each session. The notice describes the topics and sometimes offer late-breaking astronomy news. 'Cosmological Models' Paper ------------------------- This paper on cosmology is a living textbook based on the debates, comments, discussions, announcements at NYSkies Astronomy Seminar meetings, starting in March 2005. Prior to then, until the fall 2004 edition, it was released at the Recent Astronomy Seminar of Amateur Astronomers Association. Discs with files for the paper were distributed to the members only at the Seminar. Any astronomer may stop in at the next Seminar meeting and get the latest edition during the distribution season. Issuance by Internet email was limited due to the slow speed connections still in wide use then. Altho the paper is continuously revised, new discs were distributed only twice per year near the equinoctes. The first was handed out in September 1994 and continued until the treatise was uploaded into the new NYSkies yahoogroup in march 2001. 'Cosmological Models' Disc ------------------------ The computer disc for 'Cosmological Models' was a standard 90mm hi-density stiffy disc with 1.44 megabyte capacity for use in IBM operating systems. Some The fisc contents erre plain textfiles with no peculiar chars or sodes embedded in them. The files could be viewed and printed thru a word-processing software. The disc contained the complete paper with each chapter held in a separate textfile. The filenames were shown in the table of contents in the file '00100.txt'. You replaced just the revised files, as indicated by the filedates in the directory listing. New files whose dates match or precede those on your old disc can be disregarded. ' Cosmological Models' in NYSkies ------------------------------ The NYSkies yahoogroup opened in January 2001 for a rapid announcment service and discussion forum among New York astronomers. One of the earlier features of the NYSkies uahoogroup was the uploading in March 2001 of the 'Cosmological Models' disc into its article section. Then after the disc itself was no longer handed out. The yahoogroup collapsed in Septembr 2001, a colllateral vicitim of the World Trade Center attacks. It was revived later in September 2001 with most of its contents restored, including the 'Csomological Models' disc. A notice in the yahoogroup called attention to new or revised files. Over the years the 'Cosmological Models' paper expanded to cover important, but poorly treated, subjects relating to cosmology. Along the way the files were increasingly disorganized and fell into severe need of massive reworking. In fall of 2017 this work began by first combining associated short files into a single larger one and clarifying the notation in maths. The first new portions, now loaded into the NYSkies web, cover special relativity, general relativity, gravity, and blackholes. The progress is slow but steady. Announcements of new material are posted in the NYSkies yahoogroup. The files were revised or added irregularly since 2001. The initial date, posted above, of 1994 July 27 is that of the earliest surviving set of textfiles. When any one of the newly revamped files is modified, its modification date becomes the current date, entered above, for the entire treatise. The original collection of 'Cosmological Models' files is no longer updated. As they are gathered into the new chapters they are archived in their final state. Introduction ---------- This treatise on cosmological models does contain dense letterpress and maths. The paper aims to give the home astronomer a sound and proper tuition in cosmology, beyond the mish-mash of facts and stories so commonly offered to them. Cosmology, while attractive to home astronomers, is not a simple or easy subject to understand. The text and equations are an integral feature of learning cosmology. They do call for close attention. Conversance in first-year college maths and astronomy is presumed in order to follow this treatise of the cosmological models. The maths freely use algebra. calculus, geometry, and trginometry. Due to typographic constraints, all maths are written in a BASIC or FORTRAN style without the fancy symbols of typeset works. .Formulae and equations are written as one line, sometimes with wrap to a second line, like extra-long web addresses. You may have to knit the lines together. Certain operations are treated like functions. For example '1der(x,y)' means 'first derivative of x relative to y'. Symbols are written out. 'SIGMA' means 'large-sigma' and 'sigma' means 'small- sigma'. When a derivation or conversion is discussed, each step is set out, not just the end result. Table of Contents -------------- This treatise consists of separate chapters, each a separate file. Because chapters may avail of mateial in previous chapters, the files should be studied in sequence within each series, between the '- - - ' separators. - - - - - - - - - -NEWTON'S UNIVERSE-- Newton's Universe - Early Problems - Impossible World - Gravitation under Newton - Definition of Force - Two Interpretations of Field StrengthEINSTEIN'S UNIVERSE-- Cosmological Principle - Newton versus Einstein Physics - The Lambda Force - The Acceleration of the Universe - Energy of the Universe - Friedmann Model - The Standard or Classical Model - Hubble Parameter - Hubble Time - The Redshift in Galactic Spectra - Expansion or Hubble Redshift - Time Dilation - Hubble Expansion vs Recession Velocity - What's Going On Here? - Milne & McCrea's Trick - 17th Century Cosmology? - MisinterpretationsCOSMOLOGY APPLICATIONS-- Scalefactor Function of Time - True Age of the Universe - Deceleration Parameter - Density Parameter - Radius of the Universe - Mass of the Universe - Is the Universe a Blackhole? - Proper or Einstein Distance - Hubble Horizon -- Enclosed Volume - Light Travel or Lookback Time -Inverse-Square Law - Spectroillumination - Hubble Expansion of lambda - Magnitude-Distance Relation - Angular Diameter - Angular Spectroillumination

GEOMETRY OF TH UNIVERSE-- NonEuclides Geometry - Geometric curvature - Anngles of a Triangles - Curvature of the Universe - Nonzero k - Gravitational Curvature - Bending of Starlight - Curvature in Strong Graviry - The R,t Graph - Preparing the Scenarios - k = 0, q = 1/2, rho0 = rho@ - k = -1, q < 1/2, rho0 < rho@ - k = +1, q > 1/2, rho0 > rho@ - Capitulation

THE EARLY UNIVERSE- - The Early Universe - The Singularity of the Bigbang - Geometrical and Physical Cosmology - No Antimatter? - Matter -Antimatter Ratio - Abundance of the Elements - Helium in the Universe - Origin of the Helium - Nucleogenesis - Table of Particles -Table of Interactions - Initial Conditions - Conservation Rules - Interaction Flowchart - Other Reaction Chains - WWhy Stop at Helium? - The Neutron Decay - The Relics of the Bigbang

STEADY STATE UNIVERSE-- Steady State Universe - Furtherance of the Bigbang Theory - Age Problem with the Bigbang - Singularity Problem with the Bigbang - Perfect Cosmological Principle - Hubble Parameter - Redshift - Density of the Universe - Proper or Einstein Distance - Luminosity Distance - Angular Diameter - Curvature of Space - Deceleration Parameter - Comparison with Acceleration/Energy - Continuous Creation - Nature of New Matter - Formation of Galaxies - Minibangs - Cosmic Microwave Radiation - Helium Abundance -- No Cosmology? - Closing RemarksHISTORICAL COSMOLOGIES-- Historical Models of the Universe - Diversity of Cosmological Models - Einstein (Original) Universe - deSitter Universe - Einstein-deSitter Universe - Eddington Universe - leMaitre Universe - Tolman (Oscillating) Universe - leMaitre-Tolman Universe - Milne Universe - Dirac Universe - Alpher-Bethe-Gamow Universe - 'Bigbang' - Bondi-Gold (Steady State) Universe - Godel Universe - Alfven-Klein Universe - Arp Universe - Hoyle-Narlikar Universe - Brans-Dicke Universe - deWitt (Many-Worlds) Universe - Guth (Inflationary) Universe - - - - - - - - - -SPECIAL RELATIVITY-- Einstein's Physics of Relativity - Time and Space-- Spacetime -Natural Gravity - Inertial Platform or Frame - Impossibilty of Absolute Rest - The Speed of Light - Maxwell's Laws-- Michelson-Morley Experiment - Laws of Physics - The Term 'Speed of Light' -Comparing Clocks-- The Scenario - Equation of Motion - Home and Target Frame - Spacetime Interval - Four Roads to Follow -The Newton Road - Einstein's Mistake? - Behavior of Time - Why Is this Case Wrong? - Einstein's Solution - Time Dilation - The Barrier of c - The Fourth CaseRELATIVITY APPLICATIONS-- Doppler's Debacle - Absurd Doppler Speeds - Fizeau's Fixup -Frequency and Wavelength - The Historical Blunder - Reality versus Perception -Observed Time DIlation - Einstein and Doppler-Fizeau - The Low-Velocity Approximation - The Missing Step - Space Travel Near c - Twin Paradox - Simultaneous Events - Spacetime Interval for Simultaneous Events - Platforms Can Not Agree - Simultaneous in Space and Time - Lorentz Transformation - Addition of Velocities -Comparison with Newton - Fizeau's Experiments --Shift of PlatformsGENERAL RELATIVITY-- Energy and Mass - dePretto's Ideas - Rest Mass-- Conservation Law - Mass into Energy - Energy into Mass-- Electron-volt -Critiques - Atomic Bombs - Atomic Power - Recycling of Fuel - New York Els -Mass Increase - Early ideas - Relativistic Mass - Mass- Energy Equation --- No Real Increase of Mass - Invariant MassGRAVITY-- A Bit of Newton Physics - Ideal Spherical Body - Gravity Outside a Spherical Shell - Gravity Inside a Spherical Shell -Gravity Field within a Solid Globe - Range of Applicability - Nonspherical Bodies - No Defense Against Gravity -Gravity is Cumulative - Gravity Field Strength - A Useful Equivalence - Gravity Work and Energy - Gravitational Potential Energy - Gravity Well - Escape Velocity

BLACKHOLES-- Schwarzschild Blackhole - Idealized Blackhole - Spacetime with Mass - Schwarzschild Surface or Radius - Schwarzschild Spacetime Schwarzschild Blackhole - Idealized Blackhole - Space tEquation - The Safe Frame - No Change of Gravity Regime - Time Dilation versus Distance - Nonsymmetrical Nonreciprocal Relation - Tests of Schwarzschild Spacetime - Redshift of Spectral Lines - ercury's Orbit Precession - Bending of Starlight - Astronomers Neglect Relativity - Features of Schwarzschild Spacetime - Near the Schwarzschild Surface - Length and Mass near a Blackhole - Geometry near the Schwarzschild Surface - Thermodynamics and Blackholes - The Singularity - Newton Escapes the Singularity - Einstein Mandates the Singularity - - - - - - - - - -LECTROMAGNETIC RRADIATION--Electromagnetic Radiation - Frequency versus Wwavelength - Irregular Jargon - Electric Charge - Electric Field - Magnetic Poles and fields - Ampere and Faraday - Lenz Effect - Lines of Force - Lines of Force -Gauss's Law for Charge - Gauss's Law for Poles - Maxell's Equations - Gauss's Law for Mass - Maxwell's Waves - mu0 and epsilon0 - Where's the Medium? - Refraction of Light - Cherenkov Effect - Propogation of EMW - Energy of a Field - Energy in EMW - Root Mean Square - Electric Field Overwhelms - Irradiation - Sun's Irradiation

THERMODYNAMICS-- Human Use of Heart - Temperature - Nature of Heat- Laws of Thermodynamics - Second Law of Thermodynamics - Carnot Limit for Work - No Work from a Single Temperature - Clausius Entropy - Actual heat Engines - Boltzmann Entropy - ArroW of Time - Sun as a Heat Engine - Entropy from Starlight - Entropy and Energy in CMB -CMB versus Starlight - Number Density as Entropy - Blackholes

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