CCOSMOLOGICAL MODELS 
 ================= 
 John Pazmino 
 NYSkies Astronomu Inc 
 nyskies@nyskies.org
 www.nyskies.org 
 1994 July 27 initial 
 2017 October 9 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.org

In addition to NYC Events, meeting notices ar 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 follateeral vicitim 
of the World Trade Center attavcks. 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 ell into severe 
need of massive reworking. In fall of 2017 this work bean 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 and some simple calculus, but very little 
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. 
    In the entries here only those with proper names, like 
'Newotn's universe', are linked to actual files in the NYSkies web.  
Those with a numbered name, like '004000', are old files not in this 
web.
    Over time tte old filesy will be gathered into new files under 
proper names, updated, and cleaned. Eventually all files, minus those 
no longer useful, will be collected into the "Cosmological Models' 
book here. 
    Please check back here from time to time for the new files. 
 - - - - - - - - - -

NEWTON'S UNIVERSE -- Newton's Universe - Early Problems - Impossible 
World -  Gravitation under Newton - Definition of Force - Two 
 Interpretations of Field Strength

EINSTEIN'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? - Misinterpretations 

COSMOLOGY 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 

 - - - - - - - - - -





06100
 Electromagnetic Radiation -- Frequency versus Wavelength --
 Haphazard Nomenclature -- Disparate Units of Measure --
 Detection of EMR -- Miracle of Electromagnetic Radiation

06120
 Ampere's Law -- Faraday's Law -- Lenz's Law -- Orthogonal Fields --
 Lines of Force -- Potential Surface -- Inverse Square Law

06140
 Gauss's Law for Charge -- Gauss's Law for Poles -- Gauss's Law for
 Mass -- Cosmic Implications -- Maxwell's Equations -- Waves --
 Maxwell's Waves

06160
 mu0 and epsilon0 -- mu0 -- epsilon0 -- Magnetic Field Strength --
 Magnetic Pole Strength -- Refraction of Light -- Cherenkov Effect

06180
 Interacting Fields -- Electromagnetic Wave -- Creation of EMW --
 Speed of EMW

06190
 Energy of a Field -- Energy in EMW -- Root Mean Square -- Electric
 Field Overwhelms -- Irradiation -- Sun's Irradiation -- Sun's EMR
 Disturbance -- Electric Power Damage -- Radiation Pressure --
 Radiation Momentum

06200
 Spectroirradiation -- Irradiation -- Inverse-Square Law --
 Arcspectroirradiation -- [Spectro]irradiosity -- Radiation-Area Law

06300
 Light Is Nothing But EMR -- The Grand Delusion of Light --
 Spectrosensitivity -- Photometric Units -- Spectroillumination --
 Color Temperature -- Irradiation versus Illumination

06400
 Mechanism of EMR -- Blackbody Spectroirradiosity -- Two Planck
 Constants -- Stefan-Boltzmann Law -- Wien Law -- Photon-Temperature
 Law -- Density-Temperature Law -- Blackbodies in Nature -- Lowest
 Temperature in Nature

06500
 Mass/Energy Ratio -- The Bigbang Photosphere -- Cosmic
 Background Radiation -- Time and Place of the Photosphere -- The
 Bigbang

06600
 Behavior of Heat -- Second Law of Thermodynamics --  Limit on Energy
 Conversion -- No Work from Single Reservoir -- Potential Work

06610
 Entropy -- Irreversibility of Heat Engines -- Sun as a Heat Engine --
 Waste Energy in the Universe -- Total Accumulated Entropy

06700
 Randomness -- Boltzmann's Entropy -- Clausius's Method -- Boltzmann's
 Method -- Equivalence of Clausius and Boltzmann --
 Number Density as Entropy

06800
 Bigbang versus Starlight Radiation -- Conservation of Mass --
 Entropy from Starlight -- Thermal History

07000
 Nucleus -- Isotopes -- Internal Structure -- Units of Measure
 -- Symbols -- Pseudoelements -- Avogadro Number -- Mass
 Defect -- Nuclear Size -- Compared to Solar System

07020
 Radiosiotopes -- Decay Rate -- Halflife -- Alpha Decay -- Beta
 Decay -- Gamma Decay -- Electron Capture -- Other Decays --
 Summary of Decays

07040
 Ionizing Radiation -- Ionization Detectors -- Scintillation
 Detectors -- Track Detectors

07060
 Radiodating -- Suitable Materials -- Suitable Decays -- Ratio of
 Isotopes -- Major Flaw

07080
 The Melt -- The Stable isotope -- Formation of Minerals --
 Crystallization -- As the Rock Ages -- Calculation of the Age

07100
 The Early Universe -- The Singularity of the Bigbang -- Geometrical
 and Physical Cosmology -- Antimatter --  No Antimatter --
 Grandfathered Matter --  Matter-Antimatter Ratio

07150
 Abundance of the Elements -- Helium in the Universe -- Origin of the
 Helium -- Nucleogenesis -- Regimes of Element Creation

07200
 Introduction to Atomics -- Table of Particles -- Table of
 Interactions -- Reaction Kinetics

07300
 Initial Conditions -- Conservation Rules -- Melding the Reactions --
 Interaction Flowchart -- Other Reaction -- Chains -- Limits of the
 Simulation

07400
 Why Stop at Helium? -- The Mass 5 and 8 Gap -- The Relics of the
 Bigbang

08000
 Observational Difficulties -- Distance versus Redshift -- Hubble
 Parameter -- Deceleration Parameter

08100
 Difficulties with the Standard Model --  Age Problem -- History of
 Ages

08110
 Flatness Problem -- delOMEGA vs Time

08120
 Smoothness or Horizon Problem -- Horizons

08130
 Missing or Dark Matter Problem -- Dark Matter --
 Candidates for Dark Matter

09000
 NonEuclid Geometries -- Geometric Curvature -- Angles of a Triangle
 -- Curvature of the Universe -- Nonzero k

09010
 Gravitational Curvature -- Bending of Starlight -- Visualizing 4-
 Dimensional Space -- Curvature in Strong Gravity Fields -- Inside the
 Blackhole

09100
 Preparing the Scenarios -- k = 0, q = 1/2, rho0 = rho@ -- k = -1, q <
    1/2, rho0 < rho@ -- k = +1, q > 1/2, rho0 > rho@ -- Recapitulation

09200
 Neutrinos -- Neutrinos from the Bigbang -- Neutrinos as Dark Matter
 -- Neutrinos Not the Final Answer

09300
 Orbits in 3D Space -- Other Dimensions -- Anthropical Cosmology --
 Life in the Universe

09400
 Physical Constants -- Mass of the Electron -- Doubleheavy Electron --
 Halfheavy Electron -- Is All This an Accident? -- Maybe this is
 Uniquely Our Universe?

09800
 Fastest Communication by Light -- Four Dimensional World -- What Can
 We See? -- Who Can See Us? -- The Observability Zones

10000
 Historical Models of the Universe -- Diversity of Cosmological Models

11000
 Alfven-Klein Universe -- Alpher-Bethe-Gamow Universe -- Arp Universe
 -- Bondi-Gold (Steady State) Universe

11100
 Brans-Dicke Universe -- deSitter Universe -- deWitt (Many-Worlds)
 Universe -- Dirac Universe -- Eddington Universe

11200
 Einstein (Original) Universe -- Einstein-deSitter Universe -- Godel
 Universe

11300
 Guth (Inflationary) Universe -- Hoyle-Narlikar Universe -- leMaitre
 Universe -- leMaitre-Tolman Universe -- Milne Universe -- Tolman
 (Oscillating) Universe

12000
 Recent Observations -- Texture and Clumpiness -- Primordial Galaxies
 -- Keck Deuterium -- Tidal Movements -- Nearby Supernovae

12100
 Quasars -- Microwave Relic Radiation -- Tully-Fisher Distances -- M87
 Blackhole -- Cepheid Variables -- Dark Galaxies

 - - - - - - - - - -

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 Remarks 

 - - - - - - - - - -

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 Case 

RELATIVITY 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 
Platforms 

GENERAL 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 Mass 

GRAVITY -- 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 

 - - - - - - - - - -

15000 
 Introduction to Quantum Physics -- The Hydrogen Atom --  Quantized
 Orbital Motion -- Energy Levels of Hydrogen -- Spectrum Lines

15100
 Waves and Particles -- The Uncertainty Principle -- Role of Humans --
 Quantum Reality

80000
 Angle Measure -- Degrees of Angle -- Radians of Angle --Triangles --
 Ratios of Sides -- Trigonometric Functions -- Special Angles --
 Alternate Functions

80010
 Some Relations -- Sine/cosine -- sin^2 + cos^2 -- Law of Sines -- Law
 of Cosines -- Summary of Relations -- Trig Operations -- Small Angles
 -- Arclength -- How Small is Small?

80020
 Angles in Other Quadrants -- The Quadrants -- Limits of Functions --
 Inverse Function -- Arcfunction

80100
 Vectors -- Specifying Vectors -- Adding Vectors -- Subtracting
 Vectors -- Multiplying Vectors -- Dot Multiplication -- Angle between
 Vectors Cross Multiplication -- Special Cases

80200
 Logarithms -- Logs as Powers -- Exponential Notation -- Symbolism --
 Finding a Logarithm -- Uses of Logarithms -- Inverse Logarithm --
 Changing Bases -- Logarithmic Progression -- Log of Trig Functions

80300
 Units of Measure -- The Meter -- Meter as Derived Unit -- Meter,
 Metre  - The Stadion -- Columbus's Earth -- The Kilogram

80310
 The Second -- Secular Acceleration -- Ephemeris Second --
 Atomic Second -- Leapsecond -- The Offset -- Coordinated
 Universal Time -- GPS Time

80320
 Systems of Units -- Gauss Units --  Electrostatics -- CGS System --
 Heavyside-Lorentz System -- Special Names

80330
 MKS System -- Systeme Internationale -- 4*pi -- Special names --
 Prefixes -- Binary Prefixes

80340
 Europe Slowly Adapts -- America Stands Down -- Oldstyle Measures --
 Metrics Percolate In -- Home Astronomy Metrics -- Vernacular
 Metrics -- The New Millennium -- The Future

80400
 Standard Time - US Standard Time -- Greenwich Mean Time --
 Universal Time -- Timezones -- Zulu -- Specifying Local
 Time -- International Dateline

80404
 Daylight Savings -- US Daylight Savings -- Arizona
 and Hawaii

80410
 Hours of the Day -- Minutes and Seconds -- 12x12 and 24 -- 12
 AM, 12 PM -- Planetarium Clocks -- 12-Hour Dial -- Time
 Notation

80420
 The Week -- Days of the Week -- Order of the Days -- Sequence
 of Weeks

80430
 Year Numbering -- Julian Calendar --  Leapyear -- Proleptic
 Julian Calendar -- Gregorian Calendar -- Acceptance of
 Gregorian Calendar -- Date Notation -- Dates on Other Worlds
 -- Day Counts

90000
 Olber's Paradox -- Mach's Principle -- Proton Decay

91000
 Blackholes -- Density inside a Blackhole -- Destruction of Identity
 -- Four Kinds of Blackhole -- No Vacuum Cleaner or Drainhole -- No
 Funnel or Well -- No Tidal Shredding -- No Remote Relativity

92000
 Tidal Forces -- Roche Limit -- Applicability of the Roche Limit --
 Roche and Schwarzschild Limits

99000
 Cosmological Tables -- Table of beta = (1-(V/c)^2)^(1/2) --

99020
 Table of Useful Values -- Older Metric Units

99100
 References  -- 1920s -- 1930s -- 1940s -- 1950s -- 1960s -- 1970s

99120
 References -- 1980s -- 1990s

99140
 References -- 2000s

99200
 Anceint elements -- Naming elements -- International names --
 Numerical names -- Loose latin

99300
 Table of heavy elements -- Transuuranium -- Name confusion --
 Atomic address

99400
 Chart of Nuclei

99500
 Symbols Used in the Boxed Equations