The Early Universe
    Home astronomers typicly terminate their inquiries after 
cosmology at the moment the photosphere dissolved, when the matter and 
energy densities crossed, when the universe switched from energy to 
matter ruled. This is because the physics of the photospheric period 
going back to the bigbang instant is not in the general education of 
the home astronomer. In fact, the closer one approaches to the moment 
of the bigbang the heavier the physics becomes! The temperatures and 
densities increase as we roll back in time and there comes the 
question: Is the physics already in hand really up to describing the 
world at those early moments? 
    We can appreciate the concept of a breakdown in familiar physics 
when confronted with unfamiliar circumstances. Consider an ordinary 
liquid thermometer. The liquid expands in step with the temperature. 
By surrounding the thermometer with known temperatures we can 
calibrate it and thereafter use it to assay unknown temperatures. We 
can plot a graph of temperature versus liquid volume, for instance.
    We see that the volume varies linearly with temperature over the 
limited range of temperatures we can present to the thermometer. We 
generalize and say that for all temperatures the volume is 
proportional to the temperature. 
    We get bold and extrapolate our experience to low temperatures and 
find that our V(T) curve crosses the T axis (V = 0) at some particular 
temperature. There is some cold point where the liquid attains zero 
volume! This in fact is one definition of absolute zero. It's that 
temperature at which the thermometer liquid shrinks to zero volume. 
In maths this point of zero volume is called a singularity and there 
are weird implications. Like, since the mass hasn't changed and 
remains finite, the density of the liquid goes to infinity. 
    Then we continue our experiment. As we cool the thermometer the
liquid in deed contracts along the linear curve V(T). But at some one
temperature an astounding thing happens. The liquid freezes to a solid!
    We can no longer apply the rule we developed for a liquid to 
continue our experiment. We must turn to a new regime of physics, that 
governing solids like crystals, polymers, amorphics, and so on. The 
old physics of liquids is invalid and gives a false prediction.
    In point of fact many physicists believe that the freezing of the
liquid to a solid, whose volume is almost invariant with temperature, 
is nature's way to avoid the issue of a singularity. 

The Singularity of the Bigbang
    The Friedmann models, including the Einstein-deSitter or standard 
model, start the universe from a singularity. The scalefactor is 
identicly zero and swells into finite realms with increasing time. Is 
this possible? Most cosmologists say it is allowable under the 
Einstein physics that describe the expanding universe.
    Others are not so sure. One of the prime motives for physicists to 
build atom smashers of ever larger size [and higher cost] is to 
duplicate the conditions of the bigbang and see what physics is 
required to describe them. Did something happen to prevent the 
singularity, like some phase change to make the universe start from a 
nonzero volume? Was there really a time when the whole cosmos fit 
inside a true geometric point? 
    We here can not explore the early universe too far back in time 
because of the lack of the heavy physics. However, we can dip our toes 
in the waters and see what sort of thinking cosmologists go thru. 

Geometrical and Physical Cosmology
    Before World War II cosmology was essentially a geometric 
construct. Altho leMaitre tried to impute physical reality to the 
origin of the universe -- it exploded from a cosmic egg -- in his 
model, he lacked a solid grounding in the physics of the day. What is 
more important, the physics of atoms needed to deal with the origin of 
the universe was only just born in the 1930s. 
    It was World War II that drove the development of this nascent 
atomics in connection with the atom bomb project. All the major 
factions in the war had supersecret schemes to build and deploy the 
atom bomb. The workings of the bomb depended on the behavior of nuclei 
under high temperature and density. 
    Many astronomers worked on the atom bomb as part of their military 
duties and were introduced to this new physics. But with the wartime 
secrecy they could not exchange ideas and thoughts nor apply them in 
academic settings. After the war the restrictions were lifted and the 
science of atomics (also called nuclear, particle, high-energy, and
quantum physics) moved into the regular curriculum of the astronomer.

No Antimatter? 
    Despite our lack of heavy physics we can walk thru one example of 
how cosmologists inquire after the goings-on in the period before the 
photosphere dissolved. We look at matter and anitmatter. By all known 
physics matter and antimatter must be of exactly equal amounts in any 
interaction. Anitmatter is identical to matter except that it has the 
opposite electric charge. For matter of zero charge the matter is its 
own anti by identity. The anti of a proton is the antiproton, a proton 
with one minus charge in the stead of the normal one plus charge. It 
is also called the negatron. 
    When matter and antimatter meet, they annihilate and produce a 
photon. The one can not vanish by itself and leave the other intact. 
Note well that this photon marks the prior existence of two bodies, 
the matter one and the anti one. 
    Now we saw that the energy and mass in the universe are today 
virtually unchanged since the photosphere era. The photons we see 
today in the form of the universal blackbody radiation proceded to us 
directly from the time before the photosphere and are relics of the 
bigbang. Of course, we also have the mass in the universe, itself 
essentially unmodified in quantity since the bigbang. 
   If matter and antimatter must coexist in equal amounts, why then do 
we have in our universe only matter? During the 50s and 60s we 
believed the galaxies were each made of either matter or antimatter. 
Their great separations kept them from contact and selfdestruction. 
When we came onto an intense radiosource consisting of two colliding 
galaxies, we presumed that they were of opposite types. They were 
consuming themselves in annihilation and generating photons. 
    We now understand that the galaxies are not sitting in empty space 
but are connected by fields of intergalactic gas. They are in contact 
yet not self-destructing. Also we have other plausible means of 
explaining the fierce radioemissions from colliding galaxies. 
    So since the 1970s we find our universe consists of only matter 
and no antimatter. Why? 

Matter-Antimatter Ratio 
    Cosmologists think that the law of matter-antimatter equality was 
'not in force' at the bigbang instant. It was 'enacted' some short 
time later. Hence for a little while, microseconds, there was a 
permissible imbalance of matter versus animiatter as an initial state 
of the universe. When the equality law 'took effect' the preceding 
matter-antimatter ratio was 'grandfathered. How all this actually 
happened is part of the unified field theories and is not at all 
certain. In due time the annihilation of matter and antimatter 
occurred, leaving as survivor some residuum of matter. This is the 
matter we now have around us in the universe. 
    Can we assess the severity of this initial imbalance? Amazingly we 
can, even tho it occurred inside the photosphere. In a unit volume of 
space we have photons and particles. The photons are almost all from 
the relic Planck radiation and the particles are mostly protons. Being 
that there was since the bigbang quite little alteration in the 
amounts of photons or protons, their ratio today is the same as that 
at the bigbang. 
    The photon/meter^3 comes from the photon-temperature law with tau 
= 2.735K 

     N(tau) = (pi / 13) * (k / (h * c))^3 * tau^3 
            = (pi / 13) * ((1.381E-23j/K) / ((1.055E-34j.s) 
              * (2.998E8m/s)))^3 * tau^3 
            = (2.012E7/(K.m)^3) * (2.735K)^3 
            = 4.116E8/m^3 

Now we find the proton/meter^3 

     N[proton] = rho0 / m[proton] 
           = (4E-28kg/m^3) / (1.673E-27kg/proton) 
           = 0.239 proton/m^3

    Recall that each photon stands for two particles, say a proton and 
a negatron, that once existed in the bigbang. So

     N[orig] = (2 part/photon) * N(tau) 
             = (2 part/photon) * (4.116E8 photon/m^3) 
             = 8.232E8 part/m^3  

      N[prot] / N[orig] =  0.239 / 8.232E8 
                        = 2.903E-10 

    This is an awesome conclusion! The universe really started out 
with almost equal parts of matter and antimatter with an excess of one 
part in 29 BILLION in favor of matter. We here today live with just 
this left over grain of matter after all the rest annihilated itself 
in the bigbang! 

Abundance of the Elements
    Until the 1920s the mix of chemical elements in the universe 
escaped notice by astronomers. By spectrometry they assayed the stars, 
planets, &c were mainly concerned with the mere presence or absence of 
a given element.  For example, we assumed the Sun was made of a 
substantial portion of the heavy elements which produced prominent  
spectral lines. 
    Payne-Gaposchkin in the 1920s accumulated sufficient evidence and 
applied the new quantum physics to it to realize that the sun and 
stars are overwhelmingly made of hydrogen, up to 3/4 by mass. 
Astronomers were not happy with this finding and generally ignored it 
until the late 1930s, when it was confirmed by later assays. 
    The definite census of the universe was done by Urey in 1954, 
showing that hydrogen was 75% (by mass); helium, 24%; and all the 
other elements from lithium thru uranium were present in traces. 

Helium in the Universe 
    By the mid 1930s astronomers were exploring crude models of the 
stars and they hit on the fusion of hydrogen into helium and heavies 
with the consequent release of energy. This is how the stars shine, a 
mystery for all prior time. 
    The stellar energy processes yield about the correct portions of 
the heavy elements but wildly too low ratios for helium. In astronomy 
'heavy elements' are all elements other than hydrogen and helium; it 
has the unofficial symbol 'Hv'. It seems that the stars start off with 
a large portion of helium and then produce only a little additional 
    The amount of helium, and other elements, in the universe is not 
easy to assess. There is no representative place to take a sample of. 
In the solar system the original mix of elements is far too massaged 
by planetological processes to be a fair sample. Ongoing creation of 
the elements in the stars distorts the mixture. The interstellar dust 
and gas seem too nonhomogeneous for good sampling. 
    In spite of everything we feel confident that the universe at 
large is comprised of 75%, by mass, hydrogen, 24% helium, and quite 
one percent heavies. Contrast this against the Earth which is all 
heavies with almost no hydrogen and helium. 

Origin of the Helium 
    The mass converted into energy by the stars is order 1E-4 of the 
total mass of the universe and the energy emitted by the stars added 
only a few percent to the energy coming from the bigbang. Hence the 
amount of mass converted into helium in the stars is negligible and 
the huge helium portion must have existed before the stars. `   
Plausibly it was created in the photospheric era soon after the 
    Alpher, Bethe, Herman, and Gamow were among the first, in 1948, to 
calculate the creation of hydrogen and helium out of the bigbang. To 
do so they had to add thermodynamics to the standard model, thus 
introducing mainline physics into cosmology. There were several 
earlier attempts, such as that of Weizsacker in 1937, to explain the 
abundance of the various elements in the universe but they suffered 
from the prevailing weak theory of atomics. 
    To them the universe started off indefinitely hot. As it expanded 
it cooled. Gamow further noted that the radiation from the time of 
initial high temperature should be cooled by now to a few Kelvin. In 
fact this is the 2.7K microwave background, the relic radiation from 
the photospheric period. 

    The team of Alpher-Bethe-Herman-Gamow banked their calcs on the 
newly emerging atomics. The team's original scheme has long since been 
supplanted for it originally made all the elements out of the bigbang, 
ignoring the role of the stars. 
    With the Urey assay in hand Gamow, Burbidge, &a in 1957 divvied up 
the element creation regimes. Gamow demonstrated that essentially only 
hydrogen and helium are made in the bigbang while Burbidge's team 
showed that the rest (including some additional helium) was produced 
in the stars. 
    Gamow assumed that at some point in the expansion and cooling the 
universe was populated only by neutrons. There were the several 
'classical' atomic particles to work with: neutron, proton, electron, 
neutrino, and photon. As an aside, the neutrino was theorized partly 
out of the prewar work on stellar evolution but it was not discovered 
in nature until 1954. 
    Today physicists postulate that neutrons came from some other more 
elemental particles in a prior hotter denser stage of the universe. We 
start with the neutrons already in place. This is believed to occur at 
a temperature of order one billion Kelvin and time of order one 
hundred seconds after the bigbang instant. 
    Gamow showed that from this sea of neutrons hydrogen and helium 
derived in close to the observed ratios. The heavies ratio was badly 
too low but he figured the element creation in the stars made up the 
    The theory of the creation of the elements in the bigbang is 
called nucleogenesis, as sexy a term in astronomy as ever there was 
one. The creation of elements in the stars, aeons after the bigbang 
and in our own era, is called nucleosynthesis, an other sexy term.. 

Regimes of Element Creation
    Today we recognize five regimes under which elements are created 
in the universe. These regimes divide the elements into five groups 
ordered by their atomic number (count of protons). The first, the 
nucleogenesis explored in this treatise, produced the initial hydrogen 
and helium. All subsequent elements were generated by the other four 
processes from this primary reservoir of hydrogen and helium. 
    The hydrogen is then burned by the stars on the Main Sequence to 
produce more helium. This extra helium is a small addition to the 
initial helium already in the star. 
    When the star leaves the Main Sequence to live out its life as a 
redgiant and beyond it burns some of its helium into heavies. This 
process generates the elements up to iron. 
    Later the more massive stars supernovate and crush the heavies 
into still larger heavies up to uranium. The ejecta from the supernova 
dissipate into the interstellar regions as nebulae.
    This material is laced with all the elements hydrogen thru uranium 
and from it a new generation of stars is created. That is, stars are 
born with a preexisting mix of elements reflecting the deaths of the 
last generation. 
    In time the last generation of supernova ejecta will be laced with 
too much heavies and too little hydrogen. This stuff will not burn in 
a main sequence star and the creation of new stars ceases. 
    The final regime began in WW II, the production of elements 
heavier than uranium. These ultrauranium elements are not found in 
nature but exist only because of human intervention. Of course, the 
quantity of these artificial elements is minuscule even within the 
solar system. They have no cosmological importance except as specimina 
for experimentation in atomics. 
    We summarizes the regimes here: 
 elements                  how produced 
 --------                  ------------
 hydrogen and helium       in the bigbang thru nucleogenesis 
 helium                    in Main Sequence stars (minor amounts) 
 helium thru iron          in post Main Sequence stars 
 iron thru uranium         in supernovae 
 transuranium elements     ny humans 

Table of Particles 
     We need from an atomics reference the properties of the various 
particles and the reactions they can undergo among themselfs. Here are 
a few concepts to understand. Much of these are jargon terms. 
    The mass number, A, of a particle is the sum of the protons and 
neutrons in it. More properly it is the mass of the particle expressed 
in units of the neutron or proton mass. The proton and neutron have 
almost equal mass. In comparison the electron has very little mass, 
the neutrino has probably a;most with no mass, and the photon has no 
mass at all. 
    The atomic, or element, number, Z, is the number of protons in the 
particle and this number determines what element the particle is. A 
particle with no protons has atomic number zero and is not an element. 
Often if the particle is named as an element the atomic number is left 
out. For each element has its unique and proper atomic number. 
    The neutron number, N, is the number of neutrons in the particle.
Note well that A = Z+N. The neutron number is rarely stated because it 
can be derived from the atomic and mass numbers, N = A-Z. In deed the 
neutron number is sometimes called the 'A minus Z' number. 
    The decay of a particle refers to its spontaneous mutation into 
other particles without outside stimulus. Altho we are dealing with 
particles, a decay will generally yield a photon, which radiates away. 
    The halflife, tau, of a particle is the time it takes for the 
particle to decay, disintegrate, transmutate into other particles with 
a 50-50 probability. For a multitude of the particle this is the time 
for half of it to decay, leaving half as yet in its original state. 
Many particles are stable; they remain unchanged for an indefinitely 
long  time. 
    An isotope is one of several particles with the same atomic number 
but different mass numbers. Or the same number of protons but different
numbers of neutrons.
    The anti of a particle is the very particle with the electric 
charge of opposite signum. A particle with no charge is its own 
antiparticle. The anti of the electron, e-, is the antielectron, e+,
which is an electron with a positive charge in the place of a negative 
charge. We also call it the positron.
    Among atomicists there grew a nomenclature for particles as arcane 
as star nomenclature. A few are noted here. 
    An alpha [particle] is the nucleus of helium. It contains two 
protons and two neutrons. Occasionally this is referred to as a 
    A beta [particle] is the electron. It is often written as 'beta-' 
to emphasize that it has the negative electric charge associated with 
the electron. By parallel construct the antielectron is sometimes 
written as 'beta+'. 
    A gamma [ray] is the photon, the quantum of electromagnetic 
radiation. It does not have to be visible light but may have any 
wavelength, as appropriate for the particle e's reaction. 
    A deuteron is a particle of one proton and one neutron. It is also 
called heavy hydrogen or hydrogen2. Its symbol is d or H2. 
    A triton is a particle of one proton and two neutrons. It is also 
called double-heavy hydrogen and is symboled as t or H3. 
    Proton, deuteron, and triton are isotopes of hydrogen. They all 
have one proton but no, one, or two neutrons. The names 'deuteron' and 
'triton' imply the existence of actual elements called 'deuterium' and 
'tritium'. These are not separate elements but traditional names for 
isotopes of hydrogen when treated as chemical agents. All three are 
chemicly the same. 
    The symbol of a particle is letters followed by digits. The 
letters are the name of the particle and carry its associated atomic 
number. The atomic number itself is rarely explicitly written.. The 
number is the mass number. He4 is the helion (helium nucleus, alpha) 
with mass number 4. The atomic number is not specified because helium  
must have two protons. To fill up to mass number 4 the particle must 
have two neutrons. 
    The properties of many cosmologicly important particles is set out 
in the table here. Several particles are repeated under their different 
names; this saves time in looking up aliases. 

 name          symb  Z  N  A  decays    halflife  comments
 ----          ----  -  -  -  --------  --------  --------
 gamma        gamma  0  0  0  stable              = photon
 photon       gamma  0  0  0  stable              = gamma
 neutrino      nu    0  0  0  stable             
 anitneutrino  nu'   0  0  0  stable
 beta         beta-  0  0  0  stable              = electron
 electron       e-   0  0  0  stable              = beta
 antielectron   e+   0  0  0  stable              = positron
 positron     beta+  0  0  0  stable              = anitelectron 
 neutron        n    0  1  1  p,e-,nu'  1.05E1m
 proton         p    1  0  1  stable              = hydrogen 1 
 hydrogen 1     H1   1  0  1  stable              = proton
 deuteron       d    1  1  2  stable              = hydrogen 2 
 hydrogen 2     H2   1  1  2  stable              = deuteron
 triton         t    1  2  3  He3,e-    1.23E1y   = hydrogen 3 
 hydrogen 3     H3   1  2  3  He3,e-    1.23E1y   = triton
 helium 3      He3   2  1  3  stable
 helium 4      He4   2  2  4  stable              = helion, alpha
 alpha        alpha  2  2  4  stable              = helion, helium 4 
 helion        He4   2  2  4  stable              = alpha, helium 4 
 helium 5      He5   2  3  5  He4,n     2.0E-21s  instant decay 
 lithium 5     Li5   3  2  5  He4,p     1.0E-21s  instant decay 
 helium 6      He6   2  4  6  Li6,e-    8.05E-1s
 lithium 6     Li6   3  3  6  stable 
 beryllium 6   Be6   4  2  6  He4,p,p   3.0E-21s 
 lithium 7     Li7   3  4  7  stable
 beryllium 7   Be7   4  3  7  Li7       5.33E0d   electron capture 
 helium 8      He8   2  6  8  Li8,e-    1.19E-1s
 lithium 8     Li8   3  5  8  Be8,e-    8.44E-1s
 beryllium 8   Be8   4  4  8  He4,He4   1.0E-16s  instant decay 
 boron 8        B8   5  3  8  Be8,e+    7.70E-3s  positron decay 
 lithium 9     Li9   3  6  9  Be9,e-    1.77E-1s
 beryllium 9   Be9   4  5  9  stable 
 boron 9        B9   5  4  9  Be8,p     8.0E-19s
 carbon 9       C9   6  3  9  B9,e+     1.27E-1s  positron decay 
 beryllium 10  Be10  4  6 10  B10,e-    1.6E6y 
 boron 10       B10  5  5 10  stable
 carbon 10      C10  6  4 10  B10,e+    1.93E0s   positron decay 
 lithium 11    Li11  3  8 11  Be11,e-   8.7E-3s
 beryllium 11  Be11  4  7 11  B11,e-    1.38E1s 
 boron 11       B11  5  6 11  stable
 carbon 11      C11  6  5 11  B11,e+    2.03E1m   positron decay 
 beryllium 12  Be12  4  8 12  B12,e-    2.4E-2s 
 boron 12       B12  5  7 12  C12,e-    2.02E-2s
 carbon 12      C12  6  6 12  stable 
 nitrogen 12    N12  7  5 12  C12,e+    1.1E-2s   positron decay 

    A positron decay is where a proton emits a positron and turns into 
a neutron. An electron capture is where a proton sucks in a nearby 
external  electron and turns into a neutron. The electrons are 
captured from the surrounding space. 
    In the halflife column s = seconds, m = minutes, d = days, y = 
years. Note that triton and beryllium 10 have long halflifes and are
found natively on Earth as radioactive isotopes. All the others are 
either long gone or must be continuously created from other particles. 
    Every mass number has at least one stable isotope, EXCEPT FOR A = 
5 AND 8. This is a circumstance of crucial importance in the 
nucleogenesis theory. 

Table of Interactions 
    Besides natural decay, a particle can mutate by capturing certain 
particles and ejecting others. Of the many thousands of possible 
interactions, the ones here are germane to nucleogenesis right after 
the bigbang. All of these are two-particle interactions. We think that 
the conditions in the first moments after the bigbang allowed only 
two-particle reactions. 
    Many reactions are labelled '[not poss]'. The supposed outputs for 
them are either unknown at this time or are so rapidly self-decaying 
that it looks as if the reaction never occurred. 
    The reactions are listed both ways to ease searching for them. 

 input    output     |  input    output      | input    output
 -----    ------     |  -----    ------      | -----    ------
 n        p,e-,nu'   |                       |
 n,nu     p,e-       |  n,e+     p,nu'       |  n,n     [not poss} 
 n,p      d,gamma    |  n,d      t,gamma     |  n,t     [not poss]       
 n,He3    t,p        |  n,He3    alpha,gamma |  n,alpha [not poss]
 p,n      d,gamma    |  p,d      He3,gamma   |  p,t     alpha,gamma
 p,He3    [not poss] |  p,alpha  [not poss]  |
 d,n      t,gamma    |  d,p      He3,gamma   |  d,d     t,p
 d,d      He3,n      |  d,t      alpha, n    |  d,He3   alpha,p       
 d,alpha  Li6,gamma  |                       |
 t,n      [not poss] |  t,p     alpha,gamma  |  t,d     alpha,n
 t,t      [not poss] |  t,He3   Li6,gamma    |  t,alpha Li7,gamma
 He3,n    t,p        |  He3,n   alpha,gamma  |  He3,p   [not poss]
 He3,d    alpha,p    |  He3,He3 alpha,p,p    |  He3,alpha  Be7,gamma
 alpha,n  [not poss]  | alpha,p   [not poss] | alpha,d   Li6,gamma
 alpha,t  Li7,gamma   | alpha,He3  Be7,gamma | alpha,alpha  [not poss] 

Initial Conditions 
    The above reactions procede at various rates (reactions/second) 
and probabilities (based on the cross-section of the particles when 
they collide in their interaction). The rates and probabilities are 
functions of temperature and density, which in turn are functions of 
time. The universe steadily cools and dilates with its expansion. 
    At some moment after the bigbang instant the universe cooled and 
expanded enough to allow the precipitation of neutrons. Neutrons, by 
modern atomic theory, came from more elemental particles under hotter 
denser conditions. Here we wait until the neutrons are in full bloom 
and then start our nucleogenesis simulation.
    We must ignore the rates and probabilities of the interactions 
being that they involve an order of physics much outside the home 
astronomer. The neglect of the reaction kinetics compromises the 
numerical results of our simulations. Yet the qualitative results end 
up being very enlightening. 
    The universe at the start of our study consisted all of neutrons, 
no other particles, and gamma rays (photons) from other earlier 
reactions. A free neutron is not a stable particle. It spontaneously 
decays into a proton, electron, and antineutrino. The neutrons are not 
yet joined into nuclei, where they turn into stable particles. 
    Soon, after many of the neutrons self-decayed, there is a sea of 
loose native neutrons and newborn protons. The leftover neutrons and 
new protons combine among themselfs, in pairs, to create deuterons 
plus more gamma rays. The deuterons combine in pairs to yield tritons 
and newly released protons. These new protons are of a second 
generation, not from the decay of the original neutrons. 
    Tritons and deuterons combine to produce alpha particles (helions, 
helium nuclei) and ejected neutrons. These neutrons partly replenish 
the original supply and decay into protons of the third generation, 
after the initial neutron decay and the deuteron-deuteron reactions. 
    We have, then, the following interactions to work with:

    n -> p,e-,nu'
         p,n -> d,gamma 
                d,d -> t,p 
                       t,d -> alpha,n 

    Some egredients of these reactions become ingredients while others 
remain: proton, al[ha, gamma. With more familiar names: hydrogen, 
helium, radiation 

Conservation Rules 
    There are, from atomics, various conservation rules that govern 
the way we can work these reactions against each other. The number of 
neutrons and protons on both sides of the reaction must be equal. This 
is the baryon number, a baryon being a neutron or a proton, both being 
nearly equal in mass. A baryon counts as +1; an antibaryon, -1. 
    The number of electrons and neutrinos must be equal across the 
interaction. This, the lepton number, counts particles as +1 and the 
antis as -1. 
    The electric charge must be equal on both sides. Positive charges 
are +1; negative, -1. This number has no fancy name; it's just the 
charge number. 
    There is an energy conservation rule for gamma rays which we do 
not employ here. We let gamma rays be taken in or given out as necessary
to make the total energy on both sides balance. In general whenever a
single particle is the output of a reaction we allow for a gamma ray
emission with the particle.

Interaction Flowchart
    It is a lot easier to picture what is going on by diagramming the 
reactions in a flowchart. We start with six initial neutrons and end up 
with one helion (plus some other stuff). 
    In the flowchart boxes enclose the reactions, square brackets 
enclose the initial particles, angle brackets enclose the final 
particles, and vertical arrows flow from the earlier (upper) to later 
(lower) reaction. 

   [n]             [n] [n]             [n] [n]             [n] 
    |               |   |               |   |               |  
    |              \|/  |              \|/  |              \|/ 
    | +---------------+ | +---------------+ | +---------------+ 
    | | n -> p,e-,nu' | | | n -> p,e-,nu' | | | n -> p,e-,nu' | 
    | +---------------+ | +---------------+ | +---------------+ 
    |  \|/   \|/  \|/   |  \|/   \|/  \|/   |  \|/   \|/   \|/ 
    |   p    <e-> <nu'> |   p    <e-> <nu'> |   p    <e->  <nu'> 
   \|/ \|/             \|/ \|/             \|/ \|/ 
  +----------------+  +----------------+  +----------------+ 
  | p,n -> d,gamma |  | p,n -> d,gamma |  | p,n -> d,gamma |
  +----------------+  +----------------+  +----------------+
    |           \|/    \|/          \|/     |            |  
   \|/           d      d           \|/     |           \|/ 
   <gamma>      \|/    \|/          <gamma> |           <gamma> 
               +------------+              \|/ 
               | d,d -> t,p |               d 
               +------------+               |
                 |       \|/                | 
                \|/       t                 | 
                <p>      \|/              \|/ 
                         |  t, d -> alpha, n  |
                           |               \|/ 
                          \|/               n 
                         ,<alpha>          \|/ 
                                          | n -> p,e-,nu' | 
                                            |     |     |  
                                           \|/   \|/   \|/  
                                           <p>   <e-> <nu'> 

    The net transformation is 

     6 n -> alpha, 2 p, 4 gamma, 4 e-, 4 nu' 

Test this for balance against the conservation rules: 

    Baryon number:  In = 6 = 6 initial neutrons 
                   Out = 6 = 4 in the alpha and 2 protons 

    Lepton number:  In = 0 = 0 initially 
                   Out = 0 = 4 electrons cancelling 4 

    Charge number:  In = 0 = 0 initially 
                   out = 0 = 4 electrons cancelling 2 protons in 
                              the helion and 2 free protons 

Other Reaction Chains
    By studying the 'Table of Interactions' we can find other chains 
of reactions to work with. One such is the d,d -> He3,n followed by 
He3,He3 -> alpha,p,p.  We have the set of interactions 

  n -> p,e-,nu'
       p,n -> d,gamma 
                d,d -> He3,n
                   He3,He3 -> alpha,p,p 

Working with this set we get the flowchart below: 

  [n]          [n] [n]          [n] [n]          [n] [n]         [n] 
   |            |   |            |   |            |   |           | 
   |           \|/  |           \|/  |           \|/   |         \|/ 
   | +------------+ | +------------+ | +------------+ | +------------+ 
   | | n -> p,... | | | n -> p,... | | | n -> p,... | | | n -> p,... | 
   | +------------+ | +------------+ | +------------+ | +------------+ 
   |   |  |    |    |   |  |    |    |   | \|/  \|/   |  \|/ |   \|/ 
   |   p <e-> <nu'> |   p <e-> <nu'> |   p <e-> <nu'> |   p <e-> <nu'> 
   |   |            |   |            |   |            |  \|/ 
  +--------------+ +--------------+ +--------------+ +--------------+ 
  | p,n -> d,... | | p,n -> d,... | | p,n -> d,... | | p,n -> d,... |
  +--------------+ +--------------+ +--------------+ +--------------+
   |           \|/   \|/      \|/    \|/        \|/    |      | 
  \|/           d     d      <gamma> <gamma>     d     d     \|/     
 <gamma>       \|/   \|/                        \|/   \|/   <gamma> 
               +--------------+           +--------------+ 
               | d,d -> He3,n |           | d,d -> He3,n | 
               +--------------+           +--------------+ 
                |           \|/            \|/          |  
               \|/          He3            He3         \|/ 
                |n          \|/            \|/          n 
                |         +----------------------+      | 
                |         | He3,He3 -> alpha,p,p |      | 
               \|/        +----------------------+     \|/ 
  +---------------+        |          |         |     +---------------+ 
  | n -> p,e-,nu' |       \|/         |         |     | n -> p,e-,nu' 
|                        <alpha>    \|/        \|/ 
  +---------------+                 <p>        <p>    +---------------
+   |           |                                       |     | 
   \|/    |    \|/                                      |     |     | 
   <p>   <e->  <nu'>                                   <p>   <e->  <nu'>

    The net transformation is

     8 n -> alpha, 4 p, 4 gamma, 8 e-, 8 nu' 

Check with the conservation rules 

    Baryon number:  In = 8 = 8 initial neutrons 
                   Out = 8 = 4 in the alpha and 4 protons 

    Lepton number:  In = 0 = 0 initially 
                   Out = 0 = 8 electrons cancelling 8 

    Charge number:  In = 0 = 0 initially 
                   Out = 0 = 8 electrons cancelling 4 protons in 
                             the helion and 4 free protons   

Limits of the Simulation 
    Recall that we omitted any attempt to factor in the probability 
and speed of the reactions. Some may procede so rapidly that there is 
a huge excess of their output particles. Others may occur so rarely 
that their output plays no significant role in further interactions.
    To see how the numbers fail, look at the two chains here. In the 
first one we end up with one alpha and two protons (plus other low-
mass stuff). The mass ratio of alpha and proton to the entire mass of 
the system is 

     alpha ratio = 4 / (4 + 2)  |  proton ratio = 2 / (4 + 2) 
                 = 4 / 6        |               =  2/ 6 
                 = 0.667        |                = 0.333 

We created a universe of 2/3 helium and 1/3 hydrogen! Of course this 
disagrees with the observed ratio of hydrogen and helium. The other 
chain yielded one alpha and four protons. So 

     alpha ratio = 4 / (4 + 4)  |    proton ratio = 4 / (4 + 4) 
                 = 4 / 8        |                 = 4 / 8 
                 = 0.5          |                 = 0.5 
This is just as far off: a world half hydrogen and half helium. 
    Never the less, the qualitative broadbrush model is in fact dead
on target. We do with our analysis start with all neutrons in the 
universe and do come up with a universe of just hydrogen, helium, 
gammas, electrons, and antineutrinos. These are exactly the major 
particles the advanced calcs derive.

Why Stop at Helium? 
    We stopped the simulation with the production of helium4. Why?     
If we went and continued the nucleogenesis in our crude system we 
could have consumed all the helium, and probably a lot of the 
hydrogen, into heavies. Our universe would contain all heavies with 
little or no helium and hydrogen! There is nothing in our model that 
naturally terminates at helium.
    The main reason for us to stop at helium is to  follow the 
detailed model with its declining temperature and density. Under a 
proper analysis while the nucleogenesis is in progress the universe 
continues to cool and dilate. By the time helions are in place the 
density and temperature had already fallen below those required for 
further reactions of helion with other particles. 
    Amazingly, the entire nucleogenesis from the native neutrons all 
the way into the hydrogen and helium (and other stuff) takes only one 
half hour!! And the temperature at the end of the nucleogenesis is 
down to about ten million kelvin. 
    The universe grows cooler and thinner as the end-product particles 
no longer interact. They must wait for the next stage of element 
production within stars. We once thought there was no more nuclear 
activity for a couple million years while stars and galaxies were 
slowly condensing. We called this no-activity period the 'dark ages'. 
    Recent observations suggest that galaxies sprang up only several 
hundred million years after the bigbang. This allowed for the first 
stars to begin element production much earlier in the life of the 

The Neutron Decay 
    The particles in the early universe were almost all stable ones, 
not self-disintegrating into other particles. Tritons and neutrons 
aren't stab;e. They decay. The triton's halflife is some 20 years. 
Once created near the bigbang it endures long enough to engage in other 
    The neutron has two cases of life. Within a nucleus it is stable, 
like the proton. As an unattached free particle it has a halflife pf 
only 'a few minutes'. The vague halflife came from the preliminary 
data released about atmoic research after World War II and most cited 
a time of some 20 minutes. 
    The original neutrons after the bigbang were unattached into 
nuclei. They were free particles. With a 20-minute halflife the 
neutrons COULD stay intact until the end of the interaction era 
without producing protons! When the neutrons do disintegrate their 
daughter protons would be too cold to interact and we would not move 
along with nucleogenesis.  The bigbang cosmology would be discarded or 
massive revised. 
    Our world would be a era of cold protons, never able to merge into 
any other elements.  We wouldn't be here to study such a universe. 
    Better data for the neutron came in the 1960s but even into the 2-
thous there was still some concern that the neutron halflife doesn't 
quite fit into the bigbang model. In fact, the acceptance of the 
bigbang model pushes inquiry into the properties of the neutron! 
    The current value for the neutron halflife is about 14.7 minutes. 
This seems about right to sustain the nucleogenesis of the bigbang. 

The Relics of the Bigbang
    The cosmic microwave flux of 537K temperature is the relic of the 
bigbang. In our model here this flux comes from the gamma rays emitted 
by the nucleogenesis. At first they would have the ambient temperature 
when they were created, from around one billion kelvin. These gamma 
rays were constantly absorbed and reradiated all during the 
photosphere time after the initial half-hour of nucleogenesis. During 
this period they were dispersed into a Planck distribution and 
exhibited a blackbody spectrum. 
    At last, at the dissolution of the photosphere they were freed 
into space. At this moment they had cooled to around 2500K. The 
surrounding materials were able to settle into atoms with electrons 
attached to nuclei. This material no longer interacted with radiation 
and was transparent.
    There after the gamma radiation was virtually unmolested by any 
further interactions and it is felt by us today. it cooled with the 
Hubble expansion such that it has the observed temperature of 2.7 
    Our analysis shows an other possible relic: the antineutrinos. 
Antineutrinos are essentially inert against any reaction once they are 
created. They travel in straight lines from their origination point 
out thru all space. For them there was never a photosphere and the 
universe was always completely transparent. 
    Many cosmologists believe we should find relic antineutrinos all 
around us today. There actually is an isotropic and homogeneous 
background flux of antineutrinos that suggests a bigbang origin. 
    Antineutrinos, being so inert, just aren't easy to capture and 
measure. Of the zillions of [possibly] primoidal antineutrinos per 
second that pass thru our human bodies, perhaps one in a whole 
lifetime may mutate a body cell away from its normal function.. 
    Electrons and protons are also relics of the bigbang and we 
certainly have lots of them around now in an uniform deployment over 
the heavens. Because they carry electric charge they are easily 
influenced by magnetic fields. 
    They exchange energy with these fields and with other particles. 
By now they have just no vestige of their primoidal properties. We 
can extract little intelligence about the early universe from them. 
    In addition to possible original protons, protons and electrons 
are created by many astrophysical process since the bigbang. There 
seems to be no way to tell the original ones from the newer ones.