steady State Universe 
    Today the bigbang theory is the working model of the universe. 
Most astronomers and cosmologists and physicists go along with it and 
do their studies within it. Yet, despite the teachings of some of its 
adhaerents, the bigbang theory in no way is a proved theory or the 
actual solution to the way the universe originated and evolved. We saw 
many of the problems it embeds, problems which are nowayears a major 
concern to bigbang promotors. 
    Over the decades since Friedmann and leMaitre first put out their 
models the overall evidence and observations seemed to favor them. 
What's more, there never arose any other serious contender against the 
bigbang for many years. 

Furtherance of the Bigbang Theory 
    In 1948 cosmology was at a transition point. Up until then it was 
a mathematical geometrical musing. There was no idea to apply the 
maths of the expanding universe to any real goings on, save the 
presently observed Hubble expansion. leMaitre tried to inject some 
physics by asserting that the universe actually exploded from some 
primaeval egg about as big as the Earth's orbit in diameter, but he 
failed for the immaturity of atomic physics and his own weak 
experience in other physics. 
    Gamow &a were developing a modification of the bigbang model with 
the effects of temperature and atomic physics. In 1948 he and his 
associates worked up a scenario for building hydrogen and helium out 
of the bigbang under very high temperatures and densities. He even 
foretold that the energy released into space when the photosphere 
dissolved should be visible around us today. This radiation should be 
only a few Kelvin due to cooling over the eons since the bigbang. 
    Further support came from the emerging corps of atomic physicists 
who, with the new science and powerful computers, could model the 
universe. They arrived at scenarios that seemed to jibe with the 
bigbang and they used the precepts of the bigbang to push atomics to 
higher levels of achievement. Many of the new atomsmashers were built 
on the reasoning that they will help explore the events near the 
moment of the bigbang. 
    These two features, the ratios of the elements and the relic 
radiation, were taken by most astronomers as virtual proofs for the 
bigbang. When the microwave radiation was discovered in 1965 pretty 
much everyone took to the bigbang theory as the one way of life for 
the universe. 

Age Problem with the Bigbang 
    In the same year of 1948 there were already headaches for the 
bigbang school. Firstly the Hubble time T0, or 1/H0, was 1.8 billion 
years. This made, under the Einstein-deSitter form of the Friedmann 
world, the univer 1.2 billion years old. Until World War II this was 
sufficient time for the Earth and other universe objects to be born 
and grow. For the Earth was thought to be a few hundred millions of 
years old and meteorites seemed to be of the same order of age.
    But geology advanced to increase greatly the lifespan of the Earth 
and the new stellar theories vastly increased the lifespans of stars. 
The Earth was found in the postWWII years to be 3 or even 4 billion 
years old and the stars had to be several billion years old. So the 
Hubble parameter was just too small. Perhaps the Friedmann model was 
not the right one? 
    leMaitre came to the rescue thru his scheme. It started with the 
Friedmann expansion until it reached a maximum scalefactor some long 
time ago and then somehow switched to a deSitter expansion, which we 
now live in. In his original system, issued in 1931, the switchover 
was an inflection point in the R(t) curve. leMaitre now said that 
maybe the inflection point was really a pausing phase. The deSitter 
phase did not start immediately but way later. The point was a land of 
constant R for whatever time was necessary to let the Earth &a come 
about and evolve. Making this dwell period, say, two billion years, 
would suit the new age of the universe. But all this was adhoc and 
leMaitre wasn't up to the physics needed to elaborate on this 
modification to his scheme. 

Singularity Problem with the Bigbang
    The Friedmann models, all of the them, start the world from a true 
mathematical point, a singularity, at t = 0. Nothing in the theory 
explains what happened at this point, where all the universe had 
infinite density and no time. Altho much of the mystery came from the 
immature state of atomics in the first postWar years, even today the 
issue of history at identicly zero time remains.
    Philosophicly there is a discontinuity in the history. Can there 
any discussion of the era 'before' the bigbang? Did time itself 
actually originate then? What is time that it can even be born at all? 
Being that all known events occupy time, however little, how could the 
bigbang happen with no preexisting time? 
    Nowhere else in physics is a singularity accepted as an integral 
part of any theory. In all other situations a singularity is avoided. 
In some cases it seems that nature works for itself by throwing in 
some change of rules. For example, the liquid in a thermometer freezes 
into a solid to prevent it from ever attaining zero volume at some low 
    An other example is the focusing of light by a lens. The focal 
point should be a mathematical point (for each point in the source). 
But if it were the energy density at this point would be infinite, 
forming a singularity. So, some claim, nature kicks in diffraction to 
make the focal point a finite size to prevent the singularity/ 

Perfect Cosmological Principle
    Bondi & Gold, later joined by Hoyle and Narlikar, in 1948 restated 
the cosmological principle. In the Friedmann models the universe 
presents the same overall demeanor at all places, but not at all 
times. The universe as a whole can evolve from one guise into an 
other, as it supposedly did from the bigbang singularity into the 
world around us today. 
    Bondi & Gold extended the cosmological principle to time. The 
universe presents the same overall demeanor in all places AND IN ALL 
TIME. While there can be changes and evolution, like the birth and 
death of stars, there is no gross maturation of the cosmos. There 
never was a singularity, a specific origin, a beginning of time. The 
universe always was, always is, and always will be. Orbium mundus in 
saeculum saeculorum erat atque futurus est 
    This very simple extension defines the prefect cosmological 
principle but it brings with it colossal changes in the structure of 
the universe. It is not a tweeking of an old theory; it is the 
foundation of an allnew regime for the workd to live in. 

Hubble Parameter 
    Applying the perfect cosmological principle to the Hubble 
parameter it must remain constant over time. It can not steadily 
decrease as in the Friedmann universe. Thus we have 

     H(t) = constant 
          = H0 
          = (dR / dt) / R(t) 

     H0*dt = dR / R(t) 

This integrates into an amazingly simple form for the time function of 
the scalefactor!

     H0 * intl(1, t) = intl(1/R, R) 

     H0 * t = ln(R) 

     R = epsilon^(H0 * t) 

where epsilon is 2.71828..., the base of the natural logarithm system, 
a 'magic number' of the rank of pi in mathematics. This exponential 
function is sometimes written as exp(H0*t). 

 |                              | 
 | R(t) = epsilon^(H0 * t)      | 
 |      = exp(H0 * t)             | 

Right off we see the sheer simplicity of this relation compared to the 
R(t) in the standard model. From this definition of R versus t the 
steady state advocates built up their theory. 

    The definition of the cosmological redshift (Z+1) is the ratio of 
the scalefactor at the reception of the target's radiation today to 
that at the time the target emitted the radiation. 

     Z+1 = R / R0 
         = exp(H0 * t)/exp(H0*t0) 
         = exp(H0 * (t - t0)) 

We set t0 = 0 for the present epoch and t is positive as we look back 
in time. Hence 

 Z+1 = exp(H0 * t) 

    This is same as the expression for the R(t)! In the Bondi-Gold 
universe the time function of scalefactor is obtained merely by 
assessing the cosmological redshift! 

 |                          |
 | Z+1 = exp(H0 * t)        | 
 |     = epsilon^(H0 * t)   | 

Density of the Universe 
    In the Bondi-Gold universe the density of matter is a constant, 
rho(t) = constant = rho0. At first this seems implausible due to the 
continual increase of R with time. This in the standard model 
decreases the density, at least in the era surrounding us now, being 
that we live in an expanding universe. We saw how the standard model 
calls for a constant mass for the universe by making everything happen 
in the bigbang and almost nothing in the eons since then. So, yes, 
this fixed amount of matter must be dispersed thru ever larger volume 
as the universe outswells. 
    Bondi & Gold counter with the feature of continuous creation. As a 
given volume outswells allnew mass is born within it to keep the 
overall density the same. Note tat this also preserves the gross 
appearance of the universe because each volume has the same mix of old 
and new matter. 
    We satart with the time function of volume

     V(t) = R(t)^3 
          = exp(H0 * t)^3 
          = exp(3 * H0 * t) 

Then we impose the fixed density to get the time function of mass 

     m(t) = rho0 * V(t) 
          = rho0 * exp(3 * H0 * t) 

 1der(m,t) = rho0*1der(V,t) 

     1der(m, t) / V = rho0 * 1der(V , t ) /V 
      = rho0 * 1der(exp(3 * H0 * t), t) / exp(3 * H0 * t) 
      = rho0 * 3 *H0  *exp(3 * H0 * t) / exp(3 * H0 * t) 
      = 3 * rho0 * H0 

    By plugging in observed values for the density and Hubble 
parameter we get the mass creation rate under the Bondi-Gold system

     ider(m, t) / V = 3 * rho0 * H0 
                    = 3 * (4E-28kg/m^3) * (1.6E-18/s) 
                    = 19.2E-46kg/m^3.s 

This is an incredibly tiny amount! It amounts to about two Suns in a 
cubic megalightyear every century! Of course this is an absolutely 
nonobservable quantity, yet it is enough to maintain a fixed matter 
density in the Bondi-Gold universe. 
    At first there was no statement on the nature of this new matter. 
In 1948 the atomic physics was too weak to inquire after it. In 1964 
Hoyle & Narlikar did elaborate on this continuous creation, as we look 
it later. 

Proper or Einstein Distance 
    The targets in space are tied to us by lightrays, so 

     c * delt / R(t) = -delr 

The minus sign telsl us that R and t increase in opposite senses. R 
increases from us to the remote; t increases from the remote to us. 
That is r0 = 0 and t = 0. 

     delr = -c * delt / R(t) 
          = -c * delt / exp(H0 * t) 
      = -c*delt*exp(-H0*t)
     intl(1, r ,r...r0) = -c * intl(exp(-H0*t), t, t...t0) 

     r[r...r0] = -c*(exp(-H0*t)/(-H0))[t...t0] 
               = (c / H0) * exp(-H0 * t)[t...t0] 

      - r0 = (c / H0) * exp(-H0 * (t - t0)) 
     r - 0 = (c / H0) * (exp(-H0 * 0)-exp(-H0 * (t0))) 
           = (c / H0) * (1 - exp(-H0 * t0)) 


     Z+1 = exp(H0 * t) 

     Z = exp(H0 * t) - 1 
       = 1 - (1 / exp(H0 * t)) 
       =  1 -exp(-H0*t) 


     r = (c / H0) * Z 
       = c * Z / H0 

    r! = c * Z / H0 

 | GOLD MODEL                        | 
 |                                   | 
 | r! = (c / H0) * (1 - exp(-H0 * t))| 
 |    = c * Z / H0                   | 
 +-------------      ----------------+ 

    In the bigbang there is a horizon beyond which we can not see; it 
is that proper distance for Z = infinity. In the Bondi-Gold model 
there is no such limit. The entire universe, to infinite distances 
away, is visible to us! And this is not just in theory but also in 
practice. For with the infinite life of the universe and the sameness 
of its characteristics everywhere we should see events which occured 
eons and eons and eons ago. 

Luminosity Distance
    This follows directly from

     r& = r! * (Z+1) 
        = c * Z * (Z+1) / H0 

    r& = c * Z * (Z+1) / H0 

 |                         | 
 | r& = c * Z * (Z+1) / H0 | 

Angular Diameter
    This comes from

     theta0 = s0 / r! 
            = s * (Z+1) / r! 
            = s * (Z+1) / ( c * Z / H0) 
            = s * (Z+1) * H0 / (c * Z) 

 |  GOLD MODEL                       | 
 |                                   | 
 | theta0 = s * (Z+1) * H0 / (c * Z) | 

    Note what happens when Z -> infinity. (Z+1)/Z -> 1 and theta0 -> 
s*H0/c! That is, the angular diameter in the Bondi-Gold scheme 
approaches a minimum but remains finite at infinite redshift. 

Curvature of space 
    The perfect cosmological principle requires that the curvature of 
the steady state universe be fixed. Whence 

     k^2 / R = constant 

     k^2 / (exp(H0 * t)) = constant 

This relation is statisfied only by k = 0, so both sides are in deed a 
constant. Thus, the curvature is zero and the universe is flat. 

 |                           |
 | k^2 / (exp(H0 * t)        | 
 |    = constant             |  
 |                           | 
 | k = 0                     | 

Deceleration Parameter
    The steady state has an ever increasing expansion over time so we 
suspect that the deceleration parameter is negative. 

     q = -R * 2der(R, t) / (1der(R, t))^2 
       = -exp(H0 * t) * (H0 * H0 * exp(H0 * t) / (H0 * exp(H0* t ))^2 
       = -(H0 * exp(H0 * t))^2 / (H0 * exp(H0 * t))^2 
       = -1 

 | BONDI-GOLD MODEL                     | 
 |                                      | 
 | q = -R * 2der(R, t) / (1der(R, t))^2 | 
 |   = -1                               | 

Comparison with Acceleration/Energy
    When we looked at historical models we derived certain properties 
of the steady state universe by starting with the acceleration and 
energy equations. We did this to maintain a aprallel anaylsis across 
the several modles. In the Bondi-Gold model LAMBDA was 0; k, 0; and q, 
-1. We got the same results by a direct analysis with no reference to 
any energy or acceleration conditions; LAMBDA is omitted by premise. 
In substance we are really talking about the one and the same 

Continuous Creation 
    One signal feature of the steady state theory is the continuous 
creation of new matter all over the universe. This mass maintains the 
fixed rho0 within the expanding volumes of space. This contrasts with 
the bigbang theory which holds that all the matter was created at once 
(over a few minutes or so) right after the bigbang and remained 
essentially fixed thereafter. 
    The rate of this creation is fantasticly small, two Suns in the 
Milky Way and nearby space per century. 
    The natural question about continuous creation is: Where does the 
new mass come from? It comes from the same source as matter does in 
the bigbang universe -- nothingness. Natus ab nihilo est. 
    Some commentary on the steady state theory mistates that the theory 
forces a cementbound universe with no changes at all. This is absurd 
because it is manifest that changes do occur. Stars, for instance, are 
born, live, and die. What does not change is the gross overall at-
large view of the universe. If we looked at it several billion years 
ago it would look the same as now. There would be then old and new 
stars in the same mix as we find them now. 

Nature of the New Matter 
    At first there was no description for this new matter, a 
shortcoming that almost killed off the Bondi-Gold theory from the 
start. In 1964 Hoyle & Narlikar did work up a physical scenario for 
the new matter based on the maturing atomic physics. 
    Hoyle & Narlikar postulated that the new matter is neutrons. These 
neutrons then start to decay into protons. However, from this mix of 
native neutrosn and nascent protons nucleosynthesis could not procede 
unless the temperatures and densities approximate those required in 
the bigbang theory. 
    The thinking goes that the neutrons are created in bursts and as 
they decay they emit electrons at very high energy. These electrons 
heat the cloud of neutrons to the billionish kelvin to start the 
nuclear formation. Elements thru helium are formed in this process and 
the heavies are later formed by stellar processes. 
    In essence the universe perpetuates itself by a continuous series 
of little bigbangs all over space. Each one by Hoyle & Narlikar is  
the mass of a cluster of galaxies. Hence, the universe can not be 
perfectly uniform, as the bigbang wants, but is a patchwork of dense 
and sparse portions. Galaxies are bunched up in places and thinned out 
in others. And howevr far we look we should still see this largescale 
structure and not see it tend toward perfect smoothness. 
    Observations are still ambiguous on this smoothness. Some show the 
universe has ever larger and farther texture while others show a 
gradual shift from roughness nearby to far off long ago smoothness. 

Formation of Galaxies 
    By Hoyle & Narlikar the galaxies form around the sites of 
continuous creation. Suppose from an earlier period there is a 
expanding local cloud of matter, which a galactic cluster does 
resemble. From the continuous creation a new mass m' is created in the 
center of the cloud at the moment the cloud has radius r'.
    Because now the cloud is more massive by m' its expansion is 
slowed and there is a maximum radius to which it can swell. By gaging 
the sizes and masses of galaxies, m' is order one billion solar masse 
and r' is 1/100 to 1/1000 the radius of a galaxy. Some astronomers 
believe that the supermassive cores found in many, mostly elliptical, 
galaxies are the new masses formed under the steady atete theory. 
    An extension of the continuous creation theme was proposed by Arp 
in the 70s. Quasars, according to Arp, are physicly attached to 
obvious galaxies. They are connected by bridges and filaments or 
neatly lined up with the galaxy, showing that the quasar and galaxy 
are at the same distance away. But the quasar emits radiation and has 
mass both of galactic order. Perhaps these are subsidiary seats of 
creation attendent to the main one within the galaxy? 

    In 1993 Burbige joined Hoyle & Marlikar to invent a new method of
matter  creation. In this scheme, mass circulating near blackholes is
strongly distorted and excited into intense readioemmision. This, by
applying quantum physics can produce new matter. The radiation then
expells this mass into space where it condenses into galaxies &c. The
blackholes are postulated to be of galactic cluster mass spotted here
and there thruout the universe. Hence, each creates a cell of expanding
space from its own 'minibang' of order a billion lightyears in radius.
By this mechanism, they argue, the prinicpal features of the bigbang can
be produced without invoking a singular inaugural event.

Cosmic Microwave Radiation 
    Steady state advocates never call this a 'background' radiation. 
For its origin is current in time and place. There is, by them, 
nothing to be learned about the 'early days' of the universe thru 
examination of this radiation. It is nothing more than ordinary 
starlight and other radiation from galaxies (and other denizens of the 
deepspace) everywhere that has been diffused by cosmic fog. 
    This diffusion thermalizes the radiation into a Planck spectrum 
and just happens to end up as 2.7K microwaves. The principle agent for 
diffusion is a pervasive mist of fibers consisting of strings of iron 
atoms a few microns long. In laboratory tests these fibers can thoroly 
destroy all initial signal passing thru them and turn it into a 
homogenized blackbody flux. The fibers supposedly come from supernova 
explosions. When the star blows up the iron in the core is fragmented 
and dispersed as chains of atoms.  
    Note well that the mechanism for achieving this temperature is 
quite different in the steady state system than in the bigbang system. 
In the bigbang regime the temperature is an original high one at the 
dawn of the universe that is redshifted by expansion during the 
intervening eons to the low one we now see. In the steady state scheme 
the radiation is locally generated and merely diffused and thermalized 
to the low temperature. Expansion over immense timespans has nothing to 
do with the cosmic microwave radiation. 

Helium Abundance 
    The mix of helium in the universe is extremely critical to both 
the bigbang and the steady state enthusiasts. For the steady state 
people there is no ordained mix of helium; it is merely what ever is 
observed. For the bigbang camp the helium is constrained by the 
circumstances in the photospheric period. By all current calculations 
this ratio can not be less than 21%; all bigbang models produce this 
amount as a minimum.
    Hoyle & Narlikar ran the energy-temperature analysis backward from 
the observed microwave radiation temperature to arrive at the percent 
of helium in the universe. 

     u = (7.5613E-16j/m^3.K^4) * T^4 
       = (7.5613E-16j/m^3.K^4) * (2.735K)^4 
       = (7.5613E-16j/m^3.K^4) * (55.95K^4) 
       = 4.23E-14j/m^3 

This is the actually observed cosmic microwave density and it further
more represents the binding energy of helium generated in the creation 
sites. So 

     rhoHelium = u / (0.007 * c^2) 
               = (4.23E-14j/m^3) / (0.007 * 9E16m^2/s^2) 
               = 6.71E-29kg/m^3 

Compared to the total density

     ratioHelium = rhoHelium / rho 
                 = (6.71E-29kg/m^3) / (4E-28kg/m^3) 
                 = 0.17 

The universe by the Hoyle & Narlikar approach should have but 17% 
helium. But via this method there is nothing wrong with such a low 
ratio. That considerably more is found in most stars is not a worry; 
there surely are regions with far less helium in intergalactic space. 
    But this ratio is far too low for any bigbang scheme. These 
require at least 21%. Now, supposedly there are stars and clouds in 
space which do show only 22%, 21%, 20% helium. While the data are as 
yet uncertain there is the prospect that we will discover regions of 
space with under 20% of helium. Since the bigbang posits that the 
helium is of primoidal origin, there could be a conflict. Not enough 
was made according to the present theories of the bigbang. 

No Cosmology?
    The steady state, in all its variations, works to move the study
of the universe from a distinct branch of astronomy into the realm of 
mainstream astrophysics. The features of the bigbang are produced in 
accessible sites within range of observation, and not in some longago
and invisible cataclysm. Hence, there is no need for a separate science
of 'cosmology'. The whole evolution of the universe becomes applied
astrophysics, malleable under the tools of that discipline.
    That cosmologists absolutely do not relish the idea of losing their
own university departments and being placed subordinate under regular 
astrophysicists is understandable!

Closing Remarks 
    The steady state theory enjoyed respect in the 1950s and early 
1960s with the standoff between Gamow for the bigbang and Hoyle for 
the steady state. Both championed their ideas in the academic and 
popular press. A generation of astronomers grew up in this period on 
the two meterstone books 'Creation of the Universe' by Gamow and 'One, 
Two, Three,...Infinity' by Hoyle. 
    The rivalry between the two span off international rivalry. Hoyle 
and most of his supporters ruled in Europe while Gamow and his allies 
ruled in the United States. Thru all of this time the Soviet Union 
stood apart. Its ideology banned any cosmology and declared that the 
cosmos was nothing but the ultimate frontier for Communist domain. 
    It was Hoyle who mocked the Gamow theory of element creation under 
superhot conditions by terming it a 'big bang' theory. Yet this term -
- long ago condensed into one word -- instantly became the official 
name for the standard model! To be historicly correct we may refer to 
it as the Friedmann-leMaitre-Gamow model after the three majoe persons 
who in their turn assembled it. 
    Since Gamow there were armies of astronomers and physicists who 
studied the bigbang model and added to it a deep litterature. Much of 
the work was funded from the deep pockets of atomic research and 
Hollywood-style popularizers.
    The steady state theory, on the contrary, suffered from its short 
period of interest so it never had the chance to elaborate like the 
bigbang theory. The litterature is spotty and many aspects were never 
adequately explored. The intimate details of continuous creation, 
along with the resultant abundance of the elements, under a steady 
state regime remains an unfinished project. The microwave cosmic 
radiation is explained by a mechanical process involving supernovae 
which is still unproven. Nothing of the iron fibers was, for instance, 
found in the supernova of 1987 in Nubecula Major. Most astronomers 
leave the Bondi-Gold model alone as a curious but obsolete idea and 
modern works on cosmology give only passing reference to it. 
    Many many nonbigbang ideas were put forth in the later years of 
the 20th century. Yet not one ever was as deeply and broadly worked 
out as the bigbang. All too commonly they were adversary, emotional, 
qualitative, and sociological, with little cohaerent science. It was 
impossible to build on them into a true theory of the universe. In 
fact, many were never subjected to scientific inquiry but were 
promoted thru popular treatises. Many focused on a one or an other 
cosmological problem and ignored the rest of the universe. 
    Largely because of ineffective challenges to the bigbang, most 
astronomers ignore nonbigbang ideas altogether. The chances that this 
or that new one is merely an other halfbaked omelette is too great. 
    Perhaps the steady state theory is actually outdated and must be 
set aside. This does not mean the bigbang is the one and only correct 
description for the universe, as if it 'won' the war between the 
theories. It only means that if there is a credible alternative to the 
bigbang, the steady state model may not be it. An other, as yet 
unformed, theory may come along in the stead. Or with better 
observations we may actually find that the bigbang theory is the true 
way of life.