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 petemperature. 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). +------------------------------+ | SCALEFACTOR FUNCTION OF TIME | | IN THE BONDI-GOLD MODEL | | | | 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. Redshift ------ 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! +--------------------------+ | COSMOLOGICAL REDSHIFT IN | | THE BONDI-GOLD MODEL | | | | 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] Or - r0 = (c / H0) * exp(-H0 * (t - t0)) r - 0 = (c / H0) * (exp(-H0 * 0)-exp(-H0 * (t0))) = (c / H0) * (1 - exp(-H0 * t0)) But Z+1 = exp(H0 * t) Z = exp(H0 * t) - 1 = 1 - (1 / exp(H0 * t)) = 1 -exp(-H0*t) Hence r = (c / H0) * Z = c * Z / H0 r! = c * Z / H0 +-----------------------------------+ | PROPER DISTANCE IN THE BONDI- | | 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 +-------------------------+ | LUMINOSITY DISTANCE IN | | THE BONDI-GOLD MODEL | | | | 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) +-----------------------------------+ | ANGULAR DIAMETER IN THE BONDI- | | 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. +---------------------------+ | CURVATURE OF THE UNIVERSE | | IN THE BONDI-GOLD MODEL | | | | 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 +--------------------------------------+ | DECELERATION PARAMETER IN THE | | 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 universe. 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? Minibangs ------- 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.