VIII. Must There Have Been A Hot Big Bang?
The theory of the big bang for the evolution of the Universe was first conceived in the 1920s, 50 years before there was any body of observational data to support it. Space probes and the Hubble Space Telescope have begun to provide a large amount of new data over recent years, unexpected before. It is, then, interesting to ask what form the big bang theory might have taken had these data been available 80 years ago. Would another theory now hold sway?
The Hubble Law
The observations of galaxies made in the 1920s using the then new 100 inch telescope at Mount Wilson and its associated advanced technology led to the conclusion that the spectral lines of galaxies are generally shifted towards the red end of the spectrum. More than this, Edwin Hubble established that the degree of the red shift for a particular galaxy is proportional to its apparent luminosity, and so to its distance. This result is shown in Figure 1. Corrections have been made to account for the motion of the Earth relative to the Sun and to the motion of our Galaxy towards the Virgo cluster. The red shift is universally accepted to be a Doppler shift. The interpretation that the galaxies are moving apart with a speed, v, proportional to their distance apart, R, is called Hubble’s law and can be written
v = dR/dt = HR (1)
where H is Hubble’s parameter. It is sometimes called a constant because it applies to every galaxy we see at the present epoch (when it is denoted by Ho) but it is really a function of the time and will change with the epoch.
Figure.1. The linear plot of the redshift, z, of the spectra of galaxies against their apparent distance out to about 600 light years (Hubble).
The galactic distances were found initially from measurements of the time periods of Cepheid variable stars. This restricted the measurements to the nearer galaxies only where the variable stars could be discerned. More recently a wider range of distance measures has confirmed the law to the greatest distances measured so far. The slope of the straight line in Figure 1 gives the value of the Hubble constant, Ho, at the present epoch. There has been considerable uncertainty about its numerical value in the past due largely to uncertainties of the distance scale. The galaxies also show a random motion which is difficult to quantify. The best modern value is probably Ho = 72 km per second per megaparsec which can be written alternatively Ho » 2.3x10-18s-1. The inverse gives a characteristic time 1/Ho º to = 4.3x1017s-1 » 1.4x1010yrs. This is the time from zero red shift.. The big bang theory accepts this as the present “age of the Universe”, from the moment the initial expansion began. This also marks the zero point for both time and space. The expansion is presumed to have been monotonic from the start. We leave the physical significance undefined for the present
Visible and Hidden Masses
Our Galaxy contains some 1011 solar masses and it is estimated that there are some 1011 galaxies in the observable Universe. This means a nominal total mass of 1052 kg or an equivalent energy of 1069J for the Universe. The visible local mass is not known with any certainty. Oort, a reliable observer, estimated a mean (smoothed out) material density rm(oort) » 3x10-28 kg/m3 although some modern observers are inclined to a higher value, even an order of magnitude higher rm » 2.3x10-27 kg/m3. Either way, the smoothed out density is low. It is, anyway, almost certainly a vast underestimate because new galaxies are being discovered even locally as new energy ranges are explored.
The visible mass is not the only type present. The rotational stability of individual galaxies cannot be accounted for on the basis of normal mechanics if only the visible matter is included. The outer regions provide less angular momentum than it necessary and this implies that there is indeed invisible gravitating mass there. This strange conclusion is confirmed in other cases. Galaxies form clusters of very large numbers, each involving a random motion. This would cause the group to disperse. The total “visible” gravitational energy is insufficient to hold the cluster together, implying the presence of mass that is invisible. Mass is in gravitational interaction with light beams and observed galaxies show a “lensing effect” due to this interaction. To be fully understood the distortion of radiation due to either single or several galaxies requires more mass than can be seen. The nature of this dark matter is unknown but it must be in strong gravitational interaction with normal matter and physically lie near it. One computer simulation is shown in Figure 2 which predicts the distribution of visible and dark matter necessary to achieve a dynamical equilibrium for the galaxies involved. The dark matter appears widespread. Visible matter is apparently only a minor fraction of that actually there, probably no more than a few percent. This could imply a combined mass of as much as 3x10-27 kg/m3 if Oort’s density is taken, or greater if other estimates are used. It is also presumed that the dark matter would show a red shift of the same type as the local visible matter (were it visible) and that in fact they expand together.
Figure 2 A simulation of the distribution of dark matter (grey) associated with normal galaxies (coloured dots)to provide an equilibrium distribution of normal matter.
In the late 1930s Adams and Dunham observed unexpected interstellar absorption lines in the blue part of the spectrum. This was interpreted by several authors as arising from transitions between rotational levels of interstellar CH, CH+ and CN. In 1941 McKellar indentified the effect as arising specifically from the J = 1 rotational level of the ground state due to radiative excitation from the J = 0 level. The relative intensities of the observed spectral lines can be accounted for if the exciting radiation is black body with a temperature of about 2.3K. Such radiation is in the microwave region of the spectrum. This black body background radiation was rediscovered, in 1963 though more directly this time, by Penzios and Wilson who found the equilibrium spectrum corresponded to a temperature of very closely 2.73K. It is isotropic to fine limits, the temperature being uniform to within a few thousandths percent so that deviations from the mean are in microkelvins. It is well known in thermodynamics that a system that has achieved thermal equilibrium has lost all information about its origins. This will apply also to the background radiation. It is necessary, in these circumstances, to have a source which is present and immediately linked with the equilibrium that is observed. McKeelar’s effect does this.
The cosmic chemical abundance of the elements shows that the proportion of helium is closely ¼ that of hydrogen, the two elements accounting for 98% of the whole. Taking the Oort estimate for the density, r(He) = 0.25x0.98x3x10-28 = 7.35x10-29 kg/m3. It is known that the conversion of 1 kg of hydrogen into 1 kg of helium releases 6x1014J. The energy released is then 7.35x10-29 x 6x1014 = 4.41x10-14J. This is precisely the energy required to excite the interstellar molecules available for absorption by interstellar molecules to provide radiation with the characteristics of the microwave background radiation. Numerical coincidences must not be assumed to have special significance at this stage of the general argument. The important point is that a valid physical explanation of the origin of the microwave radiation is possible which is alternative to the assumption of it being a relic of the big bang.
Radiation contains energy,e, and so mass, m = e/c2. The energy in the microwave radiation is e = aT4 = 7.56x10-16 (2.73)4 = 4.2x10-14J. The associated mass is m = aT4/c2 = 4.6x10-29 kg/m3. This mass is at least one order of magnitude lower than the combined masses of visible and dark matter. A recent representation of the cosmic radiation is shown in Figure 3 noticing that the scale is microkelvin. The isotropy of the radiation is clear. The Galaxy is moving towards the Virgo cluster and this is reflected by an increase of temperature of 3.5 mK in that direction with a decrease of 3.5 mK in the direction 180o away. Detailed studies of the temperature pattern show no repetition. This, with the strong isotropy, is consistent with a flat geometry (k = 0) at least locally, since curvature would provide it own distortions and a closed (spherical) geometry would undoubtedly provide a repetitive pattern.
Figure 3 Recently measured portion of the cosmic microwave background radiation. The scale on the right is in microkelvins.
This stability is characterised by the equality between the kinetic energy K and the gravitational energy V. The total energy k is given by k = K + V = 0. For a galaxy of mass m and distant R from the centre of a spherical array, using the Hubble law the kinetic energy of its motion would be K = m(HR)2/2. The gravitational energy would be GMm/R, where M is the mass of the galaxies with distances less than R. Equating these two expressions, for k = 0, and introducing this critical density c gives
rc = 3Ho2/8G.
Putting numbers into this expression gives the critical value rc » 10-26 kg/m-3.
Another substantial energy source has been discovered recently. The furthest observed objects are less bright than expected suggesting they are further away than would be predicted by the Hubble law. Apparently, the galaxies are speeding up against gravity and have a higher acceleration than would otherwise be expected. There is, apparently, an energy forcing matter apart. This so-called dark energy opposing gravitational attraction is associated with a mass sufficient to raise the mean density to the critical value (k == 0) rt » 10-26 kg/m3. It is as if “nothing” has crystallised into a kinetic (movement) and a gravitational (attractive) component. giving zero net energy.
Stellar Populations
Although stars are composed primarily of hydrogen, heavier chemical elements are present in small proportions as well. The heavier elements are formed during supernova events and ejected into the surrounding space. The gas forming the next generation of stars is polluted, which consequently have a higher proportion of such elements. In this way the composition of stars evolves with time. It is implicit that the earliest stars had a more elementary composition presumably with no heavier elements at all. There is not a continuous spread of stellar types but three groups can be recognised, two of which have certainly been observed and the third perhaps has as well. These three groups are called Population I, II and III stars. The details are as follows.
Population II stars: these are older stars, like the Sun, with a small proportion of heavier elements (said to be low metallicity). Stars in globular clusters also fit into this category;
Population I stars: these are massive stars which have recently formed from dust clouds and have a higher proportion of heavier elements (high metallicity);
Population III stars: which are presumed to be the founding stars with a pure hydrogen composition.
The evolution of Population I and II stars is believed to be well known. They are associated with internal temperatures of the order 107K and rather higher, leading to the internal conversion of hydrogen to helium and on up to iron for the heavier members. A Population III star has not yet been definitely found and this would imply that their life time is very short. They may evolve from birth to death in as little as 106 years which would imply a mass of as large as 106 solar masses. The dynamics of such massive stars is unknown. The collapse of the star when it energy source is used up will certainly release enormous quantities of energy, in the g-ray region of the spectrum. Objects releasing energy of this magnitude have been observed recently, distributed over the sky and so well outside our Galaxy although they have not been recognised as Population III stars with certainty. A red shift implying a distance of 109 light years has been estimated but the red shift may well contain a dynamic component masking them closer to Earth than might otherwise seem to be the case.
Separately from this, young stars of very large mass have recently been discovered in irregular galaxies much nearer our Galaxy. One example is the star forming region in NGC 6822 called Hubble V, shown in Figure 4. Each star has a luminosity in excess of 105 solar luminosities. If the conventional stellar theory is applicable this could imply a mass in excess of 10 solar masses. Such irregular galaxies appear to have many features in common with those of the very early Universe and are being studied with the hope of giving some insight into stellar formation then.
There are other objects involving substantial energies such the centres of active galaxies and quasi-stellar objects (QSOs) are among these. The red-shifts associated with them may be partly extrinsic (due to rapid motion) rather than intrinsic (movement with the cosmic background). On this basis, a large red shift need not imply a great distance from us.
Figure 4 The star forming region Hubble V in NGC 6822, 1.5 million light years away (NASA)
Interpretation of Hubble’s Law
The implication associated with Figure1 is that the volume occupied by the Universe in the past was systematically smaller than the volume now. There is no direct indication of how small that volume can have been. The central constraint is the need to account for the evolution of the Universe as a whole. It is necessary to remember that our knowledge of the Universe is still incomplete but new technological advances continually improve the situation and show new features. This implies a continual development of the details of the evolutionary process. It must be remembered that there are also sociological prejudices to guide the exploration at least initially. One such requirement is that there must be a definite “beginning” to the Universe: this needs the extrapolation of the Hubble law back to zero time marked by a singular (zero) volume. The characteristic time associated with the Hubble law is on this basis interpreted as the present age of the Universe which would be 1.4x1010 years. For comparison, the age of the Sun and the Solar System is probably 4.5x109 years, the age of the oldest stars in globular clusters is estimated as 1.2x1010 years on the basis of the theory of stellar structure. There is no present contradiction between astronomical measurements and the Hubble assumption of the age of the Universe. The greatest measured distance is about 0.85 of the maximum: there is no observational evidence before that.
This approach allows all the evolutionary features of the Universe to be accounted for in a simple and natural way. Observations have not yet penetrated to the earliest times so it is not yet possible to describe conditions before about 1010 years ago. Galaxies appear to be very numerous at this early time. Future observations can be expected to clarify this situation.
Comparison with the Big Bang Hypothesis.
The raison d’être of the big bang approach is to provide an early period where the less massive chemical elements can form from hydrogen. The essential requirement is a prolific source of neutrons and this is presumed to result from a high temperature associated with a strong compression (small volume) to allow rapid interactions. It is a central assumption to relate the evolution of the Universe explicitly to a singular beginning (R = 0, t = 0). There is, of course, no direct observational evidence that this was so. According to the theory, the material composition of the Universe was fixed during the first 3.5 seconds of the expansion. The light elements had formed by 350,000 years. This is the stage where matter and radiation are assumed to become uncoupled, leaving the matter and radiation to expand separately. Needless to say, all these processes are outside observational confirmation and are entirely hypothetical. Other explanations for the presence of matter and of radiation are now available.
Models of the Universe with this characteristic have been derived from general relativity which expresses the distribution of mass and energy in terms of the curvature of space-time. Geometry is a fundamental aspect. This provides the two constants that must be assigned, associated with the type of geometry assumed. One is written k and can take one of the three values k > 0 for a spherical geometry, k < 0 for a hyperbolic geometry, and k = 0 for a flat (Euclidean) geometry. A Newtonian interpretation is possible with k as the total energy of the matter and radiation. Infinite values of the co-ordinates are avoided if the geometry is assumed to be spherical (k > 0), the volume then being finite but unbounded. The second constant arises because the metric is defined only to its divergence, leaving an arbitrary constant, called the cosmological constant and denoted by L. This represents a repulsive force acting against gravity. It was first introduced by Einstein to account for the apparent static form of the Universe observed at that time, against the attraction of gravity. The recognition of a dynamic Universe allows an equilibrium but now where the attraction of gravity is balanced by the kinetic motion of the matter. L remains today representing the dark energy which accelerates the universe.
The big bang theory is the source of many mysteries. The present observed homogeneity and isotropy in the Universe is an embarrassment which is overcome by the additional hypothesis of space-time inflation. The volume is supposed to have expanded by a huge factor after perhaps some 10-64s from the start of the expansion. The theory does not explain what caused the expansion nor how it was switched on and turned off. The initial time scale is always very short by normal standards, being the scale of high energy physics. One consequential idea off-shoot is the idea of multiple universes but this cannot be included in scientific discussion. There is also a suggestion that the speed of light in vacuo may not be the ultimate speed, at least in the initial period of the expansion. This would, of course, undermine the basis of special relativity. All these exotic problems arise entirely because of the unsupported assumption of a hot early region for the high-energy formation of the chemical elements. There is no indication where the material came from that formed the universe nor why the expansion took place.
One might guess that, were we starting from the present knowledge, there would be a reluctance to resort to a basic hypothesis such as the hot big bang model. The hot, singular beginning is not inevitable. Further observational data (perhaps involving the study of gravitational waves if they are eventually observed) could clarify these matters. The future, as usual, will be interesting.
Copyright G.H.A. Cole, 2002, Last Updated 7/04/02