Gravity and the Beginnings of the Universe
by Nigel Tolley
07/06/2005*
There is dichotomy in cosmology. If we ponder the theory of the creation of the universe, the "Big Bang". According to current theory, all the matter and energy in the Universe appeared from this single event. How?
A major issue for many years has been the "missing mass" that is required to explain the current rate of expansion of the universe, following the big bang. So far, attempts to explain the short period of rapid expansion from singularity to a universe roughly the size of a basketball, have invoked all sorts of weird effects and ideas, such as M symmetry and SuperString Theory.
The paradox is brought about by Einstein's Theory of Relativity, which gives the result that if enough mass is concentrated in one place the force of gravity resulting is strong enough to curve space-time itself and forms a singularity known as a black hole, a body with a gravitational field so strong, even light itself cannot escape. The use of the Schwarzschild radius to argue that a black hole cannot form only hold true for a few moments of expansion0.
Once the density drops due to the expansion, we must seek another mechanism. If that much matter were in one place then, according to our current theories, the Universe would simply have remained a black hole, or if it were not a black hole, it would rapidly have become one.
Some have used this to attack the big bang theory, and others have used it to attack relativity (or rather, some aspects of relativity).
However, there is a way forward. Using currently accepted theories of physics, we can explain this and indeed we can also ponder the creation of gravity itself. A little-known result of relativity is that if we have two infinite flat plates which are parallel to one another there is no gravitational attraction between them1. Now consider the early universe. Imagine that it was the size of a basketball A, and perfectly spherical.
Fig. 1- A spherical, closed universe, from the outside
Due to the curvature of space-time, due to the universe being closed, an infinite parallel plate would of necessity be both constrained and unconstrained by the curved boundary of space-time. If the universe is in a totally homogeneous state2, to an observer at the point C, at the center of the spherical universe, an arbitrary plane through that center point will form two infinite, parallel plates. The universe is isotropic around C. To an observer outside the universe, who can see the bounds of space-time, of course, the plates do not appear infinite, as the outer observer is not bounded by Euclidean geometry.
Fig. 2- One infinite plate as seen from the other infinite plate by an outside observer
Under these conditions any plane which intersects the central point would have an effectively infinite mass on either side and it would appear to the observer in real Euclidean space to be infinite.
Figures 3 & 4- The plane can be at any orientation through the point C
This plane could be oriented in any fashion and the same thing would be true, therefore at the center (or the origin) of the early universe, there was no force of gravity acting upon the point from which the universe came into being. With no gravity to constrain the expansion, the universe grows rapidly. This can also be inferred logically, since if gravity did exist, the net effect at the point C would be zero, since the attraction would be the same from all sides. An analogue of this can be seen with net electrical charges inside a conducting sphere.
Fig. 5- With no gravity to constrain the expansion, the universe grows
If we now assume that this state of affairs continues right the way back until just before the universe was a singularity, it can be reasoned that any source of expansion from that origin (as long as it was equal in all directions) would result in the universe expanding very rapidly and, according to our relativistic flat plates theory, unencumbered by gravity. As the universe expanded it would have been homogeneous and hence no matter its size there would still have been no effect from gravity until clumping began.
Fig. 6- A defect appears
The very instant that any inhomogeneity appeared gravity would effectively be created, and would instantly begin to act to slow the expansion of the universe. However, if it was a single, point event, the flat plate scenario could continue, for at least a short time. If we now arrange our plane to divide the defect, whilst still passing through the center, we see that the gravitational effect occurs only on other planes, and not on this one.
Fig. 7- The plane can be re-aligned
Fig. 7- The universe continues to expand along the other axes
Of course, the inertia of the universe would continue the expansion, and the fabric of space time would continue to expand along those planes where gravity was still nullified by the effective presence of parallel plates, and gravity would rapidly assert itself on the expansion. How rapidly depends, of course, on your thoughts on the speed of gravity.
Figure 8 – a second inhomogeneity appears
Of course, the second inhomogeneity can appear at any point in the universe, and may, indeed, have been a ripple effect, as the point inhomogeneity grew. This would further skew the shape of the universe. Eventually, by whatever mechanism, there would no longer be a plane of symmetry, and gravity would be extant everywhere. The external shape of the resulting universe could, therefore, be calculated if the locations of the “defects” were known.
Fig. 9- The inhomogeneous universe
Another result which can be inferred from this is that gravity will continue to act upon and within any black hole until it encompasses (swallows) the entire contents of the universe. Once it has done this and compressed all the matter contained in the universe, mashing it together with its incredibly powerful gravitational field, it will begin to remove any differences in the matter, reverting if you like to a primordial quark soup. Once it becomes truly homogeneous about the centre, gravity should in theory cease to be. Unbounded by gravity, the other forces (strong nuclear, weak nuclear and electrostatics) and the extreme temperature will mean that rapid expansion again occurs and the universe is reborn.
As a series of bang:crunches the universe would continue to be reborn then die and then be reborn again consisting of exactly the same components each time, reset through the primordial soup of quarks and electrons. Note the this would continue even in the event of the total heat death of the universe, as long as the gravity was sufficient to pull the universe back to the initial crunch:bang point.
It is of course possible that eventually the initial inhomogeneity that "causes" gravity could come into being so long after the expansion began that gravitational attraction was unable to overcome the expansion, resulting in the universe continuing to expand forever. The absence of enough mass to explain the current patterns of the universe without invoking “dark matter” may be explained.
According to relativity the sum of energy and the matter in the universe is a constant - as the energy increases, the mass decreases, and vice versa. Perhaps if the proportion of matter to energy were correct the universe could reach a steady state.
A. I used the "size of a basketball" to mean that, to a hypothetical outside observer who could see the entire universe at once, the whole universe would be about the size of said ball. Obviously, it could be on any scale, from the sub-atomic to the current size, but as a human reference, a sphere the size of a basketball works well. (to A)
References:
http://www.absoluteastronomy.com/encyclopedia/S/Sc/Schwarzschild_radius.htm The Schwarzschild radius (to 0)
http://newton.ex.ac.uk/aip/physnews.206.html Theory of Infinite Flat Plates (to 1)
http://www.absoluteastronomy.com/encyclopedia/F/Fr/Friedmann-Lema%EEtre-Robertson-Walker3.htm The FLRW model of the universe (to 2)
http://www.absoluteastronomy.com/encyclopedia/E/Ei/Einsteins_field_equation.htm Notes and description of Einstein's Field Equations
* I've been sitting on this idea for a long time, at least three years. I did this today instead of my lock patent, as I needed a break from it!