Time Travel Research Center © 2005 Cetin BAL - GSM:+90  05366063183 - Turkey/Denizli 

Manyfold and Pre-Bang Universes

Superstring teory predicts the universe has ten or eleven dimensions. Why don't we see these extra dimensions? Perhaps we are living on a brane (short for membrane) - floating in a space of five, six or more dimensions, like a soap bubble in the bathroom. The "manyfold universe" theory asserts that the brane we live on could be folded over on itself many times, accordion-fashion (see diagram). Light could travel only on the brane, but gravity could take a shortcut by jumping from one fold to the next. Nearby matter on other folds can be detected gravitationally as dark matter since the light it emits takes a long time to reach us traveling around the fold (see Figure 01).

Figure 01 Manyfold Universe

In 3-dimensional space the gravitational force between two mass m₁ and m₂ is (see Figure 02):

F = Gm₁m₂/(r₁₂)² ---------- (1)

where r₁₂ is the separation between the two masses, and G = 6.67x10^-8 cm³/sec²-gm is the gravitational constant defined in the 3-dimensional space.

If the gravitational force spreads over to n additional dimensions, which curl up into circles with radius R, then the force would be:

F = G'm₁m₂/(r₁₂)²⁺ⁿ ---------- (2)

where G' is the gravitational constant corresponding to the case with n additional dimensions.

Starting from the source, the lines of force spread apart rapidly through all the dimensions. At distance larger than R, the force lines have filled the extra dimensions, which then cease to exert further influence (see Figure 03). Consequently, we can equate Eq. (1) and (2) at the distance R and obtain:

G = G'/(R)ⁿ ---------- (3)
 

		which states that the value for the gravitational constant G is the result of modifying the original value G' by a factor 1/(R)n. Since the law of gravitation has been experimentally tested down to distances of only about a millimeter, we would be oblivious to changes in gravity caused by extra dimensions for which R was smaller than this size. It is found that if there is only one extra dimension (n = 1), R must be roughly the distance between the earth and the sun. Therefore, this case is already excluded by observation. For n = 2, R can be in the millimeter range and G' would be large enough to allow the production of gravitons1 copiously at energy of a few Tev.
Figure 02 Gravitational Force	Figure 03 Extra-dimension

The concept of branes floating in higher dimensional space has offered some new ideas about condition at the moment of Big Bang and further back to the time before the event (see Figure 06). According to general relativity, density and temperature become infinity at the moment of Big Bang. The nonzero size and novel symmetries of strings set upper bounds to physical quantities that increase without limit in conventional theories, and they set lower bounds to quantities that decrease. The string theory expects that the curvature of space-time increase as the history of the universe is re-winded backward in time. But instead of going all the way to infinity, it eventually hits a maximum and shrinks once more (see Figure 04). The string theory also proposes some hazarded guesses about the pre-bang universe. There are two popular models floating around - the Pre-Big Bang and the Ekpyrotic scenarios.

Figure 04 Two Views of the Big Bang

		The Pre-Big Bang model was developed in 1991 by combining T-duality with the symmetry of time reversal. The combination gives rise to a cosmological model in which there was a period of acceleration before the Big Bang and then the deceleration. The Big Bang was simply a violent transition from on phase to another (see Figure 05). The other model is the Ekpyrotic (conflagration) scenario. It relies on the idea that our universe is one of many D-branes floating within a higher-dimensional space. The branes exert attractive forces on one another and occasionally collide. The Big Bang could be the impact of another brane into ours as shown in Figure 06.
Figure 05 Pre-BB	Figure 06 Ekpyrotic Model

           D- brane

¹Gravitons are the messenger particles which carry the gravitational force in quantum theory. They play a part in quantum gravity analogous to the role of the photons in quantum electrodynamics. In the theory of superstring gravitons are represented by tiny closed loops, which can wander into all the dimensions because unlike most of the other particles they have no end points anchoring to a  D-brane  or Dp-brane ('p' is an integer which is the number of spatial dimensions of the manifold), which is a special class of branes called Dirichlet branes. The name derives from the boundary conditions assigned to the endpoint (of open string) which is fixed to move only on some manifold.

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