Gravity in Extra-dimensions, Manyfold and Pre-Big Bang Universes

Contents

Gravity in Extra-dimensions

		be probed or the consequences of quantum gravity experimentally tested. Only in the very early universe are energies on the Planck scale encountered, which is why particle physicists and cosmologists have placed such emphasis on understanding conditions immediately after the Big Bang. A further consequence of gravity's weakness is that the inverse square law of attraction has only been verified at distances greater than 0.1 cm. It is now suggested that the huge disparity in interaction strength is caused by the "leaking" of gravitational field into the extra dimensions as envisioned by the superstring theory. As it will be shown in the followings, these extra dimensions can be as large as 0.1 cm without violating known laboratory, astrophysical, or cosmological
Figure 01a Gravitational Force [view large image]	Figure 01b Coupling Strength [view large image]	data. In this picture, the particles and forces are stuck to a 3-D (3 spatial dimensions) brane sitting inside the extra dimensions, the only force in the higher-dimensional bulk is

gravity. The Large Hadron Collider (LHC) (at CERN, to be completed by 2007) should be able to detect strong quantum gravitational effects; for example, the high-energy particle beam at the LHC can cool by boiling off gravitons into the extra dimensions. More exotic gravitational objects, such as small black holes, can also be produced at the TeV energies available with LHC. In fact the LHC now becomes a quantum-gravity machine, which can look into these extra dimensions of space through apparent violations of energy conservation, as well as the appearance and disappearance of graviton's KK particles from extra dimensions (see Figure 02).

Figure 02 KK Graviton [view large image]

	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). Thus, we can equate Eq. (1a) and (1b) at the distance R and obtain:
Figure 03 Extra-dimension [view large image]

Table 01 Curled-up Size as a Function of n

Table 02 Interaction Strength as a Function of n

Thus, a black hole can be created with such energy packed into the corresponding length scale. Such mini black hole will evaporate in 10-88 seconds, losing most of its mass by Hawking radiation. It is estimated that the final burst should radiate a large number of particles in all directions with very high energies. The decay products include all the particle species in nature. The LHC could provide the first evidence for Hawking radiation from such signatures of the black holes. Figure 04a depicts the simulated decay of a black hole inside a particle detector. From the center of the accelerator pipe (black circle) emerge particles (spokes) registered by layers of detectors (concentric colored rings). The sequence from birth to death of a mini black hole with an initial mass of 10 Tev is shown schematically in Figure 04b. It is created by the collision of two energetic particles (a). The scenario suggests that it will emit gravitational and electromagnetic waves as it settles

Figure 04a Black Hole, Simulation [view large image]

down. It becomes an almost featureless body, characterized solely by charge, spin and mass (b). Even the charge quickly leaks away as the black hole gives off charged particles. At first, the black hole emission comes at the expense of spin (c), so it slows down and

	relaxes into a spherical shape, which is characterized solely by its mass (d). Finally, the mass bursts away in the form of radiation and massive particles (e). The remnant of the black hole approaches the Planck mass and disappears into nothingness.
Figure 04b Black Hole, Evaporation [view large image]

Black Hole in LHC

There were many people who worried about the Earth devoured by a black hole created within the LHC (Figure 04c). In order to forestall the LHC's operation, at least one lawsuit had been filed against CERN and a host of government agencies. Straight forward calculation shows that no black hole would be created by the maximum collision energy of 14 Tev. However, if the universe does possess extra-dimensions as predicted by the theory of superstring, black holes will be materialized depending on the number of extra-dimensions. Even then such miniature black holes will evaporate long before

Figure 04c High Energy Collision at LHC

they are able to suck anything inside. Following is a more quantitative analysis to supplement the assurance (of safety) provided by so many physicists.

• By the equivalence of energy and mass, the LHC maximum energy of E = 14 Tev has a mass of m = E/c² = 2.5x10^-20 gam.



• In quantum theory, the size of such object is determine by the Compton wavelength = /mc = 1.3x10^-18 cm.



• The Schwarzschild radius corresponding to this object is given by r_s = 2Gm/c² = 4x10^-48 cm. A black hole will not be formed as long as the Schwarzschild radius is smaller than the size of the object, i.e., when > r_s.



• As mentioned earlier in the previous section, the gravitational constant G (in 3-dimensional space) can be translated into a length scale of K = 10^-33 cm. Similarly, in extra-dimensional space the length scale is k and the ratio with K can be shown to be k/K = 10^32n/(n+2), where n is the number of extra-dimensions (n = 0 for no extra-dimensions), and the curl-up size R is assumed to be 0.1 cm.



• In extra-dimensional space the Schwarzschild radius is modified to r_n = (k/K)² r_s. According to this formula, a block hole will form for n 2.



• The black hole will become harmless if it evaporates in the form of Hawking Radiation within a time scale shorter than the Planck time t_P = 5.4x10^-44 sec. It is the flight time in between two points separated by the minimum distance in term of the Planck length 1.6x10^-33 cm, which is the most elementary length unit according to the theory of Loop Quantum Gravity.



• In extra-dimensional space the lifetime of black hole t_n = (k/K)^-4 5x10^-87 sec (for the case of E = 14 Tev). The black hole will disappear before sucking up anything if t_P > t_n.



• Table 03 below lists the n dependence of the Schwarzschild radius r_n, the black hole lifetime t_n together with comments on its effect if any. The curl-up size R has no effect on the conclusion. It can be shown that for an arbitrary value of R, (k/K) is modified by a factor of (10R)^n/(n+2). For the worst case of large n, it requires R = 4x10^-87 cm (which is much smaller than the Planck length of 10^-33 cm) to produce a black hole lifetime approaching the Planck time of 3x10^-44 sec. Thus, we can declare that the black hole created by LHC is harmless for all practical cases.




# of Extra Dimensions n	Schwarzschild Radius rn (cm)	Black Hole Lifetime tn (sec)	Comments
0	4x10-48	5x10-87	No black hole formed
1	8x10-27	10-129	No black hole formed
2	4x10-16	5x10-151	Black hole formed, and vanishes harmlessly
3	10-9	8x10-162	Black hole formed, and vanishes harmlessly
4	2x10-5	2.5x10-171	Black hole formed, and vanishes harmlessly
5	2x10-2	2x10-178	Black hole formed, and vanishes harmlessly
6	4	10-183	Black hole formed, and vanishes harmlessly

Table 03 Effect of LHC Black Hole as a Function of n

Manyfold Universe

Superstring theory 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 (Figure 05). 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 unseen dark matter, since its emitting light takes a long time to reach us traveling around the fold (see Figure 05).

Figure 05 Manyfold Universe [view large image]

Pre-Big Bang Universes

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 08). 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 06). The string theory also proposes some hazarded guesses about the pre-big bang universe. There are two popular models floating around - the Pre-Big Bang and the Ekpyrotic scenarios.

Figure 06 Two Views of the Big Bang [view large image]

		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 07). 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 08. The idea has been extended to a cyclic model, in which the two branes are held together by a spring-like force (proportional to separation). The moment of collision (zero separation) corresponds to the Big Bang when matter and radiation are produced. The spring-like force manifests itself as dark energy, which is weak at the moment of Big Bang but becomes increasingly important as the separation getting larger. The dark
Figure 07 Pre-BB [view large image]	Figure 08 Ekpyrotic Model [view large image]	matter is just the material on the other brane interacting with the visible matter on our brane only through gravitation.

		A variance of this inflation inside the Calabi-Yau throat posits that the annihilation of the incoming brane and an antibrane at the end of the throat triggered the Big Bang (Figure 09b). According to this scenario, inflation occurred as the branes approached each other. Annihilation of the branes released vast energy to heat up the universe and to initiate the Big Bang. It is purported that different Calabi-Yau configuration will yield different signature on the cosmic microwave background radiation (CMBR). Thus theoretically,
Figure 09a Calabi-Yau Space [view large image]	Figure 09b Branes Collision [view large image]	the CMBR pattern will determine uniquely the Calabi-Yau manifold for our universe.

Yet another stringy scenario found that the configuration of the extra dimensions can change over from one form to another as shown in Figure 09c. This general process is called moduli inflation because the moduli fields, which describe the geometry (the size and shape of the hidden space dimensions in huge number of possible configurations), act as the inflatons driving the inflation of the observed three dimensions. This model predicts un-observably weak gravitational waves. Thus, it would be ruled out if primordial gravitational waves are detected by observation in the future.

Figure 09c Mo- duli Variation

		becomes infinite and each part of this mother universe now detached from all the others; then the attractive aspect of the dark energy takes over. This causes each island universe to contract, but eventually it gets so dense that its radiation reverses the contraction. We are left with innumerable expanding little universes - of which ours may have been one (see Figure 11).
Figure 10 Black Hole Sea [view large image]	Figure 11 Fragmenting Universe [view large image]

The latest publication on extra-dimensional cosmology appeared in a "Special Collector's Edition, from Scientific American, on Physics at the Limits, 2016" with the title "The Black Hole at the Beginning of Time". It proposes that our 3-D spatial universe is the event horizon of a 4-D (spatial) stellar implosion to a black hole. Such theory would eliminate the conceptional problem with the singularity in Big Bang. It suggests that similar to the ignorance of Plato's prisoners about the 3-D existence, we also fail to explain a lot of phenomena by our ignorance of the 4-D bulk space.

Figure 12 4-D Black Hole [view large image]