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Calabi-Yau Manifold


End of the Universe

    According to the Superstring theory and by implication the Calabi-Yau Manifold there are at least two scenarios to hasten the end of this universe as we know it.

  1. Metastable State - As shown in Figure 21, our universe is one of those sitting on a valley in the landscape. Most probably it would not be in the one with the lowest vacuum energy. There are two ways the state of our universe can decay into a lower one (Figure 25) :
  2. End of the Universe
    • Quantum Tunneling - Quantum theory allows penetration of a barrier from one state to another with a probability inversely proportional to the width of the barrier. The initial state will decay into the other state if it is at lower energy level.
    • Thermal Activation - Another way to overcome a barrier is via thermal fluctuations, which will occur if the thermal energy is higher than the height of the potential barrier.

    Figure 25 End of the Universe
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    What would happen during and after the transition depends on the path and the state of the next incarnation. For example, it could have a negative cosmological constant, which would lead the universe into a "Big Crunch" - the reverse of the "Big Bang".
    The entity sitting inside the valley in Figures 21 and 25 is referred to as "vacuum" because it is the product of the field equation in General Relativity - the deSitter universe, which is empty (except for a cosmological constant term) without any matter (visible or dark).

  3. Decompactification - It has been mentioned that the compactified dimensions are held together by fluxes and branes. Such state is not stable since it needs energy to do the wrapping. Fluctuations provide a chance for the "explosion" in dimensions to happen; and when it does, everything from the tiniest particles to galactic superclusters, would instantly explode into the six expanding dimensions. At the end of the conflagration, spacetime would still be there (with ten large dimension now) but the laws of physics would change to an un-recognizable forms, nothing as we know it will survive. However, it is estimated that the chance for such kind of catastrophe to happen is about 1 to e(10120).

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