What is energy debt? What exactly is energy debt and why does not having energy debt mean that particles and antiparticles don't instantly annihilate each other. 
I'm struggling to understand why this happens (quote from a book): 

By 10^-32 seconds, the separation of forces had boosted the
  temperature from zero back to 10^28 degrees again, and flooded the
  universe with energy. So when virtual particle and antimatter particle
  came into being, there was no need to pay of the energy debt by
  instantly annihilating

 A: It comes from the energy-time form of the Heisenberg uncertainty relation. $\Delta E \Delta T \geq {\hbar \over 2}$.  If a state persists for a short period of time then the energy is uncertain (and the shorter the state the larger the energy uncertainty) so the conservation of energy can't be applied.
An example often used is of someone working in a shop or bar who borrows money from the till and puts it back. If they walk off with a small sum they don't have to restore it till the books are done at the end of the month: if it's a large sum then they have to get it back pretty quick or the boss will notice.  This is an easy-to understand analogy but I'm not convinced about its correctness - let alone its morality.
Using this picture, a virtual particle-antiparticle pair can be created from nothing - despite the need to provide energy $2mc^2$ if these were real particles -  provided they annihilate again within a time smaller than $\hbar / 4 m c^2$. This can be called `paying off the energy debt' - though the analogy is being pushed perhaps further than it merits.
