Narrow Results

In this paper we analyze the third quantization of Horava–Lifshitz theory of gravity without detail balance. We show that the Wheeler–DeWitt equation for Horava–Lifshitz theory of gravity in minisuperspace approximation becomes the equation for time-dependent harmonic oscillator. After interpreting the scaling factor as the time, we are able to derive the third quantized wave function for multiverse. We also show in third quantized formalism it is possible that the universe can form from nothing. Then we go on to analyze the effect of introducing interactions in the Wheeler–DeWitt equation. We see how this model of interacting universes can be used to explain baryogenesis with violation of baryon number conservation in the multiverse. We also analyze how this model can possibly explain the present value of the cosmological constant. Finally we analyze the possibility of the multiverse being formed from perturbations around a false vacuum and its decay to a true vacuum.

We will highlight that despite there being various approaches to quantum gravity, there are universal approach-independent features of quantum gravity. The geometry of space–time becomes an emergent structure, which emerges from some purely quantum gravitational degrees of freedom. We argue that these quantum gravitational degrees of freedom can be best understood using quantum information theory. Various approaches to quantum gravity seem to suggest that quantum gravity could be a third quantized theory, and such a theory would not be defined in space–time, but rather in an abstract configuration space of fields. This supports the view that space–time geometry is not fundamental, thus effectively ending the space–time description of nature.

Third quantization of canonical quantum gravity allows us to consider the multiverse as the playground of a field theory of universes. In the scenario where two universes are created by analogy with pair production in quantum field theory, we analyze the entanglement entropy between them and get some conclusions about the structure of the multiverse.

Changes of field variables may lead to multivalued fields which do not satisfy the Schwarz integrability conditions. Their quantum field theory needs special care as is illustrated here in applications to superfluid and superconducting phase transitions. Extending the notions that first qantization governs fluctuating orbits while second quantization deals with fluctuating field, the theory of multivalued fields may be considered as a theory of third quantization. The lecture is an introduction to my new book on this subject.