Tcp , Quantum Gravity , the Cosmological Constant and All That

We study cosmology from the point of view of quantum gravity. Some light is thrown on the nature of time, and it is suggested that the cosmological arrow of time is generated by a spontaneous breakdown of TCP. Conventional cosmological models in which quantum fields interact with a time dependent gravitational field are shown to describe an approximation to the quantum gravitational wave function which is valid in the long wavelength limit. Two problems with initial conditions are resolved in models in which a negative bare cosmological constant is cancelled by the classical excitation of a Bose field 9 with a very flat potential. These models can also give a natural explanation for the observed value of the cosmological constant. On the unknown continent that is quantum gravity, the shadowy outlines of three major landmarks are barely discernible. The first is the nonrenormaliaabil-ity of all unitary local quantum field theories of gravity. " It seems probable that we will have turn to a theory of strings, to discrete space-time, or to some other, as yet unimagined, modification of current ideas in order to understand the physics of distances less than the Planck length. The second landmark, somewhat more shrouded in mist than the first is the complex of questions raised by the seminal work of Hawking' on quantum field theory in the vicinity of a black hole. This includes the question of whether the topology of space-time (and not just its metric) is a dynamical variable, as well as the problem of the apparent loss of quantum coherence in quantum gravitational phenomena. The final resolution of these questions may well depend on the nature of short distance dynamics.. The third major topographical feature of quantum gravity is the question of whether it makes sense to say that " the entire universe " is in a pure quantum state. This question does not seem to depend on short distance physics. Indeed it arises even when we apply ordinary quantum field theory to cosmology. We will not attempt to give an answer to this question here. We need a lot more practical experience with quantum gravity before we can hope to understand such a deep conceptual issue. Our aim in the present paper will be to try to place cosmology in the context of the formalism of quantum gravity as it is presently understood. Contemporary cosmalogy is usually formulated in terms of …