Causal structure and quantum gravity

Abstract

In this thesis we will investigate the problem of quantum gravity from a variety of directions. Each avenue we explore begins at the quantum gravity path integral, and throughout our investigations the notion of spacetime causal structure will frequently appear.

After a brief introduction to the path integral for quantum gravity we will present several of the concepts behind Causal Set Theory - an approach to quantum gravity in which the continuum spacetime is replaced by a discrete structure. We will then familiarise ourselves with the gravitational action that appears in the path integral, and its necessary boundary terms, in preparation for our discussion of the analogous quantities in Causal Set Theory. In particular, we will focus on the boundary terms in the causal set action and propose causal set expressions for the case of a spacelike boundary. We will then formulate causal set expressions to encode other boundary geometry, and conclude our discussion of the causal set action by investigating what boundary terms, if any, are present in the current proposal for the bulk causal set action.

Finally, we will return to the continuum quantum gravity path integral and explore whether the sum over spacetimes should include spacetimes which exhibit spatial topology change. To attempt to answer this question we will focus our attention on the simple case of the trousers spacetime, and use the Sorkin-Johnston formalism to study a scalar quantum field theory living on the spacetime.