In this thesis we give a self-sufficient introduction to the trace anomaly and its applications in the problem of cosmological constant. We begin by revising the renormalization of quantum electrodynamics in flat space and the Lagrangian formalism of general relativity. Then we discuss shortly about the renormalizability of quantum general relativity, after which we turn our attention to a semiclassical theory of quantum gravitation.
We review the construction and renormalization of the semiclassical theory, and discuss shortly the stability of it. We then proceed to examine the trace anomaly of the semiclassical theory, and begin by reviewing Weyl cohomology in n-dimensions. We use the Weyl cohomology to construct the Wess-Zumino action, from which we derive a non-local action for the trace anomaly. The non-local action is then rendered local by introducing new auxiliary fields, in which the non-local behaviour of the action is contained.
After all these theoretical considerations we finally examine the non-trivial cosmological consequences of the trace anomaly. At first we review shortly the Friedman-Robertson-Walker -model and its classical perturbations, after which we examine the linear perturbations of the trace anomaly action in de Sitter space. We find that when the auxiliary fields of the action are quantized, the cosmological constant becomes dependent on the border conditions at the horizon scale of de Sitter space. We then conclude that the small but non-zero value of the cosmological constant could be a physical consequence of the presence of the horizon.
