One of the central problems in connecting fundamental theory with cosmology is how inflation emerges from within a higher-dimensional spacetime. There has been much recent progress in obtaining models within string theory, much of it pioneered in DAMTP, which include so-called 'brane inflation', 'large volume' scenarios and even more radical 'cyclic' models in which the Universe expands and recollapses perpetually. However, several open problems remain related to the stablilsation of the fields that describe the shapes and volumes of the extra dimensions, as well as difficulties with obtaining a long enough inflationary period to describe our Universe. There have been recent advances that suggest dynamical mechanisms which may fix these fields to values required by cosmological observations. However, many different scenarios exist, so we need to develop criteria for identifying a subset of cosmologically viable models out of this vast string theory landscape.

Eternal inflation arises naturally in the context of the string theory landscape, but it is difficult to consistently define probabilities and measures in order to make quantitative predictions. CTC members have made substantial progress in special cases that are well-controlled. We will continue developing these techniques for general inflation models, for example, using the no-boundary proposal. This work will enable observable quantities to be calculated on a sounder theoretical basis, providing testable signatures to distinguish between competing paradigms.