I review the present status of the problem of initial conditions for inflation and describe several ways to solve this problem for many popular inflationary models, including the recent generation of the models with plateau potentials favored by cosmological observations.

One of our greatest challenges in cosmology is understanding the origin of the structure of the universe. I will describe how the cosmic microwave background has provided a window for probing the initial conditions from which structure evolved and seeded the formation of the galaxies, and the outstanding issues that remain to be resolved. I will address our optimal choice of future strategy in order to make further progress on understanding our cosmic origins.

The singularity theorems of the 1960s showed that Lemaître’s initial symmetry assumptions were not essential for deriving a big-bang origin for a vast multitude of relativistic universe models. Yet the actual universe accords remarkably closely with models of Lemaître’s type. This is a mystery closely related to the form taken by the 2nd law of thermodynamics and is not explained by currently conventional inflationary cosmology. Conformal cyclic cosmology provides another perspective on these issues, one consequence being the necessary initial presence (...) of a dominant scalar material that interacts only gravitationally, but which must ultimately slowly decay away in a novel but perhaps detectable way. According to CCC, our current universe picture provides but one aeon of an unending succession of expanding aeons each having an initial big bang which is the conformal continuation of the remote exponential expansion of its previous aeon. The observational status of CCC is briefly discussed. (shrink)

We discuss the relation between string theory/supergravity and the observational data in cosmology, as well as at LHC, past and future. We pay particular attention to the possibility of the future detection of primordial gravitational waves and how this might affect our understanding of fundamental physics.

The present day standard cosmological model is a great theoretical achievement. This chapter surveys the main themes that have arisen and issues that are still oustanding.