Inflationary cosmology is notoriously past geodesically incomplete in many situations. However, it is generally unknown whether the geodesic incompleteness implies the existence of an initial spacetime curvature singularity or whether the spacetime may be extended beyond its null past boundary. In homogeneous and isotropic cosmology with flat spatial sections, we classify which past inflationary histories have a scalar curvature singularity and which might be extendible/non-singular. We derive rigorous extendibility criteria of various regularity classes for quasi-de Sitter spacetimes that evolve from infinite proper time in the past. Beyond homogeneity and isotropy, we show that continuous extensions respecting the Einstein field equations with a perfect fluid must have the equation of state of a de Sitter universe asymptotically. An interpretation of our results is that past-eternal inflationary scenarios are most likely physically singular, except in very special situations.
The course is an introduction to quantum field theory in curved spacetime. Upon building up the general formalism, the latter is applied to several topics in the modern theory of gravity and cosmology where the quantum properties of fundamental fields play an essential role.
Topics to be covered:
1) Radiation of particles by moving mirrors
2) Hawking radiation of black holes
3) Production of primordial density perturbations and gravity waves during inflation
4) Statistical properties of the primordial spectra
Required prior knowledge:
Foundations of quantum mechanics and general relativity