Big Bang Models in String Theory

These proceedings are based on lectures delivered at the “RTN Winter School on Strings, Supergravity and Gauge Theories”, CERN, January 16 January 20, 2006. The school was mainly aimed at Ph.D. students and young postdocs. The lectures start with a brief introduction to spacetime singularities and the string theory resolution of certain static singularities. Then they discuss attempts to resolve cosmological singularities in string theory, mainly focusing on two specific examples: the Milne orbifold and the matrix big bang. big bang black holes quantizing gravity string theory Figure 1: Can string theory make sense of spacetime singularities? 1 Lecture I: Introduction and outline Spacetime singularities are a prediction of general relativity. Examples include singularities inside black holes and the big bang singularity at the beginning of a Friedmann-LemâıtreRobertson-Walker (FLRW) universe. However, general relativity breaks down at spacetime singularities, which is one of the main motivations for pursuing a consistent quantum theory of gravity. The best developed candidate is string theory, and the purpose of these lectures is to explore what string theory has to say about spacetime singularities. Rather than attempt to give a broad overview of this subject, I will focus on a number of specific models and techniques. Complementary reviews include [1–5]. In this first lecture, I will first briefly introduce spacetime singularities in the context of general relativity, and argue that one should go beyond general relativity to try to really understand them. Next, I will indicate how certain static singularities are resolved in string theory, focusing in particular on orbifold and ALE singularities. Finally, we will have a first look at “cosmological” (spacelike or lightlike) singularities in string theory, which will be the focus of the remainder of these lectures. 1.1 General relativity and spacetime singularities In general relativity, freely falling particles follow geodesics in a curved spacetime. What is important for these lectures, is that geodesics don’t always go on forever: they can end