General relativity loses its validity at the big bang singularity. If string theory is a consistent theory of quantum gravity, it is expected to “resolve” the singularity. A popular idea in string theory is that spacetime is and “emergent” concept: it provides an excellent approximation on sufficiently large distance scales, but is absent in the most fundamental formulation of the theory. Near a spacetime singularity, one expects that the more fundamental degrees of freedom should be used. Our group has explored this idea in a number of holographic formulations of string theory.
String theory in certain classes of backgrounds has a holographic formulation in terms of “matrix theory”, where the fundamental (holographic) description is a lower dimensional theory of matrices. Using adiabaticity, we have given a detailed description of the emergence of space-time in this model (away from the singularity). In a series of papers, we have also explored the region near the singularity (but this regime remains less well-understood).
The AdS/CFT correspondence identifies string theory in asymptotically anti-de Sitter (AdS) space-times with a supersymmetric gauge theory on the conformal boundary of AdS. Certain AdS boundary conditions allow for the evolution of non-singular initial conditions to a big crunch. In the dual quantum field theory, the singularity manifests itself through the presence of a potential unbounded from below. We have attempted to define self-adjoint extensions for such quantum field theories, discussed the problem of backreaction that plagues at least the simplest models, and offered an interpretation of the unbounded potential in terms of branes being pushed to the boundary of AdS.
A more bottom-up approach consists in studying non-local gravity models inspired by string field theory. A specific class of such models allows non- singular bouncing solutions, which could offer a potential resolution of the big bang singularity. We have investigated the stability of such models, constructed inflationary solutions and explored phenomenological consequences for the cosmic microwave background.
We have proposed a new formalism for perturbative string theory in spacetimes in which all spatial dimensions are compact, and discussed how the formalism deals with the infrared divergences that plague naïve attempts. A specific motivation is string gas cosmology, but the problem is of more general interest.