Abhay Ashtekar

Time Reversal T is usually discussed in the traditional framework of quantum mechanics in which T is represented by an anti-unitary operator. But quantum gravity may well need generalization of standard quantum mechanics which may not preserve even its linear structure, let alone the unitarity of dynamics and anti-unitarity of T. Then the currently used arguments to conclude that T violation is a fundamental aspect of Nature will break down.

There is a huge body of work in Loop Quantum Cosmology comprising of several thousand journal articles. I will provide an overview of conclusions, focusing on the difficult conceptual and mathematical issues that accompany the notion of a bounce and opening the way for phenomenological implications that will be discussed by Ivan Agullo.

I will give a broad overview of this old subject which has come back to light recently in connection with the issue of black hole evaporation. It will be an informal, black board talk.

Surprisingly, several basic questions in classical and quantum gravity, which were resolved some 40-50 years ago for zero $\Lambda$, still remain open in the $\Lambda >0$ case. In particular, for $\Lambda >0$, we still do not have a satisfactory notion of gravitational radiation or Bondi 4-momentum in exact general relativity, nor a positive energy theorem. Similarly, the standard constructions of `in' and `out' Hilbert spaces that we routinely use (e.g. in the analysis of black hole evaporation) do not extend to the $\Lambda >0$ case.

Thanks to the spectacular observational advances since the 1990s, a `standard model' of the early universe has now emerged. However, since it is based on quantum field theory in curved space-times, it is not applicable in the Planck era. Using techniques from loop quantum gravity, the theory can be extended over the 12 orders of magnitude in density and curvature from the onset of inflation all the way back to the Planck regime, providing us with a possible completion of the standard model.

In LQG we work in the spirit of Antonio Machado: "Traveler, there is no path; Paths are made by walking." I will present a bird's eye view of some of the paths that have emerged since Loops 11 and offer a few suggestions.

I try to make the point about what we know and what we do not yet know about the possibility of writing a quantum theory of gravity.

Using 2-dimensional CGHS black holes, I will argue that information is not lost in the Hawking evaporation because the quantum space-time is significantly larger than the classical one. I will begin with a discussion of the conceptual underpinnings of problem and then introduce a general, non-perturbative framework to describe quantum CGHS black holes. I will show that the Hawking effect emerges from it in the first approximation.