When the universe is treated as a quantum system, it is described by a wave function. This
wave function is a function not only of the matter fields, but also of spacetime. The no …

The problem of describing the quantum behavior of gravity, and thus understanding
quantum spacetime, is still open. Loop quantum gravity is a well-developed approach to this …

A bstract In the 1980's, work by Coleman and by Giddings and Strominger linked the physics
of spacetime wormholes to 'baby universes' and an ensemble of theories. We revisit such …

The problem of time in quantum gravity calls for a relational solution. Using quantum
reduction maps, we establish a previously unknown equivalence between three approaches …

An improved Hamiltonian constraint operator is introduced in loop quantum cosmology.
Quantum dynamics of the spatially flat, isotropic model with a massless scalar field is then …

Analytical and numerical methods are developed to analyze the quantum nature of the big
bang in the setting of loop quantum cosmology. They enable one to explore the effects of …

Quantization of diffeomorphism invariant theories of connections is studied and the quantum
diffeomorphism constraint is solved. The space of solutions is equipped with an inner …

Using techniques from loop quantum gravity, the standard theory of cosmological
perturbations was recently generalized to encompass the Planck era. We now apply this …

Gauge-invariant observables for quantum gravity are described, with explicit constructions
given primarily to leading order in Newton's constant, analogous to and extending …

We describe a completely general and fully non-perturbative framework for constructing
dynamical reference frames in generally covariant theories, and for understanding the …