New ground state for quantum gravity
  In this paper we conjecture the existence of a new "ground" state in quantum
gravity, supplying a wave function for the inflationary Universe. We present
its explicit perturbative expression in the connection representation,
exhibiting the associated inner product. The state is chiral, dependent on the
Immirzi parameter, and is the vacuum of a second quantized theory of graviton
particles. We identify the physical and unphysical Hilbert sub-spaces. We then
contrast this state with the perturbed Kodama state and explain why the latter
can never describe gravitons in a de Sitter background. Instead, it describes
self-dual excitations, which are composites of the positive frequencies of the
right-handed graviton and the negative frequencies of the left-handed graviton.
These excitations are shown to be unphysical under the inner product we have
identified. Our rejection of the Kodama state has a moral tale to it: the
semi-classical limit of quantum gravity can be the wrong path for making
contact with reality (which may sometimes be perturbative but nonetheless fully
quantum). Our results point towards a non-perturbative extension, and we
present some conjectures on the nature of this hypothetical state.
