In another couple of weeks we should have a Most Important Paper poll for 3rd quarter (July-September) of 2008. As of now I have these four in mind, one of which was spotted by Francesca (thanks!) http://arxiv.org/abs/0809.3190 Evaluation of new spin foam vertex amplitudes Igor Khavkine 19 pages, 4 figures "A new numerical evaluation algorithm is proposed for the new spin foam vertex amplitudes proposed by Engle, Pereira & Rovelli and Freidel & Krasnov. The algorithm is applied to compute the high spin behavior of the new vertex amplitudes. Their asymptotics exhibit non-oscillatory, power-law decay, similar to that of the Barrett-Crane model, but with different exponents." Obviously the ability to calculate the quantum amplitudes of spacetimes (spacetimes are paths from one spatial geometry to another) is essential. The Loll Utrecht group does this for the Triangulations path integral. Christensen's West Ontario (UWO) group with its Beowulf Cluster is one of several outfits with the capability to do this for spinfoam path integrals. Igor Khavkine is with this group. I list this first among the 3rd quarter 2008 papers because of the importance of fast computer algorithms for numerical quantum gravity. About the next paper, it's clear that Triangulations QG is one of the strongest things going, and their getting a quantum version of de Sitter space to emerge (out of nothing but the chaos of microscopic degrees of freedom, no macro geometry put in by hand) is a major result. http://arxiv.org/abs/0807.4481 The Nonperturbative Quantum de Sitter Universe J. Ambjorn, A. Goerlich, J. Jurkiewicz, R. Loll 37 pages, many figures (Submitted on 28 Jul 2008) "The dynamical generation of a four-dimensional classical universe from nothing but fundamental quantum excitations at the Planck scale is a long-standing challenge to theoretical physicists. A candidate theory of quantum gravity which achieves this goal without invoking exotic ingredients or excessive fine-tuning is based on the nonperturbative and background-independent technique of Causal Dynamical Triangulations. We demonstrate in detail how in this approach a macroscopic de Sitter universe, accompanied by small quantum fluctuations, emerges from the full gravitational path integral, and how the effective action determining its dynamics can be reconstructed uniquely from Monte Carlo data. We also provide evidence that it may be possible to penetrate to the sub-Planckian regime, where the Planck length is large compared to the lattice spacing of the underlying regularization of geometry." The correctness of spinfoam in the semiclassical limit is a key issue. The following paper is an obvious nominee. It uses a powerful technique developed by the authors for translating a spinfoam into a conventional (Feynman-style) action-based path integral. This opens up other technical possibiliites besides solution of the semiclassical limit problem which they are working on here. http://arxiv.org/abs/0809.2280 On the semiclassical limit of 4d spin foam models Florian Conrady, Laurent Freidel (Perimeter Inst. Theor. Phys.) 32 pages, 5 figures (Submitted on 15 Sep 2008) "We study the semiclassical properties of the Riemannian spin foam models with Immirzi parameter that are constructed via coherent states. We show that in the semiclassical limit the quantum spin foam amplitudes of an arbitrary triangulation are exponentially suppressed, if the face spins do not correspond to a discrete geometry. When they do arise from a geometry, the amplitudes reduce to the exponential of i times the Regge action. Remarkably, the dependence on the Immirzi parameter disappears in this limit." There is currently an influx of researchers into Loop Cosmology. It has become an attractive field of research, partly because of the strength of observational cosmology and possibilities of empirical verification, partly because of interest in non-singular (prebang) cosmology and removing black hole singularities. This paper takes care of some conceptual matters in LQC and so may turn out to be useful (and cited) in the rising tide of research in this area. http://arxiv.org/abs/0809.2590 Physical time and other conceptual issues of QG in the example of LQC Wojciech Kaminski, Jerzy Lewandowski, Tomasz Pawlowski 18 pages, 1 figure (Submitted on 15 Sep 2008) "Several conceptual aspects of quantum gravity are studied on the example of the homogeneous isotropic LQC model. In particular: (i) The relativistic time of the co-moving observers is showed to be a quantum operator and a quantum spacetime metric tensor operator is derived. (ii) Solutions of the quantum scalar constraint for two different choices of the lapse function are compared and contrasted. (iii) The mechanism of the singularity avoidance is analyzed via detailed studies of an energy density operator. (iv) The relation between the kinematical and the physical quantum geometry is discussed on the level of relation between observables."