The geometrization of matter proposal in the Barrett-Crane model and resolution of cosmological problems

We give an overview of the current issues in early universe cosmology and consider the potential resolution of these issues in an as yet nascent spin foam cosmology. The model is the Barrett-Crane Model for quantum gravity along with a generalization of manifold complexes to complexes including conical singularities.

[1]  Pisin Chen.  Might Dark Matter be Actually Black , 2003 .

[2]  Alejandro Perez,et al.  Spin Foam Models for Quantum Gravity , 2003, gr-qc/0301113.

[3]  K. Noui,et al.  Cosmological deformation of Lorentzian spin foam models , 2002, gr-qc/0211109.

[4]  L. Crane.  A New Approach to the Geometrization of Matter , 2001, gr-qc/0110060.

[5]  C. Rovelli,et al.  Spin foam model for Lorentzian general relativity , 2000, gr-qc/0009021.

[6]  L. Smolin.  The strong and weak holographic principles , 2000, hep-th/0003056.

[7]  D. Aharonov.  Quantum to classical phase transition in noisy quantum computers , 1999, quant-ph/9910081.

[8]  R. Brandenberger.  Inflationary Cosmology: Progress and Problems , 1999, hep-ph/9910410.

[9]  L. Smolin,et al.  Holography in a quantum spacetime , 1999, hep-th/9910146.

[10]  R. Pietri,et al.  Barrett-Crane model from a Boulatov-Ooguri field theory over a homogeneous space , 1999, hep-th/9907154.

[11]  J. Murakami,et al.  The colored Jones polynomials and the simplicial volume of a knot , 1999, math/9905075.

[12]  R. Coquereaux,et al.  Differential calculus and connections on a quantum plane at a cubic root of unity , 1998, math-ph/9807012.

[13]  R. Kashaev.  The Hyperbolic Volume of Knots from the Quantum Dilogarithm , 1996, q-alg/9601025.

[14]  S. Majid.  Foundations of Quantum Group Theory , 1995 .

[15]  L. Smolin.  Linking topological quantum field theory and nonperturbative quantum gravity , 1995, gr-qc/9505028.

[16]  L. Crane,et al.  ON ALGEBRAIC STRUCTURES IMPLICIT IN TOPOLOGICAL QUANTUM FIELD THEORIES , 1994, hep-th/9412025.

[17]  L. Kauffman,et al.  State-Sum Invariants of 4-Manifolds , 1994, hep-th/9409167.

[18]  J. Moffat.  SUPERLUMINARY UNIVERSE: A POSSIBLE SOLUTION TO THE INITIAL VALUE PROBLEM IN COSMOLOGY , 1992, gr-qc/9211020.

[19]  A. Connes,et al.  Particle models and noncommutative geometry , 1991 .

[20]  Edward Witten,et al.  Quantum field theory and the Jones polynomial , 1989 .