Abhay Ashtekar

• ArXiv:0812.0177 - recommended review paper
• WDW quantum cosmology not mathematically rigorous
  • since 1970's worry about von Neumann uniqueness theorem * LQC is rigorous
• LQC solves these problems BoudRoukema - 03 Jul 2009
• LQC - quantum geometry - gives repulsive force during planck epoch, i.e. a bounce
• "quantum geometry resolves all strong singularities in homogeneous isotropic models with ... (Singh)
• k=1 models bounce at 't=0', i.e. avoid singularity (Ashtekar, Pawlowski, ...)
• BKL conjecture: approaching Planck era, dynamics well approximated by Bianchi I models, with Bianchi II transitions and spikes
  • LQC also resolves singularities in Bianchi I, II models
• in LQG, there may be a general singularity resolution theorem
• phenomenology - work in progress
  • super-inflation - Copeland et al
  • do inflation calculations using LQC-corrected Einstein eqns
    • horizon and flatness problems solved by super-inflation
    • nearly scale invariant spectrum for scalar mode
    • ...
  • evolution of perturbations from pre-BB to post-BB branch
    • Biswas working on this
  • all this is very much work in progress by LQC community
• summary:
  • QG gives quantum bounce
  • physics does not end at singularities
  • classical GR at low curvatures/densities (Green and Unruh)
  • the singularities analysed here are those of direct cosmological interest (not just abstract singularities!)
  • phenomeology - initial results obtained, cosmologists and LQC communities working together on this