Theoretical cosmology in BP2

last updated: December 2014


  • Nature of cosmological singularity. 
  • Spectrum of primordial gravitational radiation.
  • Time issue in quantum cosmology 
  • Coherent states in quantum cosmology 



  • Dynamic system methods were applied to investigate mathematical structure of the Bianchi IX model phase space near cosmological singularity.
  • The Bianchi II model was quantified in the context of applicability to quantify the most general model of that class (Bianchi IX).
  • Quantum chaos in the Bianchi IX model was examined on a preliminary basis.
  • Dynamics of homogenous and isotropic cosmologic models in the Brans-Dicki extended theory of gravitation was investigated. 
  • It was checked whether any significant ambiguities in quantifying procedure might result from free choice of the so-called internal clock in physical description  of gravitational systems.
  • Spectra of primary interferences within the loop quantum cosmology approach were determined.
  • Coherent states were applied to describe semi-classic dynamics of cosmological models. 



It was shown that:

  • Dynamics of the Bianchi II model may be modelled as scattering of a particle on a potential barrier. 
  • The Bianchi IX semi-classical model is not singular (classic singularity was replaced by quantum reflection).
  • Quantized anisotropic degrees of freedom in the Bianchi XI model have the form of radiated quanta of energy of the gravitational field.
  • Phase space in the Bianchi IX model contains some non-hyperbolic critical points, probably related to chaotic classical dynamics of that model.


The obtained results suggests that:

  • Energetic levels in the quantum Bianchi IX model mutually repel, which is a typical feature of chaotic models.



  • The obtained physical hamiltonian may be used to quantify the rather complicated general Bianchi IX system. 
  • The results may be a starting point for further investigation on Bianchi-type models in the Brans-Dicki theory of gravitation. 
  • Methods to quantify via coherent states helped to produce a scenario of evolution of the Universe without any singularity and to investigate the time issue. 
  • It has been suggested that quantum correlation of the Universe may be responsible for cause-effect relations observed in the CMB spectrum (no need to resort to cosmological inflation). 
  • The obtained interference spectra will help to confront theoretical predictions with experimentally observed CMB anisotropy and polarization.



  • Professor Włodzimierz Piechocki  
  • Dr. Ewa Czuchry 
  • Dr. Orest Hrycyna 
  • Dr. Przemysław Malkiewicz
  • Dr. Jakub Mielczarek

This page editoted by: Marek Pawłowski