Effective Dynamics, Big Bounces and Scaling Symmetry in Bianchi Type I Loop Quantum Cosmology

Abstract

The detailed formulation for loop quantum cosmology (LQC) in the Bianchi I model with a scalar massless field has been constructed. In this paper, its effective dynamics is studied in two improved strategies for implementing the LQC discreteness corrections. Both schemes show that the big bang is replaced by the big bounces, which take place up to three times, once in each diagonal direction, when the area or volume scale factor approaches the critical values in the Planck regime measured by the reference of the scalar field momentum. These two strategies give different evolutions: In one scheme, the effective dynamics is independent of the choice of the finite sized cell prescribed to make Hamiltonian finite; in the other, the effective dynamics reacts to the macroscopic scales introduced by the boundary conditions. Both schemes reveal interesting symmetries of scaling, which are reminiscent of the relational interpretation of quantum mechanics and also suggest that the fundamental spatial scale (area gap) may give rise to a temporal scale.

19 pages, 6 figures, 1 table; one reference added; version to appear in PRD

References in corpus (4)

• Loop quantum cosmology of k=1 FRW models
• Lattice refining loop quantum cosmology, anisotropic models and stability
• The behavior of non-linear anisotropies in bouncing Bianchi I models of loop quantum cosmology
• Effective Dynamics for the Cosmological Bounces in Bianchi Type I Loop Quantum Cosmology

Cited by in corpus (6)

• Anti-deSitter universe dynamics in LQC
• Is loop quantization in cosmology unique?
• Phenomenological loop quantum geometry of the Schwarzschild black hole
• Phenomenological dynamics of loop quantum cosmology in Kantowski-Sachs spacetime
• Exact solutions for Big Bounce in loop quantum cosmology
• Emerging singularities in the bouncing loop cosmology