1109.6636 (Brajesh Gupt et al.)

Contrasting features of anisotropic loop quantum cosmologies: the role
of spatial curvature    [PDF]

Brajesh Gupt, Parampreet Singh

A characteristic feature of loop quantization of the isotropic and Bianchi-I
spacetimes is the existence of universal bounds on the energy density and the
expansion and shear scalars, independent of the matter content. We investigate
the properties of these physical quantities in Bianchi-II and Bianchi-IX
spacetimes, which have been recently loop quantized using the connection
operator approach. Using the effective Hamiltonian approach, we show that for
Bianchi-II spacetime, energy density and the expansion and shear scalars turn
out to be bounded, albeit not by universal values. In Bianchi-IX spacetime,
when the approach to the classical singularity is isotropic, above physical
quantities are bounded. In addition, for all other cases, where the approach to
singularities is not isotropic and effective dynamics can be trusted, these
quantities turn out to be finite. These results stand in sharp distinction to
general relativity, where above physical quantities are generically unbounded,
leading to the break down of geodesic equations. In contrast to the isotropic
and Bianchi-I models, we find the role of energy conditions for Bianchi-II
model and the inverse triad modifications for Bianchi-IX to be significant to
obtain above bounds. These results bring out subtle physical distinctions
between the quantization using holonomies over closed loops performed for
isotropic and Bianchi-I models, and the connection operator approach. We find
that qualitative differences in physics exist for these quantization methods
even for the isotropic models in the presence of spatial curvature. We
highlight these important differences in the behavior of the expansion scalar
in the holonomy based quantization and connection operator approach for
isotropic spatially closed and open models.

View original: http://arxiv.org/abs/1109.6636