Phenomenological implications of an alternative Hamiltonian constraint for quantum cosmology

In this paper we review a model based on loop quantum cosmology that arises from a symmetry reduction of the self-dual Plebanski action. In this formulation the symmetry reduction leads to a very simple Hamiltonian constraint that can be quantized explicitly in the framework of loop quantum cosmology. We investigate the phenomenological implications of this model in the semiclassical regime and compare those with the known results of the standard Loop Quantum Cosmology.

Figure 1

Time dependence of the inflaton field for $j=100$. Dashed and solid curves correspond to the standard and Plebanski models respectively

Figure 2

Time dependence of the inflaton field for $j=10$. Dashed and solid curves correspond to the standard and Plebanski models respectively

Figure 3

Time dependence of the inflaton field for $j=5$. Dashed and solid curves correspond to the standard and Plebanski models respectively

Figure 4

Time dependence of the scale factor for $j=100$. Dashed and solid curves correspond to the standard and Plebanski models respectively

Figure 5

Time dependence of the scale factor for $j=10$. Dashed and solid curves correspond to the standard and Plebanski models respectively

Figure 6

Time dependence of the scale factor for $j=5$. Dashed and solid curves correspond to the standard and Plebanski models respectively

Figure 7

Spectrum of the geometrical density operator $D(q)$ (solid curve) compared to $D(q{)}^{4/3}$ (dashed curve)