Isotropic loop quantum cosmology with matter

A free massless scalar field is coupled to homogeneous and isotropic loop quantum cosmology. The coupled model is investigated in the vicinity of the classical singularity, where discreteness is essential and where the quantum model is nonsingular, as well as in the regime of large volumes, where it displays the expected semiclassical features. The particular matter content (massless, free scalar) is chosen to illustrate how the discrete structure regulates pathological behavior caused by kinetic terms of matter Hamiltonians (which in standard quantum cosmology leads to wave functions with an infinite number of oscillations near the classical singularity). Because of this modification of the small volume behavior the dynamical initial conditions of loop quantum cosmology are seen to provide a meaningful generalization of DeWitt’s initial condition.