Loop Quantum Cosmology with a noncommutative quantum deformed photon gas
  The noncommutativity of the space-time had important implications for the
very early Universe, when its size was of the order of the Planck length. An
important implication of this effect is the deformation of the standard
dispersion relation of special relativity. Moreover, in the Planck regime
gravity itself must be described by a quantum theory. We consider the
implications of the modified dispersion relations for a photon gas, filling the
early Universe, in the framework of Loop Quantum Cosmology, a theoretical
approach to quantum gravity. We consider three types of deformations of the
dispersion relations of the photon gas, from which we obtain the Planck scale
corrections to the energy density and pressure. The cosmological implications
of the modified equations of state are explored in detail for all radiation
models in the framework of the modified Friedmann equation of Loop Quantum
Cosmology. By numerically integrating the evolution equations we investigate
the evolution of the basic cosmological parameters (scale factor, Hubble
function, radiation temperature, and deceleration parameter) for a deformed
photon gas filled Universe. In all models the evolution of the Universe shows
the presence of a (nonsingular) bounce, corresponding to the transition from a
contracting to an expanding phase.
