Fermions and Bosons in Loop Quantum Gravity and Its Cosmological Implications

Abstract

Canonical gravity in real Ashtekar--Barbero variables is generalized by extending Holst's original vacuum analysis to allow for both fermionic and bosonic matter. For fermions, the effects of emerging torsion on parity and the known canonical (loop) quantization of gravity are discussed on the basis of the classical analysis by eliciting the necessity for adaptations. Then the role of these matter fields in homogeneous models of loop quantum cosmology is explored by discussing their influence on the behavior of the Wheeler-deWitt equation for the wave function of the universe. Next, quantum gravity corrections to equation of state parameters for Maxwell and Dirac fields arising from the discrete geometry of loop quantization are computed to investigate its effect on Big Bang Nucleosynthesis (BBN) to place bounds on these corrections and especially the patch size of discrete quantum gravity states. Finally, an example of the effects of these corrected equation of state on the evolution of dark energy, in particular $k$-essence and quintessence, is presented.