Fermions and Bosons in LQG and Its Cosmological Implications

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.