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.

Autorentext
Dr. Das received Ph.D. from Vanderbilt University specializing in Loop Quantum Gravity and Quantum Cosmology. Currently, he is pursuing further research in the fundamental structure of space- time.

Klappentext
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.