#### marcus

Science Advisor

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http://arxiv.org/abs/0710.5734

**Dirac Fields in Loop Quantum Gravity and Big Bang Nucleosynthesis**

Martin Bojowald, Rupam Das, Robert J. Scherrer

15 pages, 2 figures

(Submitted on 30 Oct 2007)

"

**Big Bang nucleosynthesis requires a fine balance between equations of state for photons and relativistic fermions.**Several corrections to equation of state parameters arise from classical and quantum physics, which are derived here from a canonical perspective. In particular, loop quantum gravity allows one to compute quantum gravity corrections for Maxwell and Dirac fields. Although the classical actions are very different, quantum corrections to the equation of state are remarkably similar. To lowest order, these corrections take the form of an overall expansion-dependent multiplicative factor in the total density. We use these results, along with the predictions of Big Bang nucleosynthesis, to place bounds on these corrections."

A key finding is that the LQG quantum corrections to the photon and fermion equations of state--although they are arrived at differently in the two cases--do not disturb the required balance between the two species.

I think this one by Bojowald, Das, Scherrer is the main paper and the other two, which appeared at the same time with it, work out supporting details.

http://arxiv.org/abs/0710.5721

**The radiation equation of state and loop quantum gravity corrections**

Martin Bojowald, Rupam Das

11 pages, 1 figure

Phys. Rev. D 75 (2007) 123521

(Submitted on 30 Oct 2007)

"The equation of state for radiation is derived in a canonical formulation of the electromagnetic field. This allows one to include correction terms expected from canonical quantum gravity and to infer implications to the universe evolution in radiation dominated epochs. Corrections implied by quantum geometry can be interpreted in physically appealing ways, relating to the conformal invariance of the classical equations."

http://arxiv.org/abs/0710.5722

**Canonical Gravity with Fermions**

Martin Bojowald, Rupam Das

27 pages

(Submitted on 30 Oct 2007)

"Canonical gravity in real Ashtekar-Barbero variables is generalized to allow for fermionic matter. The resulting torsion changes several expressions in Holst's original vacuum analysis, which are explicitly displayed here. This in turn requires adaptations to the known canonical (loop) quantization of gravity coupled to fermions, which is discussed on the basis of the classical analysis."