Radiation equation of state and loop quantum gravity corrections

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.

Figure 1

Decomposition of the evolution vector field $t^a$ in terms of the normal $n^a$ to spatial slices and a spacelike part $N^a$.