Large scale effective theory for cosmological bounces

An exactly solvable bounce model in loop quantum cosmology is identified which serves as a perturbative basis for realistic bounce scenarios. Its bouncing solutions are derived analytically, demonstrating why recent numerical simulations robustly led to smooth bounces under the assumption of semiclassicality. Several effects, easily included in a perturbative analysis, can however change this smoothness. The effective theory is not only applicable to such situations where numerical techniques become highly involved but also allows one to discuss conceptual issues. For instance, consequences of the notoriously difficult physical inner product can be implemented at the effective level. This indicates that even physical predictions from full quantum gravity can be obtained from perturbative effective equations.

Figure 1

Peak trajectory with surrounding area spread out by $\Delta p$ around a bounce for $H=10\hslash$. Dashed lines show the general behavior not assuming uniform spread. This figure is to be compared with the numerical solution in Fig. 2 of 5.