Arrows of time in bouncing cosmologies

Different approaches to quantum gravity, such as loop quantum cosmology and group field theory, predict the resolution of the initial cosmological singularity via a bounce: a regular spacetime region that connects the expanding branch of the universe to a contracting branch. The cosmological arrow of time, which by definition points in the direction of cosmic expansion, is reversed at the bounce. Nonetheless, it is still possible to discriminate between the two branches by considering different arrows, as defined for instance by the growth of perturbations. After reviewing general aspects of the time arrow problem in cosmology, we examine the properties of different arrows of time in bouncing cosmologies, focusing on the loop quantum cosmology bounce as a case study. These issues are examined in detail for an exact solution to the effective Friedmann equations of loop quantum cosmology with pressureless dust and a cosmological constant, which is a simplified version of the $\Lambda$CDM bounce scenario.