Nonlocal quantum effects in cosmology: Quantum memory, nonlocal FLRW equations, and singularity avoidance

We discuss cosmological effects of the quantum loops of massless particles, which lead to temporal nonlocalities in the equations of motion governing the scale factor a (t). For the effects discussed here, loops cause the evolution of a (t) to depend on the memory of the curvature in the past with a weight that scales initially as 1/ (t-t^'). As one of our primary examples, we discuss the situation with a large number of light particles, such that these effects occur in a region where gravity may still be treated classically. However, we also describe the effect of quantum graviton loops and the full set of Standard Model particles. We show that these effects decrease with time in an expanding phase, leading to classical behavior at late time. In a contracting phase, within our approximations the quantum results can lead to a bouncelike behavior at scales below the Planck mass, avoiding the singularities required classically by the Hawking-Penrose theorems. For conformally invariant fields, such as the Standard Model with a conformally coupled Higgs, this result is purely nonlocal and parameter independent.