Non-local quantum effects in cosmology 1: Quantum memory, non-local FLRW equations and singularity avoidance

We discuss cosmological effects of the quantum loops of massless particles, which lead to temporalnon-localities in the equations of motion governing the scale factor a(t). For the effects discussedhere, loops cause the evolution of a(t) to depend on the memory of the curvature in the past witha weight that scales initially as 1/(t − t′). As one of our primary examples we discuss the situationwith a large number of light particles, such that these effects occur in a region where gravity maystill be treated classically. However, we also describe the effect of quantum graviton loops and thefull set of Standard Model particles. We show that these effects decrease with time in an expandingphase, leading to classical behavior at late time. In a contracting phase, within our approximationsthe quantum results can lead to a bounce-like behavior at scales below the Planck mass, avoidingthe singularities required classically by the Hawking-Penrose theorems. For conformally invariantfields, such as the Standard Model with a conformally coupled Higgs, this result is purely non-localand parameter independent