  We discuss cosmological effects of the quantum loops of massless particles,
which lead to temporal non-localities 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 bounce-like
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 non-local and parameter independent.
