In second-order cosmological perturbation theory, products of first-order perturbations act as effective quadratic gravitational source terms. We adopt a linearly expanding closed FLRW background and study its scalar perturbations in Poisson gauge. Far from a matter overdensity, the second-order perturbations generate a nonlinear source proportional to the square of the first-order gravitational field. This quadratic dependence on the gravitational field is shared by the $p=3$ Laplacian, known to be the operator of the deep-MOND/AQUAL limit. Choosing the great-circle circumference as the characteristic length scale, the corresponding acceleration scale is $a_{\rm B}(t)=c/(2\pi t)$. Thus, the quadratic dependence associated with MOND-like low-acceleration operators can arise from nonlinear gravitational self-coupling in a closed, linearly expanding GR perturbation framework, under the stated assumptions.