Can stochastic clocks in FLRW minisuperspace prevent dynamical singularities?

Abstract We develop a stochastic extension of the Wheeler–DeWitt equation in Friedmann–Lemaître–Robertson–Walker (FLRW) minisuperspace and show that quantum backreaction can dynamically regulate the big bang singularity without imposing external boundary conditions. Using Laplace–Beltrami (LB) quantisation and an open-system treatment of coarse-grained graviton modes, we obtain a stochastic Hamiltonian evolution equation in which the diffusion coefficient takes the form σ ( a ) ∝ a 2 . This multiplicative noise vanishes at the origin and renders a = 0 an entrance boundary in Feller’s classification, leading to super-exponential suppression of the LB weighted stationary density and zero probability flux into the singular point. At large scale factor, the global behaviour depends on the cosmological sector: de Sitter and positive potential-dominated regimes exhibit power-law stationary tails, whereas confining potentials or negative effective cosmological constant lead to an entrance boundary at infinity and a globally normalisable steady state. Taken together, these results indicate that stochastic backreaction arising from semiclassical coarse-graining provides a consistent and dynamical mechanism for singularity avoidance in minisuperspace quantum cosmology.