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arXiv · 2608.19695

Can Stochastic Clocks in FLRW Minisuperspace Prevent Dynamical Singularities?

Pradosh Keshav MV
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Abstract

We develop a stochastic extension of the Wheeler--DeWitt equation in FLRW minisuperspace and show that quantum backreaction can dynamically regulate the big bang singularity without imposing external boundary conditions. Using Laplace--Beltrami 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 $\sigma(a)\propto a^2$. 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 Laplace--Beltrami 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 normalizable 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.

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Pradosh Keshav MV. 2026-08-20. Can Stochastic Clocks in FLRW Minisuperspace Prevent Dynamical Singularities?. https://doi.org/10.1088/1361-6382%2Fae3424

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