2. Stochastic collapse

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Context: The backreaction of quantum fields on spacetime can be an important source of primordial black holes, but are yet to be implemented in bouncing cosmologies. In collaboration with my wife Tays Miranda and David Wands, I introduced a model of stochastic collapse, in which I modelled backreaction of a contracting scalar field as stochastic noise.

Method: I modelled a power-law solution for a scalar field with an exponential potential in the presence of quantum perturbations which can give rise to a stochastic noise on super-Hubble scales, either during an accelerated expansion or a decelerated collapse. I performed a stability analysis in the presence of quantum perturbations, and I found under which conditions quantum diffusion drives the system away from the critical point.

Results:

• I showed there is no quantum diffusion for a wide class of solutions (including inflation and ekpyrosis), though quantum diffusion can lead to a random walk away from the fixed point in a scale-invariant collapse…
• …though for a nearly scale-invariant collapse with a slightly red-tilted power spectrum, favoured by CMB observations, classical perturbations dominate over quantum diffusion.