Primordial black holes could have been formed in the early universe from non linear cosmological perturbations re-entering the cosmological horizon when the Universe was still radiation dominated. Starting from the shape of the power spectrum on superhorizon scales, we provide a simple prescription, based on the results of numerical simulations, to compute the threshold $\delta_c$ for primordial black hole formation. Our procedure takes into account both the non linearities between the Gaussian curvature perturbation and the density contrast and, for the first time in the literature, the non linear effects arising at horizon crossing, which increase the value of the threshold by about a factor two with respect to the one computed on superhorizon scales.

Gaseous Optical Time Projection Chambers (OTPCs) aimed at Neutrino Physics and Rare Event Searches will likely exceed the tonne scale during the next decade. This will make their performance sensitive to gas contamination levels as low as 100 ppb, that is challenging at room temperature due to outgassing from structural materials. In this work we discuss gas distribution and impurity mitigation in a 5 m-length/5 m-diameter 10 bar TPC filled with Ar/CF$_4$ admixed at 99/1 per volume (1.75 tonne), loaded with technical plastics in order to enhance light collection and readout. Different distributor topologies, outgassing and flow rates are discussed. Specifically, our work is aimed at illustrating the conceptual viability of the optical readout of ND-GAr's TPC (within the DUNE Near-Detector complex), in terms of material compatibility. For our proposal, with perforated distributors aligned with the electric field, and under realistic assumptions, the concentration of contaminants can be controlled within a week after chamber filling. In the case of N$_2$, injection of fresh gas at %-level seems to represent the safest strategy to keep the concentration within operability limits.