Micromesh gas amplification structures (Micromegas) can be used as readout of Time Projection Chambers in the field of Rare Event searches dealing with dark matter, double beta decay or solar axions. The topological information of events offered by these gaseous detectors is a very powerful tool for signal identification and background rejection. However, in this kind of experiments the radiopurity of the detector components and surrounding materials must be thoroughly controlled in addition in order to keep the experimental background as low as possible.A screening program based mainly on gamma-ray spectrometry using an ultra-low background HPGe detector in the Canfranc Underground Laboratory is being developed for several years, with the aim to measure the activity levels of materials used in the Micromegas planes and also in other components involved in a plausible experimental set-up: gas vessel, field cage, electronic boards, calibration system or shielding.

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We consider stochastic inflation coarse-grained using a general class of exponential filters. Such a coarse-graining prescription gives rise to inflaton-Langevin equations sourced by colored noise that is correlated in e-fold time. The dynamics are studied first in slow-roll for simple potentials using first-order perturbative, semi-analytical calculations which are later compared to numerical simulations. Subsequent calculations are performed using an exponentially correlated noise which appears as a leading order correction to the full slow-roll noise correlation functions of the type 〈ξ(N)ξ(N')〉(n) ∼ (cosh[n(N-N'+1])-1. We find that the power spectrum of curvature perturbations 𝒫 ζ is suppressed at small e-folds, with the suppression controlled by n. Furthermore, we use the leading order, exponentially correlated noise and perform a first passage time analysis to compute the statistics of the stochastic e-fold distribution 𝒩 and derive an approximate expression for the mean number of e-folds 〈𝒩〉. Comparing analytical results with numerical simulations of the inflaton dynamics, we show that the leading order noise correlation function can be used as a very good approximation of the exact noise, the latter being more difficult to simulate.