In this talk, I will review our recent work and its attempt to extend the scope and predictive power of the stochastic formalism for inflation. After briefly introducing our gauge-invariant coarse-graining procedure, I will discuss our formulation of stochastic dynamics in full General Relativity, including all metric and scalar matter degrees of freedom, as well as gradient contributions. I will then present numerical implementations of these stochastic equations within the framework of Numerical Relativity, demonstrating their efficacy in well-understood scenarios and their application to ongoing investigations.
With this framework fully established, I will show how the formalism can be generalised beyond General Relativity, in particular to scalar–tensor theories of dark energy and multifield scenarios, and potentially beyond.
Finally, if time permits, and given the newly unlocked possibility of studying near-horizon phenomena and broader classes of theories, I will conclude by discussing how one can identify the stochastically relevant regions of spacetime.

Link to Zoom registration
https://zoom.us/meeting/register/j5gHBKwzR9GpMTxn5V0iWA