Speaker
Description
We formulate the phase-space stochastic inflationary dynamics in scalar-torsion $f(T,\phi)$ gravity. Applying cosmological perturbation theory (CPT) in the spatially flat gauge, we resolve the non-dynamical constraints, ensuring ghost-free stability with $P>0$ and luminal sound speed $c_s^2 = 1$, while deriving the anomalous effective mass $M_Q^2$ for non-linear models with $f_{,TT} \neq 0$. We analytically prove the exact equivalence in the super-horizon limit:$$\text{CPT}(k \to 0) \equiv \text{SUA}$$thereby validating the background deterministic drift. Applying Starobinsky coarse-graining, we construct the phase-space Langevin system for $(\phi, \Pi)$ and show that the diffusion matrix collapses to rank one outside the horizon. Furthermore, we define the diagnostic parameter:$$\mathcal{Q}{\text{diff}} \equiv \frac{3H^3\sqrt{P}}{2\pi |f{,\phi}|}$$ to identify the threshold where quantum diffusion dominates over classical drift. This framework provides a solid foundation for computing stochastic corrections to primordial observables and non-Gaussian tails relevant to primordial black hole production.