  Calculating the quantum evolution of a de Sitter universe on superhorizon
scales is notoriously difficult. To address this challenge, we introduce the
Soft de Sitter Effective Theory (SdSET). This framework holds for superhorizon
modes whose comoving momentum is far below the UV scale, which is set by the
inverse comoving horizon. The SdSET is formulated using the same approach that
yields the Heavy Quark Effective Theory. The degrees of freedom that capture
the long wavelength dynamics are identified with the growing and decaying
solutions to the equations of motion. The operator expansion is organized using
a power counting scheme, and loops can be regulated while respecting the low
energy symmetries. For massive quantum fields in a fixed de Sitter background,
power counting implies that all interactions beyond the horizon are irrelevant.
Alternatively, if the fields are very light, the leading interactions are at
most marginal, and resumming the associated logarithms using (dynamical)
renormalization group techniques yields the evolution equation for canonical
stochastic inflation. The SdSET is also applicable to models where gravity is
dynamical, including inflation. In this case, diffeomorphism invariance ensures
that all interactions are irrelevant, trivially implying the all-orders
conservation of adiabatic density fluctuations and gravitational waves. We
briefly touch on the application to slow-roll eternal inflation by identifying
novel relevant operators. This work serves to demystify many aspects of
perturbation theory outside the horizon, and has a variety of applications to
problems of cosmological interest.
