Late time solution for interacting scalar in accelerating spaces
  We consider stochastic inflation in an interacting scalar field in spatially
homogeneous accelerating space-times with a constant principal slow roll
parameter $\epsilon$. We show that, if the scalar potential is scale invariant
(which is the case when scalar contains quartic self-interaction and couples
non-minimally to gravity), the late-time solution on accelerating FLRW spaces
can be described by a probability distribution function (PDF) $\rho$ which is a
function of $\varphi/H$ only, where $\varphi=\varphi(\vec x)$ is the scalar
field and $H=H(t)$ denotes the Hubble parameter. We give explicit late-time
solutions for $\rho\rightarrow \rho_\infty(\varphi/H)$, and thereby find the
order $\epsilon$ corrections to the Starobinsky-Yokoyama result. This PDF can
then be used to calculate e.g. various $n-$point functions of the
(self-interacting) scalar field, which are valid at late times in arbitrary
accelerating space-times with $\epsilon=$ constant.
