Non-perturbative results for a massive scalar field during de Sitter inflation

We consider an infrared truncated massive minimally coupled scalar field with an asymmetric self-interaction $\frac{m^2}{2}{\phi }^2\text{\hspace{0.17em}⁣}+\text{\hspace{0.17em}⁣}\frac{\lambda {\phi }^4}{4!}\text{\hspace{0.17em}⁣}+\text{\hspace{0.17em}⁣}\frac{\beta {\phi }^3}{3!}(\lambda \text{\hspace{0.17em}⁣}>\text{\hspace{0.17em}⁣}0)$ during a cosmological constant driven de Sitter inflation with a constant expansion rate, $H$. The Fokker-Planck equation for the evolution of the massive scalar field is obtained and solved for this asymmetric potential. Firstly we compute the vacuum expectation values of $\phi$ and ${\phi }^2$ using the normalized late-time probability distribution $\rho (\phi ,t)$. Secondly, we evaluate the two-point correlation function and the vacuum expectation value of the massive scalar field at tree and one-loop order following Starobinsky’s approach and applying the techniques of perturbative quantum field theory. Lastly, we compare the results obtained via these two different methods. Although these results give consistent qualitative behavior at tree and one-loop order, they differ numerically.