Constraint effective potential and stochastic theory in de Sitter spacetime

The effective potential is a powerful and widely used tool in quantum field theory. However, in de Sitter spacetime, which is a good approximation for the inflationary era, it does not have a unique definition. I will discuss the constraint effective potential introduced by O'Raifeartaigh et al. in 1986, as an alternative to the usual textbook definition. I present the complete one-calculation of both potentials in scalar field theory, showing that the constraint effective potential does not suffer from the infrared problem that plagues perturbative calculations in de Sitter for light scalar fields. I further demonstrate that when the constraint effective potential is used in the Starobinsky-Yokoyama effective theory, it reproduces correctly the infrared behaviour of QFT correlation functions and the vacuum decay rate at one-loop order.