Description
The effective potential of a scalar field is a powerful tool in quantum field theory. Loosely speaking, it can be interpreted as the quantum corrected classical potential of the field, and in cosmology it is widely used to describe the evolution of the inflaton and other scalars during inflation and vacuum transition probabilities, among other things. However, for light scalar fields its standard definition has an infrared problem, which means that it is dominated by very long-wavelength fluctuations.
In this talk, I discuss an alternative definition, known as the constraint effective potential, dating back to 1980s. In Minkowski spacetime, the two definitions are equivalent, but in de Sitter spacetime they are not, and crucially the constraint effective potential does not suffer from the same infrared problem. I demonstrate this with an explicit one-loop calculation of the two effective potentials for a real scalar field in de Sitter in dimensional regularisation. I compare the resulting potentials and their physical interpretations, and in particular, I argue that the constraint effective potential is the correct one to use in certain common cosmological applications, for example stochastic inflation.
This work was carried out in collaboration with Lucas Vicente Garcia-Consuegra.
