Adiabatic regularization and preferred vacuum state for the $\lambda {\phi }^4$ field theory in cosmological spacetimes

We extend the method of adiabatic regularization by introducing an arbitrary parameter $\mu$ for a scalar field with quartic self-coupling in a Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime at one-loop order. The subtraction terms constructed from this extended version allow us to define a preferred vacuum state at a fixed time $\eta ={\eta }_0$ for this theory. We compute this vacuum state for two commonly used background fields in cosmology. We also give a possible prescription for an adequate value for $\mu$.