  We extend the method of adiabatic regularization by introducing an arbitrary
parameter $\mu$ for a scalar field with quartic self-coupling in a
Friedmann-Lema\^itre-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 $\mu$.
