  False vacuum decay, a quantum mechanical first-order phase transition in
scalar field theories, is an important phenomenon in early universe cosmology.
Recently, real-time semi-classical techniques based on ensembles of lattice
simulations were applied to the problem of false vacuum decay. In this context,
or any other lattice simulation, the effective potential experienced by
long-wavelength modes is not the same as the bare potential. To make
quantitative predictions using the real-time semi-classical techniques, it is
therefore necessary to understand the redefinition of model parameters and the
corresponding deformation of the vacuum state, as well as stochastic
contributions that require modeling of unresolved subgrid modes. In this work,
we focus on the former corrections and compute the expected modification of the
true and false vacuum effective mass, which manifests as a modified dispersion
relationship for linear fluctuations about the vacuum. We compare these
theoretical predictions to numerical simulations and find excellent agreement.
Motivated by this, we use the effective masses to fix the shape of a
parameterized effective potential, and explore the modeling uncertainty
associated with non-linear corrections. We compute the decay rates in both the
Euclidean and real-time formalisms, finding qualitative agreement in the
dependence on the UV cutoff. These calculations further demonstrate that a
quantitative understanding of the rates requires additional corrections.
