  The finite-temperature effective potential customarily employed to describe
the physics of cosmological phase transitions often relies on specific gauge
choices, and is manifestly not gauge-invariant at finite order in its
perturbative expansion. As a result, quantities relevant for the calculation of
the spectrum of stochastic gravity waves resulting from bubble collisions in
first-order phase transitions are also not gauge-invariant. We assess the
quantitative impact of this gauge-dependence on key quantities entering
predictions for gravity waves from first order cosmological phase transitions.
We resort to a simple abelian Higgs model, and discuss the case of R_xi gauges.
By comparing with results obtained using a gauge-invariant Hamiltonian
formalism, we show that the choice of gauge can have a dramatic effect on
theoretical predictions for the normalization and shape of the expected gravity
wave spectrum. We also analyze the impact of resumming higher-order
contributions as needed to maintain the validity of the perturbative expansion,
and show that doing so can suppress the amplitude of the spectrum by an order
of magnitude or more. We comment on open issues and possible strategies for
carrying out "daisy resummed" gauge invariant computations in non-Abelian
models for which a gauge-invariant Hamiltonian formalism is not presently
available.
