Variational principle and one-point functions in three-dimensional flat space Einstein gravity

We provide a well-defined variational principle for three-dimensional flat space Einstein gravity by adding one-half of the Gibbons-Hawking-York boundary term to the bulk action. We check the zero-point function, recovering consistency with thermodynamics of flat space cosmologies. We then apply our result to calculate the one-point functions in flat space Einstein gravity for the vacuum and all flat space cosmologies. The results are compatible with the ones for the zero-mode charges obtained by canonical analysis.