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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. [ABSTRACT FROM AUTHOR]

We study flat space cosmologies in two dimensions by taking the flat space limit of the Achúcarro-Ortiz model. We unravel a phase transition between hot flat space and flat space cosmologies, and derive a new dilaton-dependent counterterm required for the consistency of the Euclidean partition function. Our results generalize to asymptotically mass-dominated two-dimensional dilaton gravity models, whose thermodynamical properties we discuss. The novel case of asymptotic mass domination is covered neither by the comprehensive discussion of Grumiller and McNees [J. High Energy Phys. 04 (2007) 074] nor by the more recent generalization to dilaton gravity with confining U(1) charges in Grumiller et al. [Phys. Rev. D 90, 044032 (2014)]. [ABSTRACT FROM AUTHOR]