Flat space cosmologies in two dimensions: Phase transitions and asymptotic mass domination

We study flat space cosmologies in two dimensions by taking the flat space limit of the Achucarro-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.