Adiabatic Modes in an Open Universe

Abstract

Adiabatic modes are solutions in general relativity which are locally indistinguishable from the Friedmann-Lema\^itre-Robertson-Walker metric after an appropriate transformation. In other words, they are cosmological perturbations which resemble a pure gauge profile. Many adiabatic modes are known for spatially flat universes, providing model-independent solutions and implying soft theorems. In this thesis, we generalize the theory of adiabatic modes to open universes (i.e. universes with negative spatial curvature). The main results are the open-universe versions of Weinberg's tensor adiabatic mode in equation (5.23) and Weinberg's scalar adiabatic modes in equation (6.19). These modes are, however, puzzling. While it appears that for the tensor gauge modes are physical (sub-curvature), it seems that monochromatic scalar modes can never become adiabatic. This could imply, for single-field inflation in an open universe, that inflation does not solely produce adiabatic modes and that Maldacena's consistency condition is violated. Future research to get to the bottom of these issues is suggested.