Spatial Curvature at the Sound Horizon

Understand

The effect of spatial curvature on primordial perturbations is controlled by $ \Omega_{K,0}/c_{s}^{2} $, where $ \Omega_{K,0} $ is today's fractional density of spatial curvature and $ c_{s} $ is the speed of sound during inflation.

• Here we study these effects in the limit $ c_{s}\ll 1 $.
• First, we show that the standard cosmological soft theorems in flat universes are violated in curved universes and the soft limits of correlators can have non-universal contributions even in single-clock inflation.
• This is a consequence of the fact that, in the presence of spatial curvature, there is a gap between the spectrum of residual diffeomorphisms and that of physical modes.