Initial state effects on the cosmic microwave background and trans-Planckian physics

There exists a one complex parameter family of de Sitter invariant vacua, known as α vacua. In the context of slow roll inflation, we show that all but the Bunch-Davies vacuum generates unacceptable production of high energy particles at the end of inflation. As a simple model for the effects of trans-Planckian physics, we go on to consider non–de Sitter invariant vacua obtained by patching modes in the Bunch-Davies vacuum above some momentum scale $M_c,$ with modes in an α vacuum below $M_c.$ Choosing $M_c$ near the Planck scale $M_{\mathrm{Pl}},$ we find acceptable levels of hard particle production, and corrections to the cosmic microwave perturbations at the level of ${\mathrm{HM}}_{\mathrm{Pl}}{/M}_c^2,$ where H is the Hubble parameter during inflation. More general initial states of this type with $H\ll M_c\ll M_{\mathrm{Pl}}$ can give corrections to the spectrum of cosmic microwave background perturbations at order 1. The parameter characterizing the α vacuum during inflation is a new cosmological observable.