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 alpha 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 alpha vacuum below M-c. Choosing M-c near the Planck scale M-Pl, we find acceptable levels of hard particle production, and corrections to the cosmic microwave perturbations at the level of HMPl/M-c(2), where H is the Hubble parameter during inflation. More general initial states of this type with Hmuch less thanM(c)much less thanM(Pl) can give corrections to the spectrum of cosmic microwave background perturbations at order 1. The parameter characterizing the alpha vacuum during inflation is a new cosmological observable.