Non-Bunch–Davis initial state reconciles chaotic models with BICEP and Planck

The BICEP2 experiment has announced a signal for primordial gravity waves with tensor-to-scalar ratio r=0.2−0.05+0.07[1]. There are two ways to reconcile this result with the latest Planck experiment [2]. One is by assuming that there is a considerable tilt of r  , TrTr, with a positive sign, Tr=dln⁡r/dln⁡k≳0.57−0.27+0.29 corresponding to a blue tilt for the tensor modes of order nT≃0.53−0.27+0.29, assuming the Planck experiment best-fit value for tilt of scalar power spectrum nSnS. The other possibility is to assume that there is a negative running in the scalar spectral index, dnS/dln⁡k≃−0.02dnS/dln⁡k≃−0.02 which pushes up the upper bound on r   from 0.11 up to 0.26 in the Planck analysis assuming the existence of a tensor spectrum. Simple slow-roll models fail to provide such large values for TrTr or negative runnings in nSnS[1]. In this note we show that a non-Bunch–Davies initial state for perturbations can provide a match between large field chaotic models (like m2ϕ2m2ϕ2) with the latest Planck result [3] and BICEP2 results by accommodating either the blue tilt of r   or the negative large running of nSnS.