Red and blue tilted tensor spectrum from Gibbons-Hawking temperature

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The scale invariant scalar and tensor perturbations, which are predicted from inflation, are eigenmodes in the conformal coordinates. The 'out' observer in the de Sitter space observes a thermal spectrum with a Gibbons-Hawking temperature H/2π of these 'Bunch-Davies' particles. The tensor power spectrum observed in experiments can have an imprint of the Gibbons-Hawking thermal distribution due to the mode mixing between 'in' state conformal coordinates and the coordinate frame of the observer. We find that the the Bunch-Davies modes appear as thermal modes to the asymptotic Minkowski observer in the future and the power spectrum of the gravitational waves is blue-tilted with a spectral index nₜ 1 even in the standard slow-roll inflation. On the other hand if the coordinate frame of the observer is taken to be static coordinates, the tensor spectrum is red-tilted with nₜ -1. A likelihood analysis shows and find the best fit values of the slow-roll parameters for both cases. We find that the blue-tilted tensor gives a better fit and reconciles the PLANCK upper bound on the tensor-to-scalar ratio, r <0.11 with BICEP2 measurement of r=0.2. This supports the idea of particle production due to the mode mixing between the initial Bunch-Davies vacuum modes and the asymptotic Minkowski vacuum of the post-inflation universe.