Red and blue tilted tensor spectrum from Gibbons-Hawking temperature
  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 $H/2\pi$ 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 $n_T \sim 1$ 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 $n_T\sim -1$. 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.
