Perturbation spectrum after inflation

[smallphi]

The spectrum of perturbations at the end of inflation, which turns out to be flat and slightly red shifted, is calculated under the assumption that each perturbation mode crosses some initial time in the comoving coordinates with 'minimum energy allowed by the Heisenberg uncertainty principle'.

Does the spectrum change if the initial conditions of the modes are changed?

Isn't using the comoving coordinates in violation of the principle of general covariance in GR i. e. it singles out a preferred frame to calculate 'physical observables'?

 

[Aaron Bex]

Yes, the spectrum can change if the initial conditions of the modes are changed. However, the Heisenberg uncertainty principle still applies in this case and provides a constraint on the initial conditions of the perturbation modes. The use of comoving coordinates is not a violation of the principle of general covariance in GR, as comoving coordinates are just a choice of coordinates used to describe the spacetime. These coordinates provide a convenient way to calculate physical observables, but do not single out a preferred frame.