We study the effects of explicit spacetime-symmetry breaking on primordial
tensor fluctuations using an effective-field theory for Lorentz/CPT violation.
We find that the graviton is still massless, but that the propagation speed of
tensor modes is modified, and we obtain a constraint on the coefficient
determining the symmetry breaking on the order of $10^{-15}$ from the recent
measurements of the speed of gravity. Due to the symmetry breaking, the
de-Sitter phase is modified, and during this inflationary epoch, the power
spectrum assumes a slow oscillation around the general-relativity limit;
further, we find that the primordial tensor power spectrum retains its scale
invariance, but that the amplitude is modified. We also find that the modes
which become subhorizon during radiation domination acquire a phase shift
proportional to the coefficient for Lorentz violation.

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