Compute birefringent gravitational-wave power spectra in the open gravity EFT

Compute the gravitational-wave power spectra for both circular polarizations in the presence of dissipative birefringence (non-zero parameter χ) within the open gravitational effective field theory developed in Lecture 5, and incorporate a consistent ultraviolet modification to tame the early-time polarization instability implied by the birefringent dispersion relation.

Background

In Lecture 5 the authors derive the quadratic action for tensor modes (gravitational waves) in their open gravity framework, identifying a dissipative birefringence term proportional to χ that leads to opposite-sign contributions for the two circular polarizations. The resulting sub-Hubble dispersion relation displays an exponential instability for one polarization when χ≠0.

While the non-birefringent case (χ=0) is worked out in detail—including retarded and Keldysh propagators and the tensor-to-scalar ratio—the birefringent case is not completed. The authors note that UV modifications (e.g., time-dependent couplings as in Chern–Simons gravity) are needed to tame the divergence but do not provide the resulting power spectra. This problem seeks the full computation of the birefringent gravitational-wave power spectra in the open EFT setup, accounting for an appropriate ultraviolet modification to render the calculation well-defined.