Determine whether the Horndeski ratio is radiatively stable in broader truncations

Determine whether the approximate radiative stability of the Horndeski coupling ratio persists when additional scalar-tensor interactions are included beyond the truncation containing $C_S$ and $C_T$.

Background

The paper finds that the ratio CS/CT=−1/2C_S/C_T=-1/2 is generally not exactly preserved by gravitational renormalization-group flow, although approximate stability appears at sufficiently large absolute values of the scalar couplings. This result is based on a restricted truncation. The authors state that a more general analysis is needed to determine whether the apparent approximate protection survives after additional interactions are included.

References

Overall, we conclude that radiative stability, or even asymptotic safety of Horndeski gravity has not been ruled out with our study, as would have been our expectation. Future investigation of these questions therefore is warranted.

— Emergence of Horndeski gravity from asymptotic safety?  (2609.29369 - Eichhorn et al., 24 Sep 2026) in Section 5, Conclusion and outlook; Section 4, Radiative stability of Horndeski coupling ratios under gravitational fluctuations