Theoretical and Observational Bounds on Dynamical Chern-Simons Gravity as an Effective Field Theory

Abstract

Gravitational effective theories are essential for characterizing the space of deviations from General Relativity (GR). Testing these theories against fundamental principles, such as causality and unitarity, can yield constraints on the corresponding parameters. In this paper, we perform such an analysis on the very interesting dynamical Chern-Simons (dCS) gravity. This is a parity violating correction to GR wherein a new scalar field couples to the Pontryagin density $^*R\,R$. It has generated significant interest, including possible new gravitational wave shapes for LIGO/Virgo and new phenomena from cosmic inflation. In this work, we begin by deriving the dispersion relation and wave packet speed on top of a gravitational wave background in dCS gravity. This alters the corresponding Shapiro time delay (which we compute to second order), potentially giving superluminality. Causality then demands a bound on the dCS coupling constant, which we find to be moderately sharper than, but compatible with, standard estimates. We then examine a UV completion in the form of a set of $N$ fermions with a (pseudo) Yukawa coupling. By imposing perturbativity and a gravitational species bound, we find that the dCS coupling constant is constrained significantly more, depending on the choice of scale of the species bound. We also identify higher order operators generated from the UV completion. Overall, we find that any dCS corrections to gravitational dynamics should likely be very small on macroscopic systems of observational interest, such as in late-time merging black holes.