Causality Constrains Higher Curvature Corrections to Gravity

TL;DR

The paper investigates how causality constrains higher-curvature corrections to gravity, focusing on quartic Riemann terms in the effective action. Using ultraviolet perturbations on backgrounds with quartic corrections, it derives a dispersion relation where subluminal propagation requires the quartic couplings to be nonnegative, notably yielding $k^2 = 64 c_1 (S^{\\alpha\\beta} e_{\\alpha\\beta})^2 + 64 c_2 (\\tilde S^{\\alpha\\beta} e_{\\alpha\\beta})^2$; string-theory corrections correspond to $c_1=c_2=24$, giving positive contributions. The leading cubic-order invariants do not affect the dispersion at leading order, while quadratic Ricci/scalar terms are removable by field redefinitions. These results constrain viable quantum-gravity candidates by enforcing positivity of higher-curvature couplings.

Abstract

We show that causality constrains the sign of quartic Riemann corrections to the Einstein-Hilbert action. Our constraint constitutes a restriction on candidate theories of quantum gravity.