Constraining Cubic Curvature Corrections to General Relativity with Quasi-Periodic Oscillations

We investigate observational constraints on cubic curvature corrections to general relativity by analyzing quasi-periodic oscillations (QPOs) in accreting black hole systems. In particular, we study Kerr black hole solution corrected by cubic curvature terms parameterized by ${\beta }_5$ and ${\beta }_6$. While ${\beta }_6$ corresponds to a field-redefinition invariant structure, the ${\beta }_5$ term can in principle be removed via a field redefinition. Nonetheless, since we work in the frame where the accreting matter minimally couples to the metric, ${\beta }_5$ is in general present. Utilizing the corrected metric, we compute the QPO frequencies within the relativistic precession framework. Using observational data from GRO J1655$-$40 and a Bayesian analysis, we constrain the coupling parameters to $-12.31<\frac{{\beta }_5}{(5M_{\odot }{)}^4}<24.15$ and $-1.99<\frac{{\beta }_6}{(5M_{\odot }{)}^4}<0.30$ at 2-$\sigma$. These bounds improve upon existing constraints from big-bang nucleosynthesis and the speed of gravitational waves.