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

TL;DR

This paper uses observed quasi-periodic oscillations in black hole systems to place new constraints on cubic curvature modifications to general relativity, improving previous bounds.

Contribution

It provides the first observational constraints on cubic curvature corrections to GR using QPO data and Bayesian analysis.

Findings

Constraints on $eta_5$ and $eta_6$ parameters at 2-$\sigma$ level

Bounds improve upon previous big-bang nucleosynthesis limits

Bounds also surpass constraints from gravitational wave speed measurements

Abstract

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 $-12.31<\frac{\beta_5}{(5 M_\odot)^4}<24.15$ and $-1.99<\frac{\beta_6}{(5 M_\odot)^4}<0.30$ at 2-$\sigma$. These bounds improve upon existing constraints from big-bang nucleosynthesis and the speed of gravitational waves.