Geodesic models of quasi-periodic-oscillations as probes of quadratic gravity

Future very-large-area X-ray instruments (for which the effective area is larger than $>3$m$^2$) will be able to measure the frequencies of quasi-periodic oscillations~(QPOs) observed in the X-ray flux from accreting compact objects with sub-percent precision. If correctly modeled, QPOs can provide a novel way to test the strong-field regime of gravity. By using the relativistic precession model and a modified version of the epicyclic resonance model, we develop a method to test general relativity against a generic class of theories with quadratic curvature corrections. With the instrumentation being studied for future missions such as eXTP, LOFT, or STROBE-X, a measurement of at least two QPO triplets from a stellar mass black hole can set stringent constraints on the coupling parameters of quadratic gravity.