Gravitational Waves from Quasicircular Extreme Mass-Ratio Inspirals as Probes of Scalar-Tensor Theories

TL;DR

This paper investigates how gravitational waves from extreme mass-ratio inspirals can test scalar-tensor theories of gravity, finding that such deviations are small but certain phenomena like floating orbits could provide strong constraints.

Contribution

It provides a comprehensive analysis of scalar-tensor modifications to EMRI gravitational wave signals and assesses their detectability with future detectors like LISA.

Findings

Scalar-tensor theories reduce to Brans-Dicke in EMRI limit

Massless theories show small deviations from GR in gravitational wave flux

Massive theories can produce floating orbits causing large dephasing

Abstract

A stellar-mass compact object spiraling into a supermassive black hole, an extreme-mass-ratio inspiral (EMRI), is one of the targets of future gravitational-wave detectors and it offers a unique opportunity to test General Relativity (GR) in the strong-field. We study whether generic scalar-tensor (ST) theories can be further constrained with EMRIs. We show that in the EMRI limit, all such theories universally reduce to massive or massless Brans-Dicke theory and that black holes do not emit dipolar radiation to all orders in post-Newtonian (PN) theory. For massless theories, we calculate the scalar energy flux in the Teukolsky formalism to all orders in PN theory and fit it to a high-order PN expansion. We derive the PN ST corrections to the Fourier transform of the gravitational wave response and map it to the parameterized post-Einsteinian framework. We use the effective-one-body framework adapted to EMRIs to calculate the ST modifications to the gravitational waveform. We find that such corrections are smaller than those induced in the early inspiral of comparable-mass binaries, leading to projected bounds on the coupling that are worse than current Solar System ones. Brans-Dicke theory modifies the weak-field, with deviations in the energy flux that are largest at small velocities. For massive theories, superradiance can lead to resonances in the scalar energy flux that can lead to floating orbits outside the innermost stable circular orbit and that last until the supermassive black hole loses enough mass and spin-angular momentum. If such floating orbits occur in the frequency band of LISA, they would lead to a large dephasing (~1e6 rads), preventing detection with GR templates. A detection that is consistent with GR would then rule out floating resonances at frequencies lower than the lowest observed frequency, allowing for the strongest constraints yet on massive ST theories.