# Bounding Alternative Theories of Gravity with Multi-Band GW Observations

## TL;DR

This paper demonstrates that multi-band gravitational wave observations significantly tighten constraints on various alternative gravity theories, especially highlighting the importance of intermediate-frequency interferometers.

## Contribution

It provides the first comprehensive analysis of how multi-band GW data can improve bounds on multiple classes of modified gravity theories.

## Key findings

- Multi-band GW observations improve bounds on gravity theories by several orders of magnitude.
- Intermediate-frequency interferometers are crucial for constraining deviations from General Relativity.
- Constraints are effective for both pre- and post-Newtonian deviations.

## Abstract

We study the constraints on alternative theories of gravity that can be determined by multi-band observations of gravitational wave signals emitted from binary black hole coalescences. We focus on three types of General Relativity modifications induced by a generalised Brans-Dicke theory, and two classes of quadratic gravity, Einstein-dilaton-Gauss-Bonnet and dynamical Chern-Simons. Considering a network of space and ground-based detectors, supplied by a population of spinning binaries black hole, we show how the multi-band analysis improves the existing bounds on the theory's parameters by several orders of magnitude, for both pre- and post-Newtonian deviations. Our results also show the fundamental role played by an interferometer in the frequency range between LISA and advanced detectors, in constraining possible deviations from General Relativity.