Constraining the evolution of Newton's constant with slow inspirals observed from spaceborne gravitational-wave detectors

Understand

Spaceborne gravitational-wave (GW) detectors observing at milli-Hz and deci-Hz frequencies are expected to detect large numbers of quasi-monochromatic signals.

• The first and second time-derivative of the GW frequency ($\dot f_0$ and $\ddot f_0$) can be measured for the most favourable sources and used to look for negative post-Newtonian corrections, which can be induced by the source's environment or modifications of general relativity.
• We present an analytical, Fisher-matrix-based approach to estimate how precisely such corrections can be constrained.
• We use this method to estimate the bounds attainable on the time evolution of the gravitational constant $G(t)$ with different classes of quasi-monochromatic sources observable with LISA and DECIGO, two representative spaceborne detectors for milli-Hz and deci-Hz GW frequencies.