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General Relativity and Quantum Cosmology, gr-qc
Abstract:
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. We find that the most constraining source among a simulated
population of LISA galactic binaries could yield $\dot G/G_0 \lesssim
10^{-6}\text{yr}^{-1}$, while the best currently known verification binary will
reach $\dot G/G_0 \lesssim 10^{-4}\text{yr}^{-1}$. We also perform Monte-Carlo
simulations using quasi-monochromatic waveforms to check the validity of our
Fisher-matrix approach, as well as inspiralling waveforms to analyse binaries
that do not satisfy the quasi-monochromatic assumption. We find that our
analytical Fisher matrix produces good order-of-magnitude constraints even for
sources well beyond its regime of validity. Monte-Carlo investigations also
show that chirping stellar-mass compact binaries detected by DECIGO-like
detectors at cosmological distances of tens of Mpc can yield constraints as
tight as $\dot G/G_0 \lesssim 10^{-11}\text{yr}^{-1}$.
