Constraining the mass of the graviton using coalescing black-hole binaries

We study how well the mass of the graviton can be constrained from gravitational-wave (GW) observations of coalescing binary black holes. Whereas the previous investigations employed post-Newtonian (PN) templates describing only the inspiral part of the signal, the recent progress in analytical and numerical relativity has provided analytical waveform templates coherently describing the inspiral-merger-ringdown (IMR) signals. We show that a search for binary black holes employing IMR templates will be able to constrain the mass of the graviton much more accurately ($\sim$ an order of magnitude) than a search employing PN templates. The best expected bound from GW observatories (${\lambda }_g>7.8\times {10}^{13}\mathrm{km}$ from Advanced LIGO, ${\lambda }_g>7.1\times {10}^{14}\mathrm{km}$ from Einstein Telescope, and ${\lambda }_g>5.9\times {10}^{17}\mathrm{km}$ from LISA) are several orders of magnitude better than the best available model-independent bound (${\lambda }_g>2.8\times {10}^{12}\mathrm{km}$, from solar system tests).

Figure 1

(left) Top panels show the lower bound on the Compton wavelength ${\lambda }_g$ of the graviton that can be placed from observations of equal-mass binaries located at distances such that they produce optimal SNRs of 10 in the Advanced LIGO (black traces) and ET (grey traces) detectors using their smallest low-frequency cutoffs (10 Hz and 1 Hz, respectively). Middle panels show the same bounds from binaries located at 1 Gpc, and the bottom panels show the optimal SNR produced by these binaries. Horizontal axes report the total mass of the binary. Solid and dashed lines correspond to IMR and restricted 3.5PN waveforms, respectively. (right) Same plots for the case of binaries located at 3 Gpc detected in the LISA detector.

Figure 2

Optimal SNR (lower panel) and the lower bound on the Compton wavelength ${\lambda }_g$ of graviton (upper panel) for IMR waveforms detected at 1 Gpc by the Advanced LIGO detector. Black and grey curves correspond to low-frequency cutoffs 10 Hz and 20 Hz, respectively, while solid, dashed, and dotted curves correspond to mass ratios $\eta =1/4$, $2/9$, and $4/25$.

Figure 3

Optimal SNR (lower panel) and the lower bound on the Compton wavelength ${\lambda }_g$ of graviton (upper panel) for IMR waveforms detected at 1 Gpc by the ET detector. Black, dark grey, and light grey curves correspond to low-frequency cutoffs 1 Hz, 5 Hz, and 10 Hz, respectively, while solid, dashed, and dotted curves correspond to mass ratios $\eta =1/4$, $2/9$, and $4/25$.

Figure 4

Optimal SNR (lower panel) and the lower bound on the Compton wavelength ${\lambda }_g$ of graviton (upper panel) for IMR waveforms detected at 3 Gpc with the LISA detector. The solid, dashed, and dotted curves correspond to mass ratios $\eta =1/4$, $2/9$, and $4/25$.