Measuring the propagation speed of gravitational waves with LISA

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<jats:title>Abstract</jats:title> <jats:p>The propagation speed of gravitational waves, <jats:italic>c<jats:sub>T</jats:sub> </jats:italic>, has been tightly constrained by the binary neutron star merger GW170817 and its electromagnetic counterpart, under the assumption of a frequency-independent <jats:italic>c<jats:sub>T</jats:sub> </jats:italic>. Drawing upon arguments from Effective Field Theory and quantum gravity, we discuss the possibility that modifications of General Relativity allow for transient deviations of <jats:italic>c<jats:sub>T</jats:sub> </jats:italic> from the speed of light at frequencies well below the band of current ground-based detectors. We motivate two representative Ansätze for <jats:italic>c<jats:sub>T</jats:sub> </jats:italic>(<jats:italic>f</jats:italic>), and study their impact upon the gravitational waveforms of massive black hole binary mergers detectable by the LISA mission. We forecast the constraints on <jats:italic>c<jats:sub>T</jats:sub> </jats:italic>(<jats:italic>f</jats:italic>) obtainable from individual systems and a population of sources, from both inspiral and a full inspiral-merger-ringdown waveform. We show that LISA will enable us to place stringent independent bounds on departures from General Relativity in unexplored low-frequency regimes, even in the absence of an electromagnetic counterpart.</jats:p>

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