Measuring violations of General Relativity from single gravitational wave detection by non-spinning binary systems: higher-order asymptotic analysis

Abstract

A frequentist asymptotic expansion method for error estimation is employed for a network of gravitational wave detectors to assess the capability of gravitational wave observations, with Adv. LIGO and Adv. Virgo, to distinguish between the post-Einsteinian (ppE) description of coalescing binary systems and that of GR. When such errors are smaller than the parameter value, there is possibility to detect these violations from GR. A parameter space with inclusion of dominant dephasing ppE parameters is used for a study of first- and second-order (co)variance expansions, focusing on the inspiral stage of a nonspinning binary system of zero eccentricity detectible through Adv. LIGO and Adv. Virgo. Our procedure is more reliable than frequentist studies based only on Fisher information estimates and complements Bayesian studies. Second-order asymptotics indicate the possibility of constraining deviations from GR in low-SNR (ρ ~ 15 - 17) regimes. The errors on β also increase errors of other parameters such as the chirp mass M and symmetric mass ratio η. Application is done to existing alternative theories of gravity, which include modified dispersion relation of the waveform, non-spinning models of quadratic modified gravity, and dipole gravitational radiation (i.e., Brans-Dicke type) modifications.

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