  Future space-based gravitational-wave detectors will detect gravitational
waves with high sensitivity in the millihertz frequency band, which provides
more opportunities to test theories of gravity than ground-based ones. The
study of quasinormal modes (QNMs) and their application to testing gravity
theories have been an important aspect in the field of gravitational physics.
In this study, we investigate the capability of future space-based
gravitational wave detectors such as LISA, TaiJi, and TianQin to constrain the
dimensionless deviating parameter for Einstein-dilaton-Gauss-Bonnet (EdGB)
gravity with ringdown signals from the merger of binary black holes. The
ringdown signal is modeled by the two strongest QNMs in EdGB gravity. Taking
into account time-delay interferometry, we calculate the signal-to-noise ratio
(SNR) of different space-based detectors for ringdown signals to analyze their
capabilities. The Fisher information matrix is employed to analyze the accuracy
of parameter estimation, with particular focus on the dimensionless deviating
parameter for EdGB gravity. The impact of the parameters of gravitational wave
sources on the estimation accuracy of the dimensionless deviating parameter has
also been studied. We find that the constraint ability of EdGB gravity is
limited because the uncertainty of the dimensionless deviating parameter
increases with the decrease of the dimensionless deviating parameter. LISA and
TaiJi has more advantages to constrain the dimensionless deviating parameter to
a more accurate level for the massive black hole, while TianQin is more
suitable for less massive black holes. Bayesian inference method is used to
perform parameter estimation on simulated data, which verifies the reliability
of the conclusion.
