Frequency response of time-delay interferometry for space-based gravitational wave antennas

Understand

Space-based gravitational wave detectors cannot keep rigid structures and precise arm length equality, so the precise equality of detector arms which is required in a ground-based interferometer to cancel the overwhelming laser noise is impossible.

• The time-delay interferometry method is applied to unequal arm lengths to cancel the laser frequency noise.
• We give analytical formulas of the averaged response functions for tensor, vector, breathing and longitudinal polarizations in different TDI combinations, and obtain their asymptotic behaviors.
• At low frequencies, $f\ll f_*$, the averaged response functions of all TDI combinations increase as $f^2$ for all six polarizations.