Gravitational-wave responses and noise correlations in geometric time-delay interferometry
Abstract
Space-based gravitational-wave observations will probe the formation and growth of massive black holes and the evolution of compact binaries in the millihertz band. We develop a geometric-link representation of time-delay interferometry using six round-trip and six non-round-trip two-link blocks. Starting from the one-way Doppler response, we derive the elementary block responses and a dictionary that expresses 45 known second-generation combinations in terms of these blocks and residual one-way measurements. Representative Michelson and Relay observables admit compact forms, from which analytical sky-averaged tensor responses are obtained for a fixed, equal-arm constellation. We also derive the noise covariance of the blocks, retaining cross-spectra between blocks that share measurement streams. The resulting noise spectra agree with direct one-way assembly. We apply this formulation to a narrowband compact-binary signal in an equal-arm LISA instrument model. For the Relay example, neglecting the shared-link cross-spectrum changes the low-frequency noise scaling and overestimates the conditional Fisher uncertainties in amplitude or distance by factors of 10.71 at 1~mHz and 3.37 at 3~mHz.
Related
- Path-Degenerate Quantum Interferometry for Loss Resilience in Gravitational-Wave Detectors
- Optimizing Laguerre-Gaussian Mode Interferometry in Gravitational-Wave Detectors through Modal Degeneracy Breaking
- Parity-odd CMB Correlations induced by a Chiral Gravitational Wave Background
- First Measurement of the Hubble Constant from Gravitational Wave–Galaxy Cross Correlations
- Population-level correlations in Bayesian statistics: an illustrative model for gravitational-wave astronomy
BibTeX
@misc{luo2026gravitationalwave,
title = {{Gravitational-wave responses and noise correlations in geometric time-delay interferometry}},
author = {Rui Luo and Pan-Pan Wang and Lin-Lin Yang and Xin-Lei Zhao and Cheng-Gang Shao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.28173},
eprint = {2606.28173},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.28173},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Gravitational-wave responses and noise correlations in geometric time-delay interferometry
AU - Rui Luo
AU - Pan-Pan Wang
AU - Lin-Lin Yang
AU - Xin-Lei Zhao
AU - Cheng-Gang Shao
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2606.28173
UR - https://arxiv.org/abs/2606.28173
AB - Space-based gravitational-wave observations will probe the formation and growth of massive black holes and the evolution of compact binaries in the millihertz band. We develop a geometric-link representation of time-delay interferometry using six round-trip and six non-round-trip two-link blocks. Starting from the one-way Doppler response, we derive the elementary block responses and a dictionary that expresses 45 known second-generation combinations in terms of these blocks and residual one-way measurements. Representative Michelson and Relay observables admit compact forms, from which analytical sky-averaged tensor responses are obtained for a fixed, equal-arm constellation. We also derive the noise covariance of the blocks, retaining cross-spectra between blocks that share measurement streams. The resulting noise spectra agree with direct one-way assembly. We apply this formulation to a narrowband compact-binary signal in an equal-arm LISA instrument model. For the Relay example, neglecting the shared-link cross-spectrum changes the low-frequency noise scaling and overestimates the conditional Fisher uncertainties in amplitude or distance by factors of 10.71 at 1~mHz and 3.37 at 3~mHz.
ER -