Cross-correlation analysis of detector pairs is a standard method for probing the stochastic gravitational-wave background (SGWB). The correlation signal is determined by the SGWB intensity and the geometric sensitivity of the detector pair, which can be quantified by the overlap reduction function (ORF). In our previous work [Phys. Rev. D 111, 084065 (2025)], we developed a formula to calculate the ORF of the SGWB with tensor polarization for pulsar timing arrays (PTAs) and laser interferometer detectors without approximation. In this work, we generalize the method to calculate the ORF for vector and scalar polarizations that may be present in alternative theories of gravity. This formula is valid for any experiment measuring variations in light travel time between two points due to gravitational waves. Using this formula, we derive expressions for the ORFs of PTAs, ground-based interferometers, and space-based interferometers for all polarizations. Furthermore, this universal formula provides enhanced accuracy for ORF calculations in high-frequency regimes of third-generation ground-based interferometers and space-based interferometers. An important practical implication is its ability to break the degeneracy between scalar-breathing and scalar-longitudinal polarizations that arises in the small-antenna approximation, thereby providing a foundation for distinguishing them in data analysis.

Close

PrevNext

View figure in article

• Alternative gravity theories
• Gravitational wave detection