Effects of calibration uncertainties on the detection and parameter estimation of isotropic gravitational-wave backgrounds

Gravitational-wave backgrounds are expected to arise from the superposition of gravitational-wave signals from a large number of unresolved sources and also from the stochastic processes that occurred in the early Universe. So far, we have not detected any gravitational-wave background, but with the improvements in the detectors' sensitivities, such detection is expected in the near future. The detection and inferences we draw from the search for a gravitational-wave background will depend on the source model, the type of search pipeline used, and the data generation in the gravitational-wave detectors. In this paper, we focus on the effect of the data generation process, specifically the calibration of the detectors' digital output into strain data used by the search pipelines. Using the calibration model of the current LIGO detectors as an example, we show that for power-law source models and calibration uncertainties less than or similar to 10%, the detection of isotropic gravitational-wave background is not significantly affected. We also show that the source parameter estimation and upper limit calculations get biased. For calibration uncertainties of less than or similar to 5%, the biases are not significant (less than or similar to 2%), but for larger calibration uncertainties, they might become significant, especially when trying to differentiate between different models of isotropic gravitational-wave backgrounds.