Search for Peak Structures in the Stochastic Gravitational-Wave Background in LIGO-Virgo-KAGRA O1-O4a Datasets

Abstract: We present a dedicated search for gravitational-wave backgrounds with nontrivial peak structures using data from the first three and the initial part of the fourth observing runs of the LIGO-Virgo-KAGRA network. The analysis is motivated by a variety of early-Universe models characterized by signals with multiple peaks. We introduce a model independent parameterization of double-peaked spectra based on the superposition of two normalized broken power laws and perform a Bayesian inference study using the LIGO-Virgo-KAGRA isotropic cross-correlation data. While no statistically significant evidence for a multi-peak background is found, the analysis provides constraints on the inter-peak slopes in correlation with the signal amplitude. These results exhibit LIGO-Virgo-KAGRA's ability to probe signals beyond a single peak structure and establish a foundation for future targeted searches for nontrivial gravitational waves background spectral shapes in future observing runs and the advanced detector era.