Reconstructing stochastic gravitational-wave signals from flavour deconstruction with LISA

We investigate the reconstruction of a stochastic gravitational-wave background generated by a first-order phase transition in flavour-deconstruction models using the Laser Interferometer Space Antenna (LISA). In these scenarios, the spontaneous breaking of an extended flavour-non-universal gauge symmetry at the TeV scale can both generate the observed hierarchies of Standard Model fermion masses and mixing angles and induce a strong first-order phase transition. We consider representative benchmark points of the model, compute the corresponding thermodynamic transition parameters, and construct the resulting gravitational-wave spectra using a state-of-the-art sound-wave template. We then inject these spectra into simulated LISA data and perform Bayesian inference with SGWBinner, jointly reconstructing the cosmological signal, instrumental noise, and astrophysical foregrounds. We find that the strongest benchmark signal can be successfully reconstructed, whereas weaker signals are substantially degenerate with the unresolved extragalactic compact-binary foreground. We further show that tighter prior information on this foreground, motivated by observations with ground-based detectors, can reduce this degeneracy and improve signal reconstruction. Our results demonstrate that flavour-deconstruction models can produce signals accessible to LISA, while highlighting the importance of astrophysical-foreground modelling for their identification and characterization.