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This paper investigates the impact of a lack of knowledge of the instrumentalnoise on the characterisation of stochastic gravitational wave backgrounds withthe Laser Interferometer Space Antenna (LISA). We focus on constraints onmodelled backgrounds that represent the possible backgrounds from the mergersof binary black holes of stellar origin, from primordial black hole generation,from non-standard inflation, and from sound wave production during cosmic fluidphase transitions. We use splines to model generic, slowly varying,uncertainties in the auto and cross-spectral densities of the LISA time delayinterferometry channels. We find that allowing for noise knowledge uncertaintyin this way leads to one to two orders of magnitude degradation in our abilityto constrain stochastic backgrounds, and a corresponding increase in thebackground energy density required for a confident detection. We also find thatto avoid this degradation, the LISA noise would have to be known at thesub-percent level, which is unlikely to be achievable in practice.

Impact of the noise knowledge uncertainty for the science exploitation  of cosmological and astrophysical stochastic gravitational wave background  with LISA