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

This paper investigates the impact of a lack of knowledge of instrumental noise on the characterization of stochastic gravitational wave backgrounds with the Laser Interferometer Space Antenna (LISA). We focus on constraints on modeled backgrounds that represent the possible backgrounds from the mergers of binary black holes of stellar origin, from primordial black hole generation, from nonstandard inflation, and from sound wave production during cosmic fluid phase transitions. We use splines to model generic, slowly varying, uncertainties in the auto- and cross -spectral densities of the LISA time delay interferometry channels. We find that allowing for noise knowledge uncertainty in this way leads to 1-2 orders of magnitude degradation in our ability to constrain stochastic backgrounds and a corresponding increase in the background energy density required for a confident detection. We also find that, to avoid this degradation, the LISA noise would have to be known at the subpercent level, which is unlikely to be achievable in practice.