Exploring cosmological gravitational wave backgrounds through the synergy of LISA and the Einstein Telescope

The gravitational wave (GW) interferometers Laser Interferometer Space Antenna (LISA) and the Einstein Telescope (ET) are expected to be functional in the next decade(s), possibly around the same time. They will operate over different frequency ranges, with similar integrated sensitivities to the amplitude of a stochastic GW background (SGWB). We investigate the synergies between these two detectors, in terms of a multiband detection of a cosmological SGWB characterized by a large amplitude, and a broad frequency spectrum. We develop the notion of integrated sensitivity and propose a novel signal-to-noise ratio optimal for characterization of the geometrical properties of the interferometer systems of LISA and the ET operating simultaneously. By investigating various examples of SGWBs, such as those arising from cosmological phase transition, cosmic string, and primordial inflation, we show that LISA and the ET operating together will have the opportunity to assess more effectively the characteristics of the GW spectrum produced by the same cosmological source, but at separate frequency scales. Moreover, the two experiments in tandem can be sensitive to features of early Universe cosmic expansion before big bang nucleosynthesis (BBN), which affects the SGWB frequency profile and which would not be possible to detect otherwise, since two different frequency ranges correspond to two different pre-BBN (or postinflationary) epochs. Besides considering the GW spectrum, we additionally undertake a preliminary study of the sensitivity of LISA and the ET to soft limits of higher-order tensor correlation functions. Given that these experiments operate at different frequency bands, their synergy constitutes an ideal direct probe of squeezed limits of higher-order GW correlators, which cannot be measured operating with a single instrument only.