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Abstract The Laser Interferometer Space Antenna (LISA) will be a transformative experiment for gravitational wave astronomy, and, as such, it will offer unique opportunities to address many key astrophysical questions in a completely novel way. The synergy with ground-based and space-born instruments in the electromagnetic domain, by enabling multi-messenger observations, will add further to the discovery potential of LISA. The next decade is crucial to prepare the astrophysical community for LISA’s first observations. This review outlines the extensive landscape of astrophysical theory, numerical simulations, and astronomical observations that are instrumental for modeling and interpreting the upcoming LISA datastream. To this aim, the current knowledge in three main source classes for LISA is reviewed; ultra-compact stellar-mass binaries, massive black hole binaries, and extreme or interme-diate mass ratio inspirals. The relevant astrophysical processes and the established modeling techniques are summarized. Likewise, open issues and gaps in our understanding of these sources are highlighted, along with an indication of how LISA could help making progress in the different areas. New research avenues that LISA itself, or its joint exploitation with upcoming studies in the electromagnetic domain, will enable, are also illustrated. Improvements in modeling and analysis approaches, such as the combination of numerical simulations and modern data science techniques, are discussed. This review is intended to be a starting point for using LISA as a new discovery tool for understanding our Universe. 

Abstract Since 2015 the gravitational-wave observations of LIGO and Virgo have transformed our understanding of compact-object binaries. In the years to come, ground-based gravitational-wave observatories such as LIGO, Virgo, and their successors will increase in sensitivity, discovering thousands of stellar-mass binaries. In the 2030s, the space-based LISA will provide gravitational-wave observations of massive black holes binaries. Between the $\sim 10$ ∼ 10 –10 3 Hz band of ground-based observatories and the $\sim 10^{-4}$ ∼ 1 0 − 4 –10 − 1 Hz band of LISA lies the uncharted decihertz gravitational-wave band. We propose a Decihertz Observatory to study this frequency range, and to complement observations made by other detectors. Decihertz observatories are well suited to observation of intermediate-mass ( $\sim 10^{2}$ ∼ 1 0 2 –10 4 M ⊙ ) black holes; they will be able to detect stellar-mass binaries days to years before they merge, providing early warning of nearby binary neutron star mergers and measurements of the eccentricity of binary black holes, and they will enable new tests of general relativity and the Standard Model of particle physics. Here we summarise how a Decihertz Observatory could provide unique insights into how black holes form and evolve across cosmic time, improve prospects for both multimessenger astronomy and multiband gravitational-wave astronomy, and enable new probes of gravity, particle physics and cosmology. 

Abstract The Laser Interferometer Space Antenna (LISA) has the potential to reveal wonders about the fundamental theory of nature at play in the extreme gravity regime, where the gravitational interaction is both strong and dynamical. In this white paper, the Fundamental Physics Working Group of the LISA Consortium summarizes the current topics in fundamental physics where LISA observations of gravitational waves can be expected to provide key input. We provide the briefest of reviews to then delineate avenues for future research directions and to discuss connections between this working group, other working groups and the consortium work package teams. These connections must be developed for LISA to live up to its science potential in these areas.