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If intermediate mass black holes (IMBHs) grow efficiently in gas disks around supermassive black holes, their host active galactic nucleus (AGN) disks should exhibit myriad observational signatures. Gap-opening IMBHs in AGN disks can exhibit spectral features and variability analagous to gapped protoplanetary disks. A gap-opening IMBH in the innermost disk imprints ripples and oscillations on the broad Fe Kα line which may be detectable with future X-ray missions. A non-gap-opening IMBH will accrete and produce a soft X-ray excess relative to continuum emission. An IMBH on a retrograde orbit in an AGN disk will not open a gap and will generate soft X-rays from a bow-shock 'headwind'. Accreting IMBH in a large cavity can generate ULX-like X-ray luminosities and LINER-like optical line ratios from local ionized gas. We propose that many LINERs house a weakly accreting MBH binary in a large central disk cavity and will be luminous sources of gravitational waves (GW). IMBHs in galactic nuclei may also be detected via intermittent observational signatures including: UV/X-ray flares due to tidal disruption events, asymmetric X-ray intensity distributions as revealed by AGN transits, quasi-periodic oscillations and underluminous Type Ia supernovae. GW emitted during IMBH inspiral and collisions may be detected with eLISA and LIGO, particularly from LINERs. We summarize observational signatures and compare to current data where possible or suggest future observations.

Full list of authors: Amaro-Seoane, Pau; Andrews, Jeff; Sedda, Manuel Arca; Askar, Abbas.; Baghi, Quentin; Balasov, Razvan; Bartos, Imre; Bavera, Simone S.; Bellovary, Jillian; Berry, Christopher P. L.; Berti, Emanuele; Bianchi, Stefano; Blecha, Laura; Blondin, Stephane; Bogdanovic, Tamara; Boissier, Samuel; Bonetti, Matteo; Bonoli, Silvia; Bortolas, Elisa; Breivik, Katelyn; Capelo, Pedro R.; Caramete, Laurentiu; Cattorini, Federico; Charisi, Maria; Chaty, Sylvain; Chen, Xian; Chruslinska, Martyna; Chua, Alvin J. K.; Church, Ross; Colpi, Monica; D'Orazio, Daniel; Danielski, Camilla; Davies, Melvyn B.; Dayal, Pratika; De Rosa, Alessandra; Derdzinski, Andrea; Destounis, Kyriakos; Dotti, Massimo; Dutan, Ioana; Dvorkin, Irina; Fabj, Gaia; Foglizzo, Thierry; Ford, Saavik; Fouvry, Jean-Baptiste; Franchini, Alessia; Fragos, Tassos; Fryer, Chris; Gaspari, Massimo; Gerosa, Davide; Graziani, Luca; Groot, Paul; Habouzit, Melanie; Haggard, Daryl; Haiman, Zoltan; Han, Wen-Biao; Istrate, Alina; Johansson, Peter H.; Khan, Fazeel Mahmood; Kimpson, Tomas; Kokkotas, Kostas; Kong, Albert; Korol, Valeriya; Kremer, Kyle; Kupfer, Thomas; Lamberts, Astrid; Larson, Shane; Lau, Mike; Liu, Dongliang; Lloyd-Ronning, Nicole; Lodato, Giuseppe; Lupi, Alessandro; Ma, Chung-Pei; Maccarone, Tomas; Mandel, Ilya; Mangiagli, Alberto; Mapelli, Michela; Mathis, Stephane; Mayer, Lucio; McGee, Sean; McKernan, Berry; Miller, M. Coleman; Mota, David F.; Mumpower, Matthew; Nasim, Syeda S.; Nelemans, Gijs; Noble, Scott; Pacucci, Fabio; Panessa, Francesca; Paschalidis, Vasileios; Pfister, Hugo; Porquet, Delphine; Quenby, John; Ricarte, Angelo; Roepke, Friedrich K.; Regan, John; Rosswog, Stephan; Ruiter, Ashley; Ruiz, Milton; Runnoe, Jessie; Schneider, Raffaella; Schnittman, Jeremy; Secunda, Amy; Sesana, Alberto; Seto, Naoki; Shao, Lijing; Shapiro, Stuart; Sopuerta, Carlos; Stone, Nicholas C.; Suvorov, Arthur; Tamanini, Nicola; Tamfal, Tomas; Tauris, Thomas; Temmink, Karel; Tomsick, John; Toonen, Silvia; Torres-Orjuela, Alejandro; Toscani, Martina; Tsokaros, Antonios; Unal, Caner; Vazquez-Aceves, Veronica; Valiante, Rosa; van Putten, Maurice; van Roestel, Jan; Vignali, Christian; Volonteri, Marta; Wu, Kinwah; Younsi, Ziri; Yu, Shenghua; Zane, Silvia; Zwick, Lorenz; Antonini, Fabio; Baibhav, Vishal; Barausse, Enrico; Bonilla Rivera, Alexander; Branchesi, Marica; Branduardi-Raymont, Graziella; Burdge, Kevin; Chakraborty, Srija; Cuadra, Jorge; Dage, Kristen; Davis, Benjamin; de Mink, Selma E.; Decarli, Roberto; Doneva, Daniela; Escoffier, Stephanie; Gandhi, Poshak; Haardt, Francesco; Lousto, Carlos O.; Nissanke, Samaya; Nordhaus, Jason; O'Shaughnessy, Richard; Portegies Zwart, Simon; Pound, Adam; Schussler, Fabian; Sergijenko, Olga; Spallicci, Alessandro; Vernieri, Daniele; Vigna-Gomez, Alejandro.-- This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/., 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. © The Author(s) 2023, corrected publication 2023., P. Dayal acknowledges support from the European Research council (ERC-717001) and from the Netherlands Research Council NWO (016.VIDI.189.162). P.H. Johansson acknowledges the support from the European Research Council (ERC-818930). S. Toonen acknowledges support from the Netherlands Research Council NWO (VENI 639.041.645 Grants) C. Unal is supported by European Structural and Investment Funds and the Czech Ministry of Education, Youth and Sports (Project CoGraDS - CZ.02.1.01/0.0/0.0/15_003/0000437). S. Chaty acknowledges the LabEx UnivEarthS for the funding of Interface project I10 “From binary evolution towards merging of compact objects”. A. De Rosa acknowledges financial contribution from the agreement ASI-INAF n.2017-14-H.O E. Berti is supported by NSF Grants No. PHY-1912550 and AST-2006538, NASA ATP Grants No. 17-ATP17-0225 and 19-ATP19-0051, NSF-XSEDE Grant No. PHY-090003, and NSF Grant PHY-20043. D. Gerosa is supported by European Union’s H2020 ERC Starting Grant No. 945155–GWmining, Leverhulme Trust Grant No. RPG-2019-350 and Royal Society Grant No. RGS-R2-202004. T. Bogdanovic acknowledges support by the NASA award No. 80NSSC19K0319 and by the NSF award AST-1908042. D. Porquet acknowledges funding support from CNES. C. Danielski acknowledges financial support from the State Agency for Research of the Spanish MCIU through the “Center of Excellence Severo Ochoa” award to the Instituto de Astrofísica de Andalucía (SEV-2017-0709) B.L. Davis acknowledges support from Tamkeen under the NYU Abu Dhabi Research Institute Grant CAP3. F. Pacucci acknowledges support from a Clay Fellowship by the SAO and from the Black Hole Initiative, which is funded by grants from the John Templeton Foundation and the Gordon and Betty Moore Foundation. A.J. Ruiter acknowledges support from the Australian Research Council Future Fellowship Grant FT170100243. V. Paschalidis is supported by NSF Grant PHY-1912619 and NASA Grant 80NSSC20K1542 to the University of Arizona, and NSF-XSEDE Grant TG-PHY190020. D. Haggard acknowledges support from the NSERC Discovery Grant and Canada Research Chairs programs, and the Bob Wares Science Innovation Prospectors Fund. M. Toscani acknowledges European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant Agreement No. 823823 (RISE DUSTBUSTERS project) and COST Action CA16104 - Gravitational waves, black holes and fundamental physics, supported by COST (European Cooperation in Science and Technology). M. Chruslinska, A. Istrate and G. Nelemans acknowledge support from Netherlands Research Council NWO. T. Fragos and S. Bavera acknowledge support from a Swiss National Science Foundation Professorship Grant (project numbers PP00P2_176868 and PP00P2_211006)., With funding from the Spanish government through the "Severo Ochoa Centre of Excellence" accreditation (CEX2021-001131-S).