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This review is an up-to-date account of the use of numerical relativity to study dynamical, strong-gravity environments in a cosmological context. First, we provide a gentle introduction into the use of numerical relativity in solving cosmological spacetimes, aimed at both cosmologists and numerical relativists. Second, we survey the present body of work, focusing on general relativistic simulations, organised according to the cosmological history—from cosmogenesis, through the early hot Big Bang, to the late-time evolution of the universe. We discuss the present state-of-the-art, and suggest directions in which future work can be fruitfully pursued.

LISA, the Laser Interferometer Space Antenna, will usher in a new era in gravitational-wave astronomy. As the first anticipated space-based gravitational-wave detector, it will expand our view to the millihertz gravitational-wave sky, where a spectacular variety of interesting new sources abound: from millions of ultra-compact binaries in our Galaxy, to mergers of massive black holes at cosmological distances; from the early inspirals of stellar-mass black holes that will ultimately venture into the ground-based detectors’ view to the death spiral of compact objects into massive black holes, and many sources in between. Central to realising LISA’s discovery potential are waveform models, the theoretical and phenomenological predictions of the pattern of gravitational waves that these sources emit. This White Paper is presented on behalf of the Waveform Working Group for the LISA Consortium. It provides a review of the current state of waveform models for LISA sources, and describes the significant challenges that must yet be overcome.

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.

Due to the absence of symmetries under time and spatial translations in a general curved spacetime, the energy and momentum of matter is not conserved as it is in flat space. This means, for example, that the flux of matter energy through a surface is in general not balanced by an equal increase in the energy of the matter contained within the enclosed volume - there is an additional \"source\" resulting from the curvature of spacetime acting on the matter (and vice versa). One can calculate this source term and reconcile the flux and energy accumulation over time in an arbitrary volume, although a foliation of the spacetime must be chosen, making the quantities inherently coordinate dependent. Despite this dependence, these quantities are practically useful in numerical relativity simulations for a number of reasons. We provide expressions for general matter sources in a form appropriate for implementation in the ADM decomposition, and discuss several applications in simulations of compact object dynamics and cosmology.

This set of notes was designed to accompany two hours of lectures and practical exercises at the New Horizons for Psi workshop in Lisbon in July 2024 entitled \"Studying fundamental fields with numerical relativity\". Numerical relativity is a tool used to help understand the behaviours of metric and matter fields in dynamical, strong gravity situations. It has been used to study a range of situations involving fundamental fields, including superradiance, modified gravity, dynamical friction, dark matter accretion and early universe cosmology. The purpose of this course is to provide some background and hands-on experience in numerical relativity that will help students to better understand the possibilities provided by this tool, as well as its limitations.

LISA, the Laser Interferometer Space Antenna, will usher in a new era in gravitational-wave astronomy. As the first anticipated space-based gravitational-wave detector, it will expand our view to the millihertz gravitational-wave sky, where a spectacular variety of interesting new sources abound: from millions of ultra-compact binaries in our Galaxy, to mergers of massive black holes at cosmological distances; from the early inspirals of stellar-mass black holes that will ultimately venture into the ground-based detectors’ view to the death spiral of compact objects into massive black holes, and many sources in between. Central to realising LISA’s discovery potential are waveform models, the theoretical and phenomenological predictions of the pattern of gravitational waves that these sources emit. This White Paper is presented on behalf of the Waveform Working Group for the LISA Consortium. It provides a review of the current state of waveform models for LISA sources, and describes the significant challenges that must yet be overcome.

Despite originating in science fiction, warp drives have a concrete description in general relativity, with Alcubierre first proposing a spacetime metric that supported faster-than-light travel. Whilst there are numerous practical barriers to their implementation in real life, including a requirement for negative energy, computationally, one can simulate their evolution in time given an equation of state describing the matter. In this work, we study the signatures arising from a warp drive \"containment failure\", assuming a stiff equation of state for the fluid. We compute the emitted gravitational-wave signal and track the energy fluxes of the fluid. Apart from its rather speculative application to the search for extraterrestrial life in gravitational-wave detector data, this work is interesting as a study of the dynamical evolution and stability of spacetimes that violate the null energy condition. Our work highlights the importance of exploring strange new spacetimes, to (boldly) simulate what no one has seen before.

If we imagine rewinding the universe to early times, the scale factor shrinks and the existence of a finite spatial volume may play a role in quantum tunnelling effects in a closed universe. It has recently been shown that such finite volume effects dynamically generate an effective equation of state that could support a cosmological bounce. In this work we extend the analysis to the case in which a (homogeneous) anisotropy is present, and identify a criteria for a successful bounce in terms of the size of the closed universe and the properties of the quantum field.

This review is an up-to-date account of the use of numerical relativity to study dynamical, strong-gravity environments in a cosmological context. First, we provide a gentle introduction into the use of numerical relativity in solving cosmological spacetimes, aimed at both cosmologists and numerical relativists. Second, we survey the present body of work, focusing on general relativistic simulations, organised according to the cosmological history -- from cosmogenesis, through the early hot Big Bang, to the late-time evolution of universe. We discuss the present state-of-the-art, and suggest directions in which future work can be fruitfully pursued.

We study the non-perturbative evolution of inflationary fluctuations during preheating using fully non-linear general-relativistic field-theory simulations. We choose a single-field inflationary model that is consistent with observational constraints and start the simulations at the end of inflation with fluctuations both in the field and its conjugate momentum. Gravity enhances the growth of density perturbations, which then collapse and virialize, forming long-lived stable oscillon-like stars that reach compactnesses \\(\\mathcal{C}\\equiv GM/R \\sim 10^{-3}-10^{-2}\\). We find that \\(\\mathcal{C}\\) increases for larger field models, until it peaks due to the interplay between the overdensity growth and Hubble expansion rates. Whilst gravitational effects can play an important role in the formation of compact oscillons during preheating, the objects are unlikely to collapse into primordial black holes without an additional enhancement of the initial inflationary fluctuations.