Bodo Schwabe, Jens C. Niemeyer

Fuzzy dark matter (FDM) made of ultra-light bosonic particles is a viable alternative to cold dark matter (CDM) with clearly distinguishable small-scale features in collapsed structures. On large scales, it behaves gravitationally like CDM deviating only by a cut-off in the initial power spectrum and can be studied using N-body methods. In contrast, wave interference effects near the de Broglie scale result in new phenomena unique to FDM. Interfering modes in filaments and halos yield a stochastically oscillating granular structure which condenses into solitonic cores during halo formation. Investigating these highly non-linear wave phenomena requires the spatially resolved numerical integration of the Schr\"odinger equation. In previous papers we introduced a hybrid zoom-in scheme that combines N-body methods to model the large-scale gravitational potential around and the mass accretion onto pre-selected halos with simulations of the Schr\"odinger-Poisson equation to capture wave-like effects inside these halos. In this work, we present a new, substantially improved reconstruction method for the wave function inside of previously collapsed structures. We demonstrate its capabilities with a deep zoom-in simulation of a well-studied sub-$L_\ast$-sized galactic halo from cosmological intitial conditions. With a particle mass of $m = 2.5\times 10^{-22}\,$eV and halo mass $M_{\text{vir}}=1.7\times 10^{11}\,M_{\odot}$ in a ($60$h${^{-1}}$ comoving Mpc)${}^{3}$ cosmological box, it reaches an effective resolution of 20 comoving pc. This pushes the values of $m$ and $M$ accessible to simulations significantly closer to those relevant for studying galaxy evolution in the allowed range of FDM masses.

Kara Farnsworth, Kurt Hinterbichler, Ondrej Hulik

We examine the question of scale vs. conformal invariance for the linearized Einstein-Hilbert action, which describes the IR fixed point of quantum gravity. In $D = 4$, although the action is not conformally invariant in the usual sense, we explicitly show that the theory is a conformal field theory at the level of correlation functions. In higher dimensions, we show that the theory is scale but not conformally invariant, but can be embedded into a larger non-unitary conformal field theory, analogous to what has been found for Maxwell theory in $D>4$. We give evidence that similar statements are true for all free higher spin theories.

Steven B. Giddings

A "black hole theorem" is stated, exhibiting the basic conflict of the information problem. This is formulated in a more general context than that of quantum field theory on a background, and is based on describing a black hole as a quantum subsystem of a larger system, including its environment. As with the Coleman-Mandula theorem, the most important point is probably the loophole in the "theorem," and what this tells us about the fundamental structure of quantum gravity. This "theorem" in particular connects to the general question of how to define quantum subsystems in quantum gravity. If black holes do behave as quantum subsystems, at least to a good approximation, evolve unitarily, and do not leave remnants, the "theorem" implies the presence of interactions between a black hole and its environment that go beyond a description based on local quantum fields. These can be parameterized in a principled way, and with motivated additional assumptions indicate possible observational signatures, which can be investigated by electromagnetic or gravitational wave observations of black holes.

Martin Bojowald, Pip Petersen

Quasiclassical methods for non-adiabatic quantum dynamics can reveal new features of quantum effects, such as tunneling evolution, that are harder to reveal in standard treatments based on wave functions of stationary states. Here, these methods are applied to an oscillating universe model introduced recently. Our quasiclassical treatment correctly describes several expected features of tunneling states, in particular just before and after tunneling into a trapped region where a model universe may oscillate through many cycles of collapse and expansion. As a new result, the oscillating dynamics is found to be much less regular than in the classical description, revealing a succession of cycles with varying maximal volume even when the matter ingredients and their parameters do not change.

Timothy Cohen, Kara Farnsworth, Rachel Houtz, Markus A. Luty

Hamiltonian truncation is a non-perturbative numerical method for calculating observables of a quantum field theory. The starting point for this method is to truncate the interacting Hamiltonian to a finite-dimensional space of states spanned by the eigenvectors of the free Hamiltonian with eigenvalues below some energy cutoff $E_\text{max}$. In this work, we show how to treat Hamiltonian truncation systematically using effective field theory methodology. We define the finite-dimensional effective Hamiltonian by integrating out the states above $E_\text{max}$. The effective Hamiltonian can be computed by matching a transition amplitude to the full theory, and gives corrections order by order as an expansion in powers of $1/E_\text{max}$. The effective theory has a number of unusual features at higher orders, such as non-local interactions and non-Hermiticity of the effective Hamiltonian, whose physical origin we clarify. We apply this formalism to the theory of a relativistic scalar field $\phi$ with a $\lambda \phi^4$ coupling in 2 and 3 spacetime dimensions. We perform numerical tests of the method in 2D, and find that including our matching corrections yields significant numerical improvements consistent with the expected dependence on the $E_\text{max}$ cutoff.