Ali Rida Khalifeh, Raul Jimenez

Dark Energy models are numerous and distinguishing between them is becoming difficult. However, using distinct observational probes can ease this quest and gives better assessment to the nature of Dark energy. To this end, the plausibility of neutrino oscillations to be a probe of Dark Energy models is investigated. First, a generalized formalism of neutrino (spinor field) interaction with a classical scalar field in curved space-time is presented. This formalism is then applied to two classes of Dark Energy models in a flat Friedman-Lema\^itre-Robertson-Walker metric: a Cosmological Constant and scalar field Dark Energy coupled to neutrinos. By looking at the neutrino oscillation probability's evolution with redshift, these models can be distinguished, for certain neutrino and scalar field coupling properties. This evolution could be traced by neutrino flux in future underground, terrestrial or extraterrestrial neutrino telescopes, which would assess probing Dark Energy models with this technique.

Oliver H. E. Philcox, Jeremy Goodman, Zachary Slepian

A fundamental relation in celestial mechanics is Kepler's equation, linking an orbit's mean anomaly to its eccentric anomaly and eccentricity. Being transcendental, the equation cannot be directly solved for eccentric anomaly by conventional treatments; much work has been devoted to approximate methods. Here, we give an explicit integral solution, utilizing methods recently applied to the "geometric goat problem" and to the dynamics of spherical collapse. The solution is given as a ratio of contour integrals; these can be efficiently computed via numerical integration for arbitrary eccentricities. The method is found to be highly accurate in practice, with our C++ implementation outperforming conventional root-finding and series approaches by a factor greater than two.

Dhruba Dutta Chowdhury, Frank C. van den Bosch, Victor H. Robles, Pieter van Dokkum, Hsi-Yu Schive, Tzihong Chiueh, Tom Broadhurst

Fuzzy Dark Matter (FDM), consisting of ultralight bosons ($m_{\rm b} \sim 10^{-22}\ \rm eV$), is an intriguing alternative to Cold Dark Matter. Numerical simulations that solve the Schr\"odinger-Poisson (SP) equation show that FDM halos consist of a central solitonic core, which is the ground state of the SP equation, surrounded by an envelope of interfering excited states. These excited states also interfere with the soliton, causing it to oscillate and execute a confined random walk with respect to the halo center of mass. Using high-resolution numerical simulations of a $6.6 \times 10^9 M_{\odot}$ FDM halo with $m_{\rm b} = 8 \times 10^{-23}\ \rm eV$ in isolation, we demonstrate that the wobbling, oscillating soliton gravitationally perturbs nuclear objects, such as supermassive black holes or dense star clusters, causing them to diffuse outwards. In particular, we show that, on average, objects with mass $\lesssim 0.3 \%$ of the soliton mass ($M_{\rm sol}$) are expelled from the soliton in $\sim 3\ \rm Gyr$, after which they continue their outward diffusion due to gravitational interactions with the soliton and the halo granules. More massive objects ($\gtrsim 1 \% M_{\rm sol}$), while executing a random walk, remain largely confined to the soliton due to dynamical friction. We also present an effective treatment of the diffusion, based on kinetic theory, that accurately reproduces the outward motion of low mass objects and briefly discuss how the observed displacements of star clusters and active galactic nuclei from the centers of their host galaxies can be used to constrain FDM.