Cosmology

Quasi-Einstein equations are generalizations of the Einstein equation. They arise from warped product Einstein metrics (Kaluza-Klein reductions), Ricci solitons, cosmology, near-horizon geometries, and smooth measured Lorentzian length spaces. Despite their apparent generality, they often have a surprising rigidity. I will review some recent developments in the area, focusing on near-horizon geometries, including Dunajski and Lucietti's near-horizon version of the Hawking rigidity theorem. I will discuss an application to 5-dimensional extreme (Myers-Perry type) black holes whose horizons admit the structure of the group SU(2).

The 21-cm line from neutral hydrogen holds immense potential as a probe of early astrophysics and cosmic evolution. Realizing the potential of this observational probe, however, is limited by our ability to control systematic effects in the data and model the cosmological 21-cm signal. In this talk, I will provide an overview of the observational prospects made possible through the cosmic 21-cm signal and discuss the challenges confronting interferometric experiments that are targeting a high-redshift detection. I will focus on recent developments from the Hydrogen Epoch of Reionization Array (HERA), covering our latest upper limits on the 21-cm power spectrum and their implications for early X-ray heating of the intergalactic medium. I will additionally discuss our latest efforts to understand and mitigate mutual coupling, a complex systematic effect in the data that threatens to thwart our efforts to detect the cosmological 21-cm signal. I will conclude by discussing the path forward with HERA, with a preliminary view of what to expect from forthcoming analyses.