George Efstathiou, Steven Gratton

We revisit the observational constraints on spatial curvature following recent claims that the Planck data favour a closed Universe. We use a new and statistically powerful Planck likelihood to show that the Planck temperature and polarization spectra are consistent with a spatially flat Universe, though because of a geometrical degeneracy cosmic microwave background spectra on their own do not lead to tight constraints on the curvature density parameter Omega_K. When combined with other astrophysical data, particularly geometrical measurements of baryon acoustic oscillations, the Universe is constrained to be spatially flat to extremely high precision, with Omega_ K = 0.0004 +/-0.0018 in agreement with the 2018 results of the Planck team. In the context of inflationary cosmology, the observations offer strong support for models of inflation with a large number of e-foldings and disfavour models of incomplete inflation.

Vassilios Mewes, Yosef Zlochower, Manuela Campanelli, Thomas W. Baumgarte, Zachariah B. Etienne, Federico G. Lopez Armengol, Federico Cipolletta

We present SphericalNR, a new framework for the publicly available Einstein Toolkit that numerically solves the Einstein field equations coupled to the equations of general relativistic MHD (GRMHD) in a 3+1 split of spacetime in spherical coordinates without symmetry assumptions. The spacetime evolution is performed using reference-metric versions of either the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) equations or the fully covariant and conformal Z4 (fCCZ4) system with constraint damping. We have developed a reference-metric version of the Valencia formulation of GRMHD with a vector potential method, guaranteeing the absence of magnetic monopoles during the evolution. In our framework, every dynamical field (both spacetime and matter) is evolved using its components in an orthonormal basis with respect to the spherical reference metric. Furthermore, all geometric information about the spherical coordinate system is encoded in source terms appearing in the evolution equations. This allows for the straightforward extension of Cartesian high-resolution shock-capturing finite volume codes to use spherical coordinates with our framework. To this end, we have adapted GRHydro, a Cartesian finite volume GRMHD code already available in the Einstein Toolkit, to use spherical coordinates. We present the full evolution equations of the framework, as well as details of its implementation in the Einstein Toolkit. We validate SphericalNR by demonstrating it passes a variety of challenging code tests in static and dynamical spacetimes.

Chethan Krishnan, Eoin Ó Colgáin, Ruchika, Anjan A. Sen, M. M. Sheikh-Jabbari, Tao Yang

We consider a low redshift $(z<0.7)$ cosmological dataset comprising megamasers, cosmic chronometers, type Ia SNe and BAO, which we bin according to their redshift. For each bin, we read the value of $H_0$ by fitting directly to the flat $\Lambda$CDM model. Doing so, we find that $H_0$ descends with redshift, allowing one to fit a line with a non-zero slope of statistical significance $2.1 \, \sigma$. Our results are in accord with a similar descending trend reported by the H0LiCOW collaboration. If substantiated going forward, early Universe solutions to the Hubble tension will struggle explaining this trend.