Numerical integration and uncertainty-propagation workbook for "Cosmic heterogeneity shapes the evolution of dark energy and time"

This workbook (Microsoft Excel, one worksheet) contains the numerical computations underlying the manuscript "Cosmic heterogeneity shapes the evolution of dark energy and time" by Jacky David Yang and Hans-Otto Carmesin (submitted to Nature Astronomy). The workbook implements: (1) the redshift-dependent dark-energy density parameter Omega_Lambda,het(z) and the heterogeneous Hubble constant H_0,het(z), following equations (3), (4) and (23) to (25) of the manuscript; (2) the numerical integration of the cosmic expansion history, equations (22), (26) and (28), with increment Delta x = 4e-4, yielding the present-day ages of the heterogeneous and homogeneous universe, t_U,het = 13.318 Gyr and t_U,hom = 13.827 Gyr, and the global time difference Delta t_U = t_U,hom − t_U,het = 0.509 Gyr, equation (29); (3) a worst-case uncertainty propagation in which sigma_8, Omega_Lambda and H_0,LambdaCDM are varied by ±1 sigma (Planck 2018 results VI, Table 2, column 2), with the H_0 uncertainty applied opposite to that of sigma_8. The switches k_sigma_8, k_Om_L and k_H_0LCDM (0 or 1) activate the respective uncertainties; with all switches set to zero, the workbook returns the central curves shown in Figures 4 to 6 of the manuscript. All input constants are cross-referenced to the corresponding equation numbers of the manuscript.