Spreadsheet calculations for: Cosmic Heterogeneity Shapes the Evolution of Dark Energy and Time

This dataset contains the spreadsheet calculations underlying the manuscript "Cosmic Heterogeneity Shapes the Evolution of Dark Energy and Time" (J. D. Yang and H.-O. Carmesin). Both workbooks integrate the expansion history of the homogeneous and the heterogeneous Universe and evaluate the resulting cosmic ages and the global time dilation, including a worst-case propagation of the measurement uncertainties. Workbook A (Planck parameters): all cosmological parameters are taken from the Planck 2018 results. Results: t_U,het = 13.521 (+0.355/−0.338) Gyr, t_U,hom = 13.827 (+0.357/−0.340) Gyr, Δt_U = 0.306 ± 0.013 Gyr. Workbook B (derived parameters): Ω_vol = 2/3, Ω_k = 0, Ω_r = Ω_m/(1+z_eq) and Ω_m = 1 − Ω_Λ − Ω_r − Ω_k are derived as described in the manuscript; H_0 and σ_8 remain measured inputs. Results: t_U,het = 13.371 (+0.183/−0.178) Gyr, Δt_U = 0.311 (+0.008/−0.007) Gyr. In the age integrand of the heterogeneous Universe, the matter density parameter is consistently normalized, Ω_m → Ω_m,het = 1 − Ω_Λ,het, following equation (S22) of the Supplemental Material, so that the density parameters in the integrand add up to unity exactly. These workbooks supersede a preliminary calculation (t_U,het = 13.318 Gyr, Δt_U = 0.509 Gyr) in which this normalization was not yet applied.