Regular Cosmologies: Three Distinct Routes

Abstract

Regular black holes avoid the central singularity by replacing it with a de Sitter core. We ask what cosmology follows if the same idea is brought to the early universe. Regular metrics define a position-dependent cosmological term, $Λ_{\rm eff}(r)=8πG ρ_{\rm MS}(r)$, and there is no unique way to carry it over to the expanding universe. We follow three different prescriptions: a Newtonian one following McCrea and Milne, a running vacuum evaluated at Hubble radius and a quasi-local one based on Misner-Sharp mass. We apply each of them to six regular black hole metrics and explore their consequences. In the Newtonian case the Friedmann equations are solved in closed form for the Hayward metric, and in terms of standard special functions or numerically for the others, and describe a universe that starts in a de Sitter phase and ends as dust (i.e. an inflationary model instead of dark energy). We find that in all three prescriptions a monotonically decreasing core density gives an equation of state that never crosses $w=-1$, and thus the phantom behaviour suggested by DESI would require a density shell which a regular core does not have. The three prescriptions agree on the de Sitter core but differ at late times, and we quantify the difference against the DESI DR2 results. We also point out that a single regularisation length cannot serve as both the inflationary and the dark-energy scale.