Non-singular cosmologies matching regular black holes

TL;DR

The paper addresses cosmological singularities by constructing a non-singular cosmos via a modified Oppenheimer--Snyder setup that matches an interior FRW dust region to a Minkowski-core regular BH exterior. Using a unified Friedmann form $H^2=F(\rho)$, it analyzes both dust-only and scalar-field evolutions and compares the new model to LQC, Hayward, and classical GR. The key finding is a novel asymptotically Minkowski cosmology that is geodesically complete and exhibits symmetry between the infinite past and future, with inflation naturally appearing in the scalar-field case. This work demonstrates how regular BH interiors with Minkowski cores can imprint non-singular, symmetric early- and late-time cosmologies and provides a new testing ground for quantum gravity-inspired regular BHs in cosmology.

Abstract

We construct a new non-singular cosmological model matched to a Minkowski-core regular black hole by means of a modified Oppenheimer--Snyder framework. Its dynamics is studied in both dust-only and scalar-field scenarios, and compared with that of two other non-singular models as well as the classical standard cosmology. The results show that, although all three non-singular cosmologies share identical late-time behavior and allow for a natural embedding of inflation in the scalar-field setting, they exhibit qualitatively distinct non-singular features at very early times. In particular, the new cosmology approaches Minkowski spacetime in the limits of both the infinite past and the infinite future, thereby manifesting an intriguing symmetry between the two asymptotic regimes.

Figures (3)

• Figure 1: Plots of (a) $H\!\left ( \rho \right )^2$, (b) $a\!\left ( t \right )$, (c) $H\!\left ( t \right )^2$, and (d) $\dot a\!\left ( t \right )$ for the four cosmologies. Here, $r_0 = 1$, $M = 10$, and $a_0 = 5$.
• Figure 2: (a) and (c): $R_{\text{int}}$ and $K_{\text{int}}$ (for the four cosmological models) versus $a\!\left( t \right) {r_0}$, respectively; (b) and (d): $R_{\text{ext}}$ and $K_{\text{ext}}$ (for the four corresponding BH models) versus ${\tilde{r}}$, respectively. Here, $r_0 = 1$ and $M = 10$.
• Figure 3: Phase trajectories of the scalar field in the four cosmologies. Here, $m = 1$.