Releasing pbh-rem: A framework for PBH remnants
The pbh-rem repository is a Mathematica-based model designed to simulate the cosmological evolution of Primordial Black Holes and the remnants they leave behind.
In standard physics, semi-classical Hawking radiation suggests that black holes evaporate completely. However, mechanisms like Loop Quantum Gravity or the Memory Burden effect introduce a limit to this evaporation, leaving behind stable or very long-lived remnants. To understand the impact of these objects on our universe, we need to carefully track their energy density across all cosmic eras; from radiation to matter and dark energy.
This code provides a rigorous way to do exactly that.
How the framework works
Built for Mathematica 14.1, the pbh-rem pipeline is designed to handle the differential equations that occur around the exact moment a black hole evaporates. The workflow is split into three main parts:
- Analytical Derivations (
01_alpha.nb): A helper notebook that computes the analytical expressions for the initial abundance coefficients \(\alpha_{A}\) for each species \(A\). - The Numerical Engine (
02_model.nb): The core solver. It integrates the evolution of the PBH population across cosmic time, computing the transitions between standard evaporation and the stable remnant phase. - Visualization & Data Export (
03_visuals.nb): This notebook generates plots of the universe’s history. It also runs an optimization algorithm to find the maximum allowed initial PBH abundance \(\beta_{\rm max}\), exporting detailed datasets. For every tested configuration, it tracks 96 different physical variables across four distinct cosmological milestones (Formation, Evaporation, Remnant Diffusion, and Today).
The Paper
This code was developed for our paper: “Signatures of loop quantum gravity in primordial black hole cosmologies” (Antoine Dierckx, Sébastien Clesse, Francesca Vidotto).
You can find the preprint here. Feel free to explore the repository, run the visualizer notebook to see the cosmic history plots, or adapt the model to test your own phenomenological constraints.