# Numerical simulations of loop quantum Bianchi-I spacetimes

## TL;DR

This paper uses high-performance numerical simulations to study the quantum evolution of anisotropic Bianchi-I spacetimes, confirming the robustness of the quantum bounce and validating effective dynamics in most regimes.

## Contribution

It provides the first extensive numerical analysis of loop quantum Bianchi-I models, demonstrating the accuracy of effective dynamics and exploring departures at Planck-scale volumes.

## Key findings

- Big bang singularity replaced by anisotropic bounces
- Effective dynamics accurately approximates quantum evolution for large-volume states
- Effective dynamics underestimates volume and overestimates curvature at the bounce

## Abstract

Due to the numerical complexities of studying evolution in an anisotropic quantum spacetime, in comparison to the isotropic models, the physics of loop quantized anisotropic models has remained largely unexplored. In particular, robustness of bounce and the validity of effective dynamics have so far not been established. Our analysis fills these gaps for the case of vacuum Bianchi-I spacetime. To efficiently solve the quantum Hamiltonian constraint we perform an implementation of the Cactus framework which is conventionally used for applications in numerical relativity. Using high performance computing, numerical simulations for a large number of initial states with a wide variety of fluctuations are performed. Big bang singularity is found to be replaced by anisotropic bounces for all the cases. We find that for initial states which are sharply peaked at the late times in the classical regime and bounce at a mean volume much greater than the Planck volume, effective dynamics is an excellent approximation to the underlying quantum dynamics. Departures of the effective dynamics from the quantum evolution appear for the states probing deep Planck volumes. A detailed analysis of the behavior of this departure reveals a non-monotonic and subtle dependence on fluctuations of the initial states. We find that effective dynamics in almost all of the cases underestimates the volume and hence overestimates the curvature at the bounce, a result in synergy with earlier findings in isotropic case. The expansion and shear scalars are found to be bounded throughout the evolution.