Effective dynamics of the hybrid quantization of the Gowdy T^3 universe

TL;DR

This paper investigates the quantum dynamics of the Gowdy T^3 universe using effective Loop Quantum Cosmology, demonstrating that key features like the big bounce persist even with inhomogeneities and analyzing gravitational wave mode amplitudes.

Contribution

It provides the first systematic effective analysis of an inhomogeneous universe in Loop Quantum Cosmology, confirming the robustness of homogeneous results.

Findings

The initial singularity is replaced by a big bounce.

The universe size at the bounce is comparable to the homogeneous case.

Amplitude differences of gravitational waves are affected by inhomogeneity levels.

Abstract

The quantum dynamics of the linearly polarized Gowdy T^3 model (compact inhomogeneous universes admitting linearly polarized gravitational waves) is analyzed within Loop Quantum Cosmology by means of an effective dynamics. The analysis, performed via analytical and numerical methods, proves that the behavior found in the evolution of vacuum (homogeneous) Bianchi I universes is preserved qualitatively also in the presence of inhomogeneities. More precisely, the initial singularity is replaced by a big bounce which joins deterministically two large classical universes. In addition, we show that the size of the universe at the bounce is at least of the same order of magnitude (roughly speaking) as the size of the corresponding homogeneous universe obtained in the absence of gravitational waves. In particular, a precise lower bound for the ratio of these two sizes is found. Finally, the comparison of the amplitudes of the gravitational wave modes in the distant future and past shows that, statistically (i.e., for large samples of universes), the difference in amplitude is enhanced for nearly homogeneous universes, whereas this difference vanishes in inhomogeneity dominated cases. The presented analysis constitutes the first systematic effective study of an inhomogeneous system within Loop Quantum Cosmology, and it proves the robustness of the results obtained for homogeneous cosmologies in this context.