Role of internal space correlations in the dynamics of a higher-dimensional Bianchi type-I universe: shear scalar and Hubble parameter perspectives

TL;DR

This paper explores exact solutions in higher-dimensional Bianchi type-I cosmologies with a correlation parameter, revealing diverse behaviors including accelerated expansion, isotropization, and wormhole structures, which could impact dark energy and Hubble tension models.

Contribution

It introduces a real parameter linking external and internal space expansion rates, extending cosmological models beyond Robertson--Walker spacetime with novel anisotropic and wormhole solutions.

Findings

Positively correlated models mimic dark energy and accelerate isotropization.

Negative correlations lead to steady-state universes with constant shear scalar.

Analytic continuation reveals wormhole-like topologies connecting asymptotic regions.

Abstract

We investigate exact solutions of the Einstein field equations in higher-dimensional, spatially homogeneous Bianchi type-I spacetimes, introducing a real parameter $\lambda$ that correlates the expansion rates of external and internal spaces. Extending beyond Robertson--Walker spacetime, our approach includes positive and negative correlations, suggesting a broader and isotropic/anisotropic cosmological model space. Positively correlated dimensions manifest as a cosmological constant at late times, while at early times, they mimic stiff-fluid-like dark energy that dilutes faster than radiation, paralleling early dark energy models. This suggests a pathway for alleviating the Hubble tension by tailoring higher-dimensional dynamics to reduce the sound horizon. When anisotropic expansion is allowed, these models achieve isotropization more efficiently than predicted by Wald's cosmic no-hair theorem. Negative correlations, in contrast, yield a higher-dimensional steady-state universe where the shear scalar remains constant, effectively emulating a negative cosmological constant. These distinct behaviors arise from a simple signature change: positive correlation accelerates shear scalar decay, while negative correlation stabilizes it. We demonstrate that the solutions admit analytic continuation from the Lorentzian to Euclidean regime ($t \to -i\tau$), revealing a wormhole-like topology that connects two asymptotic regions via a throat, with $\lambda \to -\lambda$.