More on Bianchi I spacetimes and f(T) gravity

TL;DR

This work investigates Bianchi I cosmologies within $f(\mathbb T)$ gravity using diagonal tetrads in the pure teleparallel (Weitzenböck) framework. It develops a minisuperspace formulation, derives generalized Friedmann equations and torsion/Riemannian quantities, and demonstrates analytic tractability for vacuum and perfect-fluid cases, including power-law and anisotropic solutions. A key finding is the strong unpredictability arising from tetrad freedom: even isotropic Friedmann universes admit arbitrary time-dependent spatial rotations of the tetrad without altering the cosmological equations, revealing fundamental ambiguities in the teleparallel connection and challenging well-posedness in modified teleparallel gravity. The paper also presents a Hamiltonian analysis, contrasting brute-force and linearisations, and discusses non-diagonal tetrads for Bianchi I to illustrate how tetrad choice can obscure or distort dynamical content, underscoring caution in applying $f(\mathbb T)$ models to cosmology and motivating covariant approaches. Overall, the work highlights both analytical accessibility of the cosmological equations and deep foundational issues related to tetrad and connection degrees of freedom in teleparallel gravity.

Abstract

Bianchi I cosmological solutions in f(T) gravity are discussed. We start from diagonal metrics and tetrads and show that their dynamical equations are pretty much tractable analytically, with a possible arena for physical applications. Then we derive a very bad unpredictability of the teleparallel connection in these configurations. Namely, even for the simple isotropic Friedmann universes, one might apply an arbitrary time-dependent spatial rotation to the standard tetrad without changing anything in the cosmological equations.