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<p>The parallel theory of relativity predicts conserved energy–momentum currents for an arbitrary metric, without invoking Killing symmetries. By treating the reference frame as an independent variational field and requiring it to carry no energy, the theory naturally unifies Einstein’s two formulations of gravity and yields uniquely defined covariant charges. In isotropic and homogeneous cosmology, the canonical time direction selected by the reference frame coincides with the Kodama vector, and the associated Noether energy reproduces the Misner–Sharp mass.</p>

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The canonical energy-momentum currents in cosmology

  • 期刊论文

  • 发表日期：

    2026年1月28日

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  • Tomi S. Koivisto

摘要

The parallel theory of relativity predicts conserved energy–momentum currents for an arbitrary metric, without invoking Killing symmetries. By treating the reference frame as an independent variational field and requiring it to carry no energy, the theory naturally unifies Einstein’s two formulations of gravity and yields uniquely defined covariant charges. In isotropic and homogeneous cosmology, the canonical time direction selected by the reference frame coincides with the Kodama vector, and the associated Noether energy reproduces the Misner–Sharp mass.