TL;DR
This paper proposes a scalar-based averaging scheme for cosmological models to address the averaging problem, providing a rigorous mathematical framework and illustrating it with a static spherically symmetric example.
Contribution
It introduces a novel scalar curvature invariant-based averaging method for cosmological models, enhancing the mathematical rigor of cosmological data interpretation.
Findings
A scalar averaging scheme is defined for cosmological models.
The scheme is illustrated with a static spherically symmetric spacetime.
Averaging scales are explicitly identified in the example.
Abstract
The averaging problem in cosmology is of considerable importance for the correct interpretation of cosmological data. A rigorous mathematical definition of averaging in a cosmological model is necessary. In general, a spacetime is completely characterized by its scalar curvature invariants, and this suggests a particular spacetime averaging scheme based entirely on scalars. We clearly identify the problems of averaging in a cosmological model. We then present a precise definition of a cosmological model, and based upon this definition, we propose an averaging scheme in terms of scalar curvature invariants. This scheme is illustrated in a simple static spherically symmetric perfect fluid cosmological spacetime, where the averaging scales are clearly identified.
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