Metric-affine gravity: Nonmetricity of space as dark matter/energy ?

Abstract

A possibility of using a metric-affine theory to consider dark matter and dark energy through the properties of nonmetricity is discussed. In the framework of proposed metric-affine theory, the gravity field is described by the standard Einstein tensor, which depends only on the metric tensor and its derivatives. The nonmetricity and torsion are considered as property of space–time, which is source gravity that can be interpreted as a specific (maybe dark) form of matter and energy. This form of matter and energy, which are described by nonmetricity and torsion tensors, are sources of ”metric” gravity. For the observers, these non-metric properties are manifested as the specific properties of perfect (or non-perfect) fluid interacting with metric gravity only. The proposed metric-affine theory cannot be considered as standard theory of metric-affine gravity. The suggested theory is the metric theory of gravity and the affine theory of a specific (dark) form of matter and energy. The stress–energy tensor of this specific matter and energy is described by the non-metric part of the generalized (metric-affine) Einstein tensor. The specific matter and energy manifest itself as specific perfect or non-perfect fluid (and its energy), which interacts with standard matter only through gravity. The non-metric part is described as a stress–energy tensor, which is supposed to be considered as a candidate for the role of a stress–energy tensor of dark matter/energy. The article discusses a potential possibility to assume that nonmetricity simulates dark matter/energy by introducing a new source term of gravity into general relativity.