On the dilation current in metric-affine gravity

Abstract

We review $F(R,\mathcal{D})$ gravity in the metric-affine framework, where $\mathcal{D}$ is the divergence of the dilation current appearing in the hypermomentum tensor. We assume only linear couplings between the general affine connection and the matter fields (minimal coupling) and break projective invariance to preserve a nonvanishing dilation current. For $F(R,\mathcal{D})$ linear in $\mathcal{D}$ the dilation current dependence in the function $F(R,\mathcal{D})$ does not contribute to the field equations of the theory. We show that, on the other hand, in more complicated cases (e.g., considering the function $F(R,\mathcal{D})=R+\alpha {\mathcal{D}}^2$), the $\mathcal{D}$ contribution to the metric field equations is nontrivial and can affect the cosmology of the theory.

arXiv comment17 pages, comments and conclusions added, misprints corrected, accepted for publication in Annals of Physics

References in corpus (19)

• f(R) Theories Of Gravity
• f(R,T) gravity
• Metric-Affine Gauge Theory of Gravity: Field Equations, Noether Identities, World Spinors, and Breaking of Dilation Invariance
• f(R) Gravity and scalar-tensor theory
• Generalized curvature-matter couplings in modified gravity
• Palatini formulation of $f(R,T)$ gravity theory, and its cosmological implications
• The dynamics of metric-affine gravity
• Cosmological Hyperfluids, Torsion and Non-metricity
• Metric-affine f(R,T) theories of gravity and their applications
• An exact solution of the metric-affine gauge theory with dilation, shear, and spin charges
• Inflation in Metric-Affine Quadratic Gravity
• Parity Violating Metric-Affine Gravity Theories
• Einstein manifolds with torsion and nonmetricity
• Electroweak vacuum decay in metric-affine gravity
• The Cosmology of Quadratic Torsionful Gravity
• Bimetric-Affine Quadratic Gravity
• Non-Riemannian Cosmology: The role of Shear Hypermomentum
• Cosmic Acceleration with Torsion and Non-metricity in Friedmann-like Universes
• Metric-Affine Vector-Tensor Correspondence and Implications in $F(R,T,Q,\mathcal{T},\mathcal{D})$ gravity