  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.
