scales in cosmology

The Hubble-scale can be defined by looking at the size of a freely falling frame, in which a locally a Minkowski-geometry applies: This size \(\delta\) is given by the condition \(\delta^2 \times R=1\) with the Ricci-scalar \(R\) containing the second derivatives of the metric. Evaluating \(\delta\) with a FLRW-solution for \(R\) would imply \(\delta = c / H_0\), or alternatively, the field equation would imply \(\delta=1/\sqrt{\Lambda}\). Why are the two similar in magnitude?