We have that
if expressed in inverse time-squared or
if expressed in inverse length-squared (more
precisely, the natural scale associated with the cosmological constant is
). Another way of expressing
this coincidence is to say that predictions of GR from visible matter alone always break down for physics involving a
length-scale constant on the order of the Hubble radius
. This scale
could perhaps play a similar role to
the Planck scale
[233
, 43], at the other end of the ladder (as we have
. However, this is not the length at
which the modification would be seen, exactly as quantum mechanics does not depart from classical physics at a given
length.