Implications on the cosmic coincidence by a dynamical extrinsic
  curvature
  In this work, we apply the smooth deformation concept in order to obtain a
modification of Friedmann equations. It is shown that the cosmic coincidence
can be at least alleviated using the dynamical properties of the extrinsic
curvature. We investigate the transition from nucleosynthesis to the
coincidence era obtaining a very small variation of the ratio
$r=\frac{\rho_{m}}{\rho_{ext}}$, that compares the matter energy density to
extrinsic energy density, compatible with the known behavior of the
deceleration parameter. We also show that the calculated "equivalence" redshift
matches the transition redshift from a deceleration to accelerated phase and
the coincidence ceases to be. The dynamics on $r$ is also studied based on
Hubble parameter observations as the latest Baryons Acoustic
Oscillations/Cosmic Microwave Background Radiation (BAO/CMBR) + SNIa.
