  In the paper, we consider two models in which dark energy is coupled with
either dust matter or dark matter, and discuss the conditions that allow more
time for structure formation to take place at high redshifts. These models are
expected to have a larger age of the universe than that of $\Lambda$CDM
[universe consists of cold dark matter (CDM) and dark energy (a cosmological
constant, $\Lambda$)], so it can explain the formation of high redshift
gravitationally bound systems which the $\Lambda$CDM model cannot interpret. We
use the observational Hubble parameter data (OHD) and Hubble parameter obtained
from cosmic chronometers method ($H(z)$) in combination with baryon acoustic
oscillation (BAO) data to constrain these models. With the best-fitting
parameters, we discuss how the age, the deceleration parameter, and the energy
density parameters evolve in the new universes, and compare them with that of
$\Lambda$CDM.
